From d1efc925562ab4f2863eeecf5ac2ac4aa4f08560 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 00:46:56 -0700 Subject: [PATCH 01/22] refactor: shared LM substrate -- split utility.py, merge state types, base class utility.py (1099 lines) splits into lm_types.py (status/hyperparams/state/ info/action/context/result), solve_loop.py (the jitted while_loop driver, its Python mirror, save_steps buffers), multi_start.py (MultiStart, DrawNNXModule, the three drivers), and utilities.py (tree selection/masking, static-key hashing, residual canonicalization). LMState/RidgeLMState and LMInfo/RidgeLMInfo merge into one pair each: the ridge fields default to None and stay None for the metric solver, where a None subtree costs nothing in the while_loop carry -- the same design the optional resid/Jt/aux slots already relied on. New LevenbergMarquardtBase holds what both solvers did identically: solve() and its custom_jvp implicit-AD wrapper, _solve_impl/_multi_start_impl, the callback-action plumbing, dense Jacobian assembly, and value-based __eq__/ __hash__. RidgeLevenbergMarquardt subclasses it and keeps only the ridge contract, through five hooks (_validate_tolerances, _solve_lm_state, _initial_ad_point, _check_action_state, _apply_action_state). The metric solver ports in a later commit; here it only follows the moved imports. Pure refactor: 596 passed, 12 skipped, unchanged from baseline. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/ridge_lm.md | 2 +- src/nlls_gram/__init__.py | 16 +- src/nlls_gram/gram_lm.py | 207 ++--- src/nlls_gram/lm_core.py | 505 ++++++++++++ src/nlls_gram/lm_types.py | 280 +++++++ src/nlls_gram/metrics.py | 2 +- src/nlls_gram/multi_start.py | 438 +++++++++++ src/nlls_gram/preconditioners.py | 2 +- src/nlls_gram/ridge_lm.py | 825 +++----------------- src/nlls_gram/solve_loop.py | 301 ++++++++ src/nlls_gram/utilities.py | 225 ++++++ src/nlls_gram/utility.py | 1099 --------------------------- tests/test_float64_subprocess.py | 4 +- tests/test_ridge_lm.py | 6 +- tests/test_ridge_metrics.py | 2 +- tests/test_ridge_preconditioners.py | 8 +- 16 files changed, 1933 insertions(+), 1989 deletions(-) create mode 100644 src/nlls_gram/lm_core.py create mode 100644 src/nlls_gram/lm_types.py create mode 100644 src/nlls_gram/multi_start.py create mode 100644 src/nlls_gram/solve_loop.py create mode 100644 src/nlls_gram/utilities.py delete mode 100644 src/nlls_gram/utility.py diff --git a/docs/ridge_lm.md b/docs/ridge_lm.md index 26ce6d8..0c86ada 100644 --- a/docs/ridge_lm.md +++ b/docs/ridge_lm.md @@ -270,7 +270,7 @@ float64; only go below that with a measured `gtol`. A `Metric` supplies the factor through four ops, each taking a metric-block vector — or a matrix whose *leading* axis is `size` (columns batched) — and a `MetricContext` carrying everything the solver knows at the call site -(the flat iterate `x`, the live `RidgeLMState`, `args`, `p`; the shipped +(the flat iterate `x`, the live `LMState`, `args`, `p`; the shipped metrics ignore it, a custom metric may key off it): - `factor_apply(v, ctx)` — \(F v\) diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index e9640f4..3411e83 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -44,8 +44,12 @@ """ from nlls_gram.gram_lm import ( - DrawNNXModule, LevenbergMarquardt, + MetricFactory, + PreconditionerFactory, + WhitenedPreconditioner, +) +from nlls_gram.lm_types import ( LMHyperparams, LMInfo, LMSolveAction, @@ -53,11 +57,6 @@ LMSolveResult, LMState, LMStatus, - MetricFactory, - MultiStart, - MultiStartInfo, - PreconditionerFactory, - WhitenedPreconditioner, ) from nlls_gram.lsmr import LSMRState, lsmr from nlls_gram.metrics import ( @@ -71,6 +70,7 @@ repeated_shifted_dense_metric, repeated_shifted_state_space_metric, ) +from nlls_gram.multi_start import DrawNNXModule, MultiStart, MultiStartInfo from nlls_gram.preconditioners import ( BlockEigenPreconditioner, IdentityPreconditioner, @@ -96,8 +96,6 @@ CholeskyCache, QRCache, RidgeLevenbergMarquardt, - RidgeLMInfo, - RidgeLMState, ridge_continuation, ) from nlls_gram.solver_config import ( @@ -146,8 +144,6 @@ "LSMRState", "ridge_continuation", "RidgeLevenbergMarquardt", - "RidgeLMInfo", - "RidgeLMState", "matern_state_space", "metric_from_cholesky", "metric_from_diagonal", diff --git a/src/nlls_gram/gram_lm.py b/src/nlls_gram/gram_lm.py index 9a3aca9..4f810c0 100644 --- a/src/nlls_gram/gram_lm.py +++ b/src/nlls_gram/gram_lm.py @@ -1,6 +1,4 @@ import dataclasses -from dataclasses import dataclass -from typing import Any import jax import jax.numpy as jnp @@ -9,36 +7,41 @@ import numpy as np from jax.flatten_util import ravel_pytree -from nlls_gram.lsmr import lsmr_solve -from nlls_gram.metrics import GramMetric, _metric_with_compute_dtype -from nlls_gram.preconditioners import WhitenedPreconditioner -from nlls_gram.recycled_cg import ( - RecycleConfig, - RecycleState, - build_coarse_operator, - deflated_pcg, -) -from nlls_gram.utility import ( - DrawNNXModule, +from nlls_gram.lm_types import ( LMHyperparams, + LMInfo, LMSolveAction, LMSolveContext, LMSolveResult, + LMState, LMStatus, + _cast_hyper, + _damping_floor, +) +from nlls_gram.lsmr import lsmr_solve +from nlls_gram.metrics import GramMetric, _metric_with_compute_dtype +from nlls_gram.multi_start import ( + DrawNNXModule, MultiStart, MultiStartInfo, _accept_converged, _accept_converged_or_max_steps, - _cast_hyper, _check_drawn_types, - _damping_floor, - _hashable_hook, - _mask_tangent_tree, _multi_start_parallel_jit, _multi_start_python_impl, _multi_start_sequential_jit, - _solve_loop_jit, - _solve_python_impl, +) +from nlls_gram.preconditioners import WhitenedPreconditioner +from nlls_gram.recycled_cg import ( + RecycleConfig, + RecycleState, + build_coarse_operator, + deflated_pcg, +) +from nlls_gram.solve_loop import _solve_loop_jit, _solve_python_impl +from nlls_gram.utilities import ( + _hashable_hook, + _mask_tangent_tree, _static_key_component, _tree_changed, _where_tree, @@ -75,100 +78,6 @@ # branching. Dtypes flow from the residual; damping scalars are cast to match. -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMState: - """Carried LM solver state threaded through ``init``/``update``/``solve``. - - Only ``damping`` is always live; the remaining fields are populated by the - features that need them and stay ``None`` on the default path (compiled away - at no cost). A ``solve`` callback that rebuilds ``lm_state`` must PRESERVE the - fields it does not mean to change -- in particular the ``recycle`` basis and - the ``precond``/``precond_valid`` and ``metric_state``/``metric_valid`` - factory state, which carry across steps. - - Attributes: - damping: ``()`` current LM damping ``lambda``. - resid: cached residual at the current ``x`` (``cache_jacobian=True`` only, - else ``None``). - Jt: cached transpose-Jacobian ``J'`` output at the current ``x`` - (``cache_jacobian=True`` only). - jacobian_valid: ``()`` bool -- the cached ``resid``/``Jt`` are still - current because the last step was rejected so ``x`` did not move - (``cache_jacobian=True`` only). - aux: residual aux pytree at the current ``x`` (``has_aux=True``). - hyper: per-step :class:`LMHyperparams`, populated by ``solve``; ``None`` - (``init``'s default) falls back to the constructor values with - identical compiled code and no extra per-call buffers in manual - ``update`` loops. - recycle: :class:`~nlls_gram.RecycleState` carrying the deflation basis and - warm starts across steps (``recycle`` set only). - precond: ``preconditioner_factory`` prepared state (the ``prepare``-built - pytree) at the current ``x``; ``None`` on the default path. - precond_valid: ``()`` bool -- the carried ``precond`` is still current - because ``x`` has not moved since it was built (so it is reused, not - rebuilt); ``None`` on the default path. - metric_state: ``metric_factory`` prepared state (the ``prepare``-built - pytree) at the current ``x``; ``None`` on the default path. - metric_valid: ``()`` bool -- the carried ``metric_state`` is still - current because ``x`` has not moved since it was built (so it is - reused, not rebuilt); ``None`` on the default path. - """ - - damping: jax.Array - resid: jax.Array | None = None - Jt: jax.Array | None = None - jacobian_valid: jax.Array | None = None - aux: Any = None - hyper: LMHyperparams | None = None - recycle: RecycleState | None = None - precond: Any = None - precond_valid: jax.Array | None = None - metric_state: Any = None - metric_valid: jax.Array | None = None - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMInfo: - """Per-step diagnostics returned by ``update`` (and for each ``solve`` step). - - The loss/damping fields report the accept/reject outcome of the step, while - ``grad_norm``/``step_norm``/``aux`` are evaluated at the PRE-step ``x`` (the - iterate the step was computed from), so they describe the point entering the - step, not the one it produced. - - Attributes: - loss: ``min(loss_old, loss_candidate)`` sum of squared residuals (at the - retained iterate). - loss_old: sum of squared residuals at the pre-step ``x``. - loss_candidate: sum of squared residuals at the trial point. - accepted: ``()`` bool, whether the trial step was accepted. - damping: ``()`` post-update damping ``lambda``. - damping_factor: ``()`` multiplicative damping update applied this step. - used_geodesic: ``()`` bool, whether the geodesic-acceleration correction - entered the accepted step. - acceleration_ratio: ``()`` geodesic acceleration-to-velocity norm ratio. - grad_norm: ``()`` ``||J' r||`` at the pre-step ``x``. - step_norm: ``()`` ``||candidate step||``, reported even when the step is - rejected. - aux: residual aux output at the pre-step ``x`` (``has_aux=True``, else - ``None``). - """ - - loss: jax.Array - loss_old: jax.Array - loss_candidate: jax.Array - accepted: jax.Array - damping: jax.Array - damping_factor: jax.Array - used_geodesic: jax.Array - acceleration_ratio: jax.Array - grad_norm: jax.Array - step_norm: jax.Array - aux: Any = None - - class PreconditionerFactory: """θ-adaptive dual preconditioner: a value-hashable ``(prepare, apply)`` pair. @@ -1060,10 +969,10 @@ def init(self, x0, args=None, *, p=None): theta, _ = ravel_pytree(x0) return LMState( damping, - jnp.zeros(residual.shape, dtype=residual.dtype), - jnp.zeros((theta.size, residual.size), dtype=residual.dtype), - jnp.asarray(False, dtype=jnp.bool_), - jax.tree.map(jnp.zeros_like, aux), + resid=jnp.zeros(residual.shape, dtype=residual.dtype), + Jt=jnp.zeros((theta.size, residual.size), dtype=residual.dtype), + jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), + aux=jax.tree.map(jnp.zeros_like, aux), recycle=recycle, precond=precond, precond_valid=precond_valid, @@ -1200,17 +1109,17 @@ def _initial_info(self, x, lm_state, args, p): zero = jnp.zeros((), dtype=residual.dtype) one = jnp.ones((), dtype=residual.dtype) return LMInfo( - loss, - loss, - loss, - jnp.asarray(False, dtype=jnp.bool_), - jnp.asarray(lm_state.damping, dtype=residual.dtype), - one, - jnp.asarray(False, dtype=jnp.bool_), - zero, - jnp.asarray(jnp.inf, dtype=residual.dtype), - zero, - aux, + loss=loss, + loss_old=loss, + loss_candidate=loss, + accepted=jnp.asarray(False, dtype=jnp.bool_), + damping=jnp.asarray(lm_state.damping, dtype=residual.dtype), + damping_factor=one, + used_geodesic=jnp.asarray(False, dtype=jnp.bool_), + acceleration_ratio=zero, + grad_norm=jnp.asarray(jnp.inf, dtype=residual.dtype), + step_norm=zero, + aux=aux, ) def update(self, x, lm_state, args=None, p=None): @@ -1816,16 +1725,16 @@ def accelerated_loss(_): if self.cache_jacobian: new_lm_state = LMState( new_damping, - resid, - Jt, - ~improved, - aux, - lm_state.hyper, - new_recycle, - new_precond, - new_precond_valid, - new_metric_state, - new_metric_valid, + resid=resid, + Jt=Jt, + jacobian_valid=~improved, + aux=aux, + hyper=lm_state.hyper, + recycle=new_recycle, + precond=new_precond, + precond_valid=new_precond_valid, + metric_state=new_metric_state, + metric_valid=new_metric_valid, ) else: new_lm_state = LMState( @@ -1841,17 +1750,17 @@ def accelerated_loss(_): unravel(theta_new), new_lm_state, LMInfo( - loss, - loss_old, - loss_candidate, - improved, - new_damping, - damping_factor, - used_geodesic, - acceleration_ratio, - jnp.linalg.norm(grad), - jnp.linalg.norm(step), - aux, + loss=loss, + loss_old=loss_old, + loss_candidate=loss_candidate, + accepted=improved, + damping=new_damping, + damping_factor=damping_factor, + used_geodesic=used_geodesic, + acceleration_ratio=acceleration_ratio, + grad_norm=jnp.linalg.norm(grad), + step_norm=jnp.linalg.norm(step), + aux=aux, ), ) diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py new file mode 100644 index 0000000..5770732 --- /dev/null +++ b/src/nlls_gram/lm_core.py @@ -0,0 +1,505 @@ +"""``LevenbergMarquardtBase`` -- everything the two solvers do identically. + +The subclasses supply the objective and its algebra (``init``, ``update``, +``_initial_info``, ``_converged``, ``_cast_state``, ``_cold_state``, +``_ranking_objective``, ``_ad_x_tangent``); the loop driving, callback action +handling, Jacobian assembly, static-key identity, and the ``custom_jvp`` +implicit-AD wrapper live here. +""" + +import dataclasses + +import jax +import jax.numpy as jnp + +from nlls_gram.lm_types import ( + LMSolveAction, + LMStatus, +) +from nlls_gram.multi_start import ( + MultiStart, + _accept_converged, + _accept_converged_or_max_steps, + _check_drawn_types, + _multi_start_parallel_jit, + _multi_start_python_impl, + _multi_start_sequential_jit, +) +from nlls_gram.solve_loop import _solve_loop_jit, _solve_python_impl +from nlls_gram.utilities import ( + _hashable_hook, + _mask_tangent_tree, + _tree_changed, + _where_tree, + _zero_tangent_leaf, +) + + +class LevenbergMarquardtBase: + # Value-based identity: the jitted solve loop marks the solver itself + # static, so equal-config solvers built around the same residual share the + # compiled loop across instances. Subclasses set _static_key/_static_hash + # in __init__ from their constructor arguments. + def __eq__(self, other): + if self is other: + return True + if type(other) is not type(self): + return NotImplemented + return self._static_key == other._static_key + + def __hash__(self): + return self._static_hash + + def _resolve_jacobian_mode(self, m, n): + # "auto" vmaps the identity basis of the SMALL side: n forward-mode + # columns when the system is tall or square (n <= m), m reverse-mode + # rows only when strictly fat. + if self.jacobian_mode != "auto": + return self.jacobian_mode + return "fwd" if n <= m else "rev" + + def _assemble_jt(self, jvp_fn, theta, resid): + if self._resolve_jacobian_mode(resid.shape[0], theta.shape[0]) == "fwd": + parameter_basis = jnp.eye(theta.shape[0], dtype=theta.dtype) + return jax.vmap(jvp_fn)(parameter_basis) + transpose_fn = jax.linear_transpose(jvp_fn, theta) + residual_basis = jnp.eye(resid.shape[0], dtype=resid.dtype) + return jax.vmap(lambda cotangent: transpose_fn(cotangent)[0])(residual_basis).T + + def _dense_resid_jt_aux(self, residual_flat, theta): + if self.has_aux: + resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) + else: + resid, jvp_fn = jax.linearize(residual_flat, theta) + aux = None + return resid, self._assemble_jt(jvp_fn, theta, resid), aux + + def _residual_and_aux(self, x, args, p): + if self.has_aux: + value, aux = self.residual_fn(x, args, p) + return jnp.ravel(value), aux + return jnp.ravel(self.residual_fn(x, args, p)), None + + def _check_residual_args(self, args, p): + # Silently dropping args/p a residual never sees would, in particular, + # make the implicit derivative with respect to p a silent zero. + if args is not None and self.residual_arity < 2: + raise ValueError( + "args was passed but residual_fn takes only (x); " + "use residual_fn(x, args)" + ) + if p is not None and self.residual_arity < 3: + raise ValueError( + "p was passed but residual_fn takes no p argument; " + "use residual_fn(x, args, p)" + ) + + def _ad_cg_tol(self, dtype): + if self.ad_solver_tol is not None: + return jnp.asarray(self.ad_solver_tol, dtype=dtype) + default_tol = 1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6 + return jnp.asarray(default_tol, dtype=dtype) + + def _action_or_default(self, action): + if action is None: + return LMSolveAction() + return action + + def _apply_action(self, action, x, lm_state, args, user_state): + action = self._action_or_default(action) + # The step's diagnostics and every cache describe the pre-action + # problem, so they are stale iff the action actually changed the + # values -- a traced comparison, so a jit-style callback that returns + # the field every step with unchanged values changes nothing. + xargs_changed = jnp.asarray(False) + state_changed = jnp.asarray(False) + if action.x is not None: + xargs_changed = xargs_changed | _tree_changed(action.x, x) + x = action.x + if action.lm_state is not None: + previous = lm_state + lm_state = action.lm_state + if self.cache_jacobian and lm_state.jacobian_valid is None: + raise ValueError( + "cache_jacobian=True but the callback action returned an " + "lm_state without the Jacobian cache; use " + "dataclasses.replace(ctx.lm_state, ...) to preserve the " + "cache fields" + ) + self._check_action_state(lm_state) + # Trace-time guard so the hyper contract fails identically with + # and without jit (jit would reject the carry mismatch anyway). + previous_hyper = previous.hyper + if previous_hyper is not None and ( + lm_state.hyper is None + or jax.tree_util.tree_structure(previous_hyper) + != jax.tree_util.tree_structure(lm_state.hyper) + or [leaf.dtype for leaf in jax.tree_util.tree_leaves(previous_hyper)] + != [leaf.dtype for leaf in jax.tree_util.tree_leaves(lm_state.hyper)] + ): + raise ValueError( + "the callback action changed the structure or dtypes of " + "lm_state.hyper; reset values with " + "dataclasses.replace(ctx.lm_state.hyper, ...) using arrays " + "of the same dtype — a knob constructed as None cannot be " + "enabled mid-solve" + ) + lm_state, state_changed = self._apply_action_state(lm_state, previous) + if action.args is not None: + xargs_changed = xargs_changed | _tree_changed(action.args, args) + args = action.args + if action.user_state is not None: + user_state = action.user_state + problem_changed = xargs_changed | state_changed + if self.cache_jacobian and (action.x is not None or action.args is not None): + lm_state = dataclasses.replace( + lm_state, jacobian_valid=lm_state.jacobian_valid & ~xargs_changed + ) + touched = ( + action.x is not None + or action.args is not None + or action.lm_state is not None + ) + lm_state = self._invalidate_caches(lm_state, action, touched, problem_changed) + return action, x, lm_state, args, user_state, problem_changed + + # Subclass hooks for the callback-action path. The defaults are inert. + def _check_action_state(self, lm_state): + pass + + def _apply_action_state(self, lm_state, previous): + return lm_state, jnp.asarray(False) + + def _invalidate_caches(self, lm_state, action, touched, problem_changed): + if touched and lm_state.solver_cache is not None: + cache = lm_state.solver_cache + lm_state = dataclasses.replace( + lm_state, + solver_cache=dataclasses.replace( + cache, valid=cache.valid & ~problem_changed + ), + ) + return lm_state + + def solve( + self, + x0, + args=None, + *, + p=None, + lm_state=None, + max_steps=256, + max_steps_is_success=True, + atol=0.0, + gtol=0.0, + xtol=0.0, + callback=None, + user_state=None, + save_steps=False, + multi_start=None, + jit=True, + ): + """Run repeated LM updates until a stopping rule fires. + + Parameters are ``update``'s plus loop controls. ``max_steps`` is always + enforced; ``max_steps_is_success=True`` (the default) treats + ``LMStatus.MAX_STEPS`` as usable for implicit AD and for the default + multi-start acceptance, while keeping the status for diagnostics. + + ``atol``/``gtol``/``xtol`` bound the residual norm, the stationarity + residual ``info.grad_norm``, and an accepted step's ``info.step_norm``; + ``0`` disables a check and every firing rule reports + ``LMStatus.CONVERGED``. How the three combine is the solver's own + contract -- see each subclass. + + ``callback`` receives an ``LMSolveContext`` after each step and may + return an ``LMSolveAction`` to stop or to override x/lm_state/args/ + user_state; ``p`` is passed through but cannot be replaced. A callback + that installs an invalid ``x`` or ``args`` must also stop with a failed + status. + + ``save_steps=True`` records the iterate history on the result: + ``x_history`` stacks ``x0`` and every kept post-step iterate along a + ``(max_steps + 1)`` leading axis (rows beyond ``steps`` are zero + padding), plus the row-aligned ``args_history`` and, with ``has_aux``, + ``aux_history``. The buffers are differentiation-inert and make the + jitted loop retrace when ``max_steps`` changes. + + ``multi_start`` (a ``MultiStart``) retries or parallelizes over fresh + initial conditions and returns the single best result, with + diagnostics on ``result.multi_start``. + + Implicit AD uses ``CONVERGED``, and ``MAX_STEPS`` when + ``max_steps_is_success=True``; every failed status receives zero + tangents for ``result.x`` and ``result.aux``, with the failed lane's + linear tangent program evaluated at differentiation-inert copies of the + original ``(x0, args, p)``. + """ + self._check_residual_args(args, p) + if max_steps <= 0: + raise ValueError("max_steps must be positive") + # Tolerances are traced data inside the loop, so vmapped/traced values + # skip the concrete-only sign validation. + if not isinstance(atol, jax.core.Tracer) and atol < 0: + raise ValueError("atol must be nonnegative") + if not isinstance(gtol, jax.core.Tracer) and gtol < 0: + raise ValueError("gtol must be nonnegative") + if not isinstance(xtol, jax.core.Tracer) and xtol < 0: + raise ValueError("xtol must be nonnegative") + self._validate_tolerances(atol, gtol, xtol) + lm_state = self._solve_lm_state(x0, args, p, lm_state) + if lm_state.hyper is None: + lm_state = dataclasses.replace(lm_state, hyper=self.hyperparams()) + history_len = max_steps + 1 if save_steps else None + + if multi_start is not None: + num_starts = multi_start.num_starts + draw = _hashable_hook(multi_start.draw if num_starts > 1 else None) + default_accept = ( + _accept_converged_or_max_steps + if max_steps_is_success + else _accept_converged + ) + accept = _hashable_hook( + default_accept if multi_start.accept is None else multi_start.accept + ) + parallel = multi_start.parallel and num_starts > 1 + if draw is not None and jit: + drawn = jax.eval_shape(draw, multi_start.key, x0, args) + _check_drawn_types(x0, args, drawn) + + @jax.custom_jvp + def solve_multi_start_with_ad_p( + x, lm_state, args, p, user_state, key, max_steps, atol, gtol, xtol + ): + return self._multi_start_impl( + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + jit, + num_starts, + draw, + accept, + parallel, + ) + + @solve_multi_start_with_ad_p.defjvp + def solve_multi_start_with_ad_p_jvp(primals, tangents): + p_dot = tangents[3] + result = solve_multi_start_with_ad_p(*primals) + point = self._initial_ad_point( + primals[0], primals[1], primals[2], primals[3] + ) + return result, self._ad_result_tangent( + result, p_dot, point, max_steps_is_success + ) + + return solve_multi_start_with_ad_p( + x0, + lm_state, + args, + p, + user_state, + multi_start.key, + max_steps, + atol, + gtol, + xtol, + ) + + @jax.custom_jvp + def solve_with_ad_p( + x, lm_state, args, p, user_state, max_steps, atol, gtol, xtol + ): + return self._solve_impl( + x, + lm_state, + args, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + jit, + ) + + @solve_with_ad_p.defjvp + def solve_with_ad_p_jvp(primals, tangents): + p_dot = tangents[3] + result = solve_with_ad_p(*primals) + point = self._initial_ad_point( + primals[0], primals[1], primals[2], primals[3] + ) + return result, self._ad_result_tangent( + result, p_dot, point, max_steps_is_success + ) + + return solve_with_ad_p( + x0, lm_state, args, p, user_state, max_steps, atol, gtol, xtol + ) + + # Subclass hooks for solve. The defaults suit a solver with no extra + # state contract beyond the shared LMState. + def _validate_tolerances(self, atol, gtol, xtol): + pass + + def _solve_lm_state(self, x0, args, p, lm_state): + return self.init(x0, args, p=p) if lm_state is None else lm_state + + def _initial_ad_point(self, x, lm_state, args, p): + return (x, args, p) + + def _solve_impl( + self, + x, + lm_state, + args, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + jit, + ): + driver = _solve_loop_jit if jit else _solve_python_impl + return driver( + self, + x, + lm_state, + args, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + ) + + def _multi_start_impl( + self, + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + jit, + num_starts, + draw, + accept, + parallel, + ): + if not jit: + return _multi_start_python_impl( + self, + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + num_starts, + draw, + accept, + parallel, + ) + if parallel: + return _multi_start_parallel_jit( + self, + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + draw, + accept, + num_starts, + ) + return _multi_start_sequential_jit( + self, + x, + lm_state, + args, + p, + user_state, + key, + jnp.asarray(num_starts, dtype=jnp.int32), + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + draw, + accept, + ) + + def _ad_result_tangent(self, result, p_dot, initial_ad_point, max_steps_is_success): + # A successful tangent relinearizes at the returned solution. A failed + # tangent uses the differentiation-inert original initial point, so the + # linear tangent program stays finite under vmap. Everything except x, + # p, and aux is bookkeeping with zero tangents. + initial_x, initial_args, initial_p = jax.tree.map( + jax.lax.stop_gradient, initial_ad_point[:3] + ) + ad_success = result.status == LMStatus.CONVERGED + if max_steps_is_success: + ad_success = ad_success | (result.status == LMStatus.MAX_STEPS) + ad_x = _where_tree(ad_success, result.x, initial_x) + ad_args = _where_tree(ad_success, result.args, initial_args) + ad_p = _where_tree(ad_success, result.p, initial_p) + ad_p_dot = _mask_tangent_tree(ad_success, p_dot) + zero_result = jax.tree.map(_zero_tangent_leaf, result) + x_dot = self._ad_x_tangent( + ad_x, ad_args, ad_p, ad_p_dot, result, ad_success, initial_ad_point + ) + x_dot = _where_tree(ad_success, x_dot, zero_result.x) + aux_dot = zero_result.aux + if self.has_aux and ad_p is not None: + # aux depends on p directly and through the solution x*(p). + def aux_at_solution(x_value, p_value): + return self.residual_fn(x_value, ad_args, p_value)[1] + + aux_dot = jax.jvp(aux_at_solution, (ad_x, ad_p), (x_dot, ad_p_dot))[1] + aux_dot = _where_tree(ad_success, aux_dot, zero_result.aux) + return dataclasses.replace(zero_result, x=x_dot, p=p_dot, aux=aux_dot) + + +# Re-exported for the solvers' isinstance-free solve signature. +__all__ = ["LevenbergMarquardtBase", "MultiStart"] diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py new file mode 100644 index 0000000..ee2fea4 --- /dev/null +++ b/src/nlls_gram/lm_types.py @@ -0,0 +1,280 @@ +"""State, hyperparameter, action, and result types shared by both solvers. + +One ``LMState`` and one ``LMInfo`` serve ``LevenbergMarquardt`` and +``RidgeLevenbergMarquardt``: fields a configuration does not use stay ``None`` +and compile away as empty pytree subtrees. Nothing here imports the metric, +preconditioner, or linear-solver modules, so it sits at the bottom of the +import graph. +""" + +import enum +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp + +__all__ = [ + "LMHyperparams", + "LMInfo", + "LMSolveAction", + "LMSolveContext", + "LMSolveResult", + "LMState", + "LMStatus", +] + + +class LMStatus(enum.IntEnum): + """Integer status codes returned by ``solve``. + + Members are real ints (``IntEnum``): they work as dict keys, compare + against status arrays, and ``LMStatus(int(result.status)).name`` recovers + the label for logging. Callbacks may return bare members (or any weak + integer value) as ``LMSolveAction.status`` -- the solver canonicalizes to + int32 at the boundary, so no explicit dtype casts are needed. + """ + + RUNNING = 0 + CONVERGED = 1 + MAX_STEPS = 2 + NONFINITE = 3 + CALLBACK_STOP = 4 + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMHyperparams: + """Per-step LM hyperparameters, carried in ``LMState.hyper``. + + All fields are traced, so a ``solve`` callback can reset them -- e.g. grow + the inner CG budget as the loss falls -- via + ``dataclasses.replace(ctx.lm_state, hyper=dataclasses.replace( + ctx.lm_state.hyper, iterative_maxiter=...))``. A field constructed as + ``None`` (uncapped ``max_damping``, backend-default ``iterative_maxiter``) + is compiled out and stays ``None``. Static configuration -- the linear + solver, the metric, ``geodesic_acceleration``, ``cache_jacobian``, + ``has_aux`` -- shapes the compiled program and lives on the solver. + """ + + damping_decrease: jax.Array + damping_increase: jax.Array + min_damping: jax.Array + max_damping: jax.Array | None + geodesic_acceptance_ratio: jax.Array + iterative_tol: jax.Array + iterative_atol: jax.Array + iterative_maxiter: jax.Array | None + + +def _damping_floor(min_damping, dtype): + if dtype is None: + seed = 0.0 if min_damping is None else min_damping + dtype = jnp.asarray(seed).dtype + dtype_floor = jnp.asarray(jnp.finfo(dtype).tiny, dtype=dtype) + if min_damping is None: + return dtype_floor + return jnp.maximum(jnp.asarray(min_damping, dtype=dtype), dtype_floor) + + +def _cast_hyper(hyper, dtype): + if hyper is None: + return None + return LMHyperparams( + jnp.asarray(hyper.damping_decrease, dtype=dtype), + jnp.asarray(hyper.damping_increase, dtype=dtype), + _damping_floor(hyper.min_damping, dtype), + None + if hyper.max_damping is None + else jnp.asarray(hyper.max_damping, dtype=dtype), + jnp.asarray(hyper.geodesic_acceptance_ratio, dtype=dtype), + jnp.asarray(hyper.iterative_tol, dtype=dtype), + jnp.asarray(hyper.iterative_atol, dtype=dtype), + None + if hyper.iterative_maxiter is None + else jnp.asarray(hyper.iterative_maxiter, dtype=jnp.int32), + ) + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMState: + """Carried solver state threaded through ``init``/``update``/``solve``. + + Only ``damping`` is always live; every other field is populated by the + configuration that needs it and stays ``None`` otherwise. A ``solve`` + callback that rebuilds the state must PRESERVE the fields it does not mean + to change -- use ``dataclasses.replace(ctx.lm_state, ...)``. + + Attributes: + damping: ``()`` current LM damping. + ridge: ``()`` ridge weight, strictly positive, for + ``RidgeLevenbergMarquardt``; ``None`` for the metric solver. + Replacing it is the supported way to anneal mid-solve (see + ``RidgeContinuation``); the solver treats a ridge change as a + problem change, suppressing that step's convergence test and + invalidating the ridge-keyed caches. + resid: cached residual at the current ``x`` (``cache_jacobian`` dense + paths only). + Jt: cached transpose-Jacobian ``J'`` at the current ``x``. + jacobian_valid: ``()`` bool -- the cached ``resid``/``Jt`` are still + current because the last step was rejected, so ``x`` did not move. + aux: residual aux pytree at the current ``x`` (``has_aux=True``). + hyper: per-step :class:`LMHyperparams`, populated by ``solve``; + ``None`` (``init``'s default) falls back to the constructor values. + solver_cache: the linear solver's own reject-step cache, whose pytree + structure is fixed by the static ``linear_solver`` config. + metric_state: the metric's ``prepare`` output at the current ``x``. + metric_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. + precond: the preconditioner's ``prepare`` output at the current ``x``. + precond_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. + recycle: Krylov recycling state. + """ + + damping: jax.Array + ridge: jax.Array | None = None + resid: jax.Array | None = None + Jt: jax.Array | None = None + jacobian_valid: jax.Array | None = None + aux: Any = None + hyper: LMHyperparams | None = None + solver_cache: Any = None + metric_state: Any = None + metric_valid: jax.Array | None = None + precond: Any = None + precond_valid: jax.Array | None = None + recycle: Any = None + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMInfo: + """Per-step diagnostics returned by ``update`` and by each ``solve`` step. + + The loss/damping fields report the accept/reject outcome of the step, while + ``grad_norm``/``step_norm``/``aux`` are evaluated at the PRE-step ``x`` -- + the iterate the step was computed from. + + ``loss`` is always the objective the running solver minimizes: the sum of + squared residuals for ``LevenbergMarquardt``, and the RIDGE OBJECTIVE + ``||r||^2 + ridge * ||x_m||_W^2`` (penalty included) for + ``RidgeLevenbergMarquardt`` -- ridge code that means equation error must + read ``resid_loss``. + + The ridge solver runs in the whitened variable ``y = F_bar x``, so its + ``grad_norm``, ``step_norm``, and ``penalty_grad_norm`` are Euclidean in + ``y``: steps measured in the W-norm, gradients in the dual W^{-1}-norm. + Objective values are unaffected -- whitening is a linear bijection of the + same objective. + + Attributes: + loss: objective at the retained iterate, ``min(loss_old, + loss_candidate)``. + loss_old: objective at the pre-step ``x``. + loss_candidate: objective at the trial point. + accepted: ``()`` bool, whether the trial step was accepted. + damping: ``()`` post-update damping. + damping_factor: ``()`` multiplicative damping update applied this step. + used_geodesic: ``()`` bool, whether the geodesic correction entered the + accepted step. + acceleration_ratio: ``()`` acceleration-to-velocity norm ratio. + grad_norm: ``()`` stationarity residual at the pre-step ``x``: + ``||J' r||`` for the metric solver, and the whitened + ``||F_bar^{-T} J'r + ridge [y_m; 0]||`` for the ridge solver. + step_norm: ``()`` norm of the candidate step, reported even when the + step is rejected. + ridge: ``()`` the ridge weight used this step (ridge solver only). + resid_loss: ``||r||^2`` at the retained iterate (ridge solver only). + penalty_value: ``||x_m||_W^2 = ||y_m||^2`` at the retained iterate. + penalty_grad_norm: ``()`` ``||[y_m; 0]|| = sqrt(penalty_value)`` at the + pre-step ``x``, reported so ``gtol`` can be CALIBRATED rather than + guessed: at a ridge minimizer the gradient is the cancellation of + the residual pullback against ``ridge * [y_m; 0]``, so demanding + ``grad_norm < c * ridge * penalty_grad_norm`` resolves the + selection coordinates to ~``c`` relative accuracy. The recipe is + ``gtol ~ 1e-3 * ridge * sqrt(q(x*))`` with ``q`` the solution's + squared seminorm. + aux: residual aux output at the pre-step ``x`` (``has_aux=True``). + """ + + loss: jax.Array + loss_old: jax.Array + loss_candidate: jax.Array + accepted: jax.Array + damping: jax.Array + damping_factor: jax.Array + used_geodesic: jax.Array + acceleration_ratio: jax.Array + grad_norm: jax.Array + step_norm: jax.Array + ridge: jax.Array | None = None + resid_loss: jax.Array | None = None + penalty_value: jax.Array | None = None + penalty_grad_norm: jax.Array | None = None + aux: Any = None + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMSolveAction: + """Optional callback action for ``solve``. + + A field left as ``None`` is unchanged. ``status`` is used only when + ``stop`` is true. ``stop`` and ``status`` are canonicalized by the solver + (to bool and int32), so callbacks may return Python bools, bare + ``LMStatus`` members, or weak-typed arrays without explicit casts. + """ + + stop: Any = None + status: Any = None + x: Any = None + lm_state: Any = None + args: Any = None + user_state: Any = None + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMSolveContext: + """Information passed to a ``solve`` callback after each LM update.""" + + step: jax.Array + x: Any + x_old: Any + lm_state: Any + lm_state_old: Any + initial_lm_state: Any + args: Any + p: Any + user_state: Any + info: Any + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class LMSolveResult: + """Final result returned by ``solve``.""" + + x: Any + lm_state: Any + info: Any + steps: jax.Array + status: jax.Array + args: Any + p: Any + user_state: Any + # With has_aux=True: aux evaluated at the returned (x, args, p) -- one extra + # residual evaluation, well-defined for every status. Differentiable with + # respect to p through the implicit rule (directly and through x*(p)). + aux: Any = None + # With save_steps=True: the iterate history as a pytree shaped like x with a + # (max_steps + 1) leading axis -- row 0 is x0, row s the kept iterate after + # step s (post-callback-action), rows beyond ``steps`` are zero padding. + # aux_history (has_aux only) and args_history (None when args is None) align + # row-for-row. Differentiation-inert (zero tangents through the implicit rule). + x_history: Any = None + aux_history: Any = None + args_history: Any = None + # MultiStartInfo when solve ran with multi_start=...; None otherwise (an + # empty pytree node, so the leaf count is unchanged when the feature is off). + multi_start: Any = None diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index 0ec7016..8938bf6 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -36,7 +36,7 @@ class MetricContext: - ``x``: the current FLATTENED iterate (the full parameter vector, not just the metric block). - - ``lm_state``: the live :class:`~nlls_gram.RidgeLMState` (damping, + - ``lm_state``: the live :class:`~nlls_gram.LMState` (damping, ridge, caches). In the implicit-AD rule this is the returned state under ``stop_gradient`` -- inert conditioning data, like the ridge. - ``args`` / ``p``: the residual's auxiliary data and differentiation diff --git a/src/nlls_gram/multi_start.py b/src/nlls_gram/multi_start.py new file mode 100644 index 0000000..d420473 --- /dev/null +++ b/src/nlls_gram/multi_start.py @@ -0,0 +1,438 @@ +"""Multi-start configuration and the three drivers behind +``solve(multi_start=...)``: an unjitted Python loop, a jitted sequential +retry loop, and a jitted parallel ``vmap`` race. +""" + +import dataclasses +from dataclasses import dataclass +from typing import Any + +import jax +import jax.numpy as jnp + +from nlls_gram.lm_types import LMStatus +from nlls_gram.solve_loop import _solve_loop_impl, _solve_python_impl +from nlls_gram.utilities import _typed_key + +__all__ = ["DrawNNXModule", "MultiStart", "MultiStartInfo"] + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class MultiStartInfo: + """Diagnostics attached to ``LMSolveResult.multi_start`` by a multi-start solve. + + ``attempt`` is the winning attempt/lane index (0 = the caller's + ``(x0, args)``), ``accepted`` whether the winner passed the success test + (``MultiStart.accept``, or the solve's ``max_steps_is_success`` policy), and + ``attempts_run`` how many starts were solved (sequential mode stops at the + first success; parallel mode always runs ``num_starts``). ``loss`` is the + ranking objective used for selection -- the sum of squared residuals at the + returned solution for ``LevenbergMarquardt``, the ridge objective for + ``RidgeLevenbergMarquardt`` -- masked to ``+inf`` when nonfinite. Note + ``accepted`` describes the multi-start success test, not ``LMInfo.accepted`` + (last-step acceptance). + """ + + attempt: jax.Array + accepted: jax.Array + attempts_run: jax.Array + loss: jax.Array + + +@dataclass(frozen=True, eq=False) +class MultiStart: + """Multi-start configuration for ``solve(multi_start=...)``. + + ``draw(key, x, args) -> (x_new, args_new)`` generates a fresh initial + condition; it must be traceable and type-stable (returning the same pytree + structure, shapes, and dtypes as its ``(x, args)`` inputs). ``accept(key, + result) -> bool`` optionally overrides the success test (default: + ``CONVERGED`` plus ``MAX_STEPS`` when the solve's + ``max_steps_is_success=True``); it receives its own key so it can draw fresh + validation data, and may return any scalar boolean-like value. + Sequential mode (``parallel=False``) solves from ``(x0, args)`` and retries + on failure, chaining each attempt's *initial* values into the next + ``draw``; parallel mode solves all ``num_starts`` lanes under ``vmap`` + (lane 0 = the caller's ``(x0, args)``, the rest drawn from the originals) + and selects the accepted lane with the lowest loss. The key schedule is + ``draw_key, accept_key = jax.random.split(jax.random.fold_in(key, k))`` + for attempt ``k``. + + ``draw`` and ``accept`` enter the jit cache by identity (like + ``callback``): define them once at setup scope, not inline per call. + ``MultiStart`` is not a pytree -- ``solve`` unpacks it before tracing, with + ``key`` the only traced field. + """ + + key: Any + num_starts: int + draw: Any = None + accept: Any = None + parallel: bool = False + + def __post_init__(self): + if isinstance(self.num_starts, bool) or not isinstance(self.num_starts, int): + raise ValueError("num_starts must be a Python int >= 1") + if self.num_starts < 1: + raise ValueError("num_starts must be a Python int >= 1") + if self.num_starts > 1 and self.draw is None: + raise ValueError( + "num_starts > 1 requires draw; pass " + "draw=(key, x, args) -> (x_new, args_new)" + ) + if self.draw is not None and not callable(self.draw): + raise TypeError("draw must be callable") + if self.accept is not None and not callable(self.accept): + raise TypeError("accept must be callable") + + +class DrawNNXModule: + """Multi-start ``draw`` hook re-initializing a flax ``nnx.Module`` from a fresh key. + + Given a ``MultiStart`` retry key, builds + ``module_cls(*args, rngs=nnx.Rngs(key), **kwargs)`` and returns its ``nnx.Param`` + state as the new solver start, passing ``args`` through unchanged. Use it instead + of hand-rolling a re-init closure per driver:: + + draw = DrawNNXModule(SequentialMLP, settings, dtype=dtype) + ms = MultiStart(key=key, num_starts=5, draw=draw) + + The drawn parameter state must be type-stable against the solver's ``x0`` (same + pytree structure, shapes, and dtypes) -- construct the module with a matching + ``param_dtype``/``dtype`` (e.g. pass ``dtype=`` through). The paired + ``nnx.GraphDef`` used by the residual's ``nnx.merge`` must come from the same + ``module_cls(*args, **kwargs)`` spec. + + Value-hashable on ``(module_cls, args, kwargs)`` with jit's strict-type semantics + (``1``, ``1.0``, and ``True`` key distinct compilations): equal specs compare equal + and share one jit compilation instead of recompiling per instance (a fresh closure + would not). ``args``/``kwargs`` must be hashable for that sharing, and their values + must not be mutated after construction (a stale key would reuse the wrong compile); + unhashable specs still work but recompile per instance. Requires ``flax`` installed + (imported lazily on first draw). + """ + + def __init__(self, module_cls, *args, **kwargs): + self.module_cls = module_cls + self.args = args + self.kwargs = tuple(sorted(kwargs.items())) + + def __call__(self, key, x_old, args_old): + from flax import nnx + + module = self.module_cls(*self.args, rngs=nnx.Rngs(key), **dict(self.kwargs)) + _, theta = nnx.split(module, nnx.Param) + return theta, args_old + + def __hash__(self): + return hash((self.module_cls, _typed_key(self.args), _typed_key(self.kwargs))) + + def __eq__(self, other): + return ( + isinstance(other, DrawNNXModule) + and self.module_cls is other.module_cls + and _typed_key(self.args) == _typed_key(other.args) + and _typed_key(self.kwargs) == _typed_key(other.kwargs) + ) + + +def _accept_converged(_, result): + return result.status == LMStatus.CONVERGED + + +def _accept_converged_or_max_steps(_, result): + return (result.status == LMStatus.CONVERGED) | (result.status == LMStatus.MAX_STEPS) + + +def _attempt_success(accept_fn, accept_key, result, loss): + value = jnp.asarray(accept_fn(accept_key, result)) + if value.shape != (): + raise ValueError( + f"multi_start.accept must return a scalar; got shape {value.shape}" + ) + # An accepted-but-nonfinite result never wins: its masked loss is +inf. + return value.astype(jnp.bool_) & jnp.isfinite(loss) + + +def _type_spec(tree): + # weak_type is part of the spec: a weak/strong mismatch would break the + # while_loop carry avals just like a dtype mismatch. + leaves, treedef = jax.tree_util.tree_flatten(tree) + specs = [] + for leaf in leaves: + if not (hasattr(leaf, "shape") and hasattr(leaf, "dtype")): + leaf = jnp.asarray(leaf) + specs.append((tuple(leaf.shape), leaf.dtype, getattr(leaf, "weak_type", False))) + return treedef, specs + + +def _check_drawn_types(x, args, drawn): + # Works on concrete draws and on jax.eval_shape outputs alike; a mismatch + # would otherwise surface as an inscrutable while_loop/vmap error. + if _type_spec(drawn) != _type_spec((x, args)): + raise ValueError( + "multi_start.draw must return (x, args) matching the structure, " + f"shapes, and dtypes of its inputs; expected {_type_spec((x, args))}, " + f"got {_type_spec(drawn)}" + ) + + +def _multi_start_python_impl( + solver, + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + num_starts, + draw, + accept, + parallel, +): + accept_fn = accept + cold = solver._cold_state(lm_state) + + def run_attempt(x_a, lm_state_a, args_a, attempt): + result = _solve_python_impl( + solver, + x_a, + lm_state_a, + args_a, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + ) + accept_key = jax.random.split(jax.random.fold_in(key, attempt))[1] + loss = solver._ranking_objective(result, p, callback) + success = _attempt_success(accept_fn, accept_key, result, loss) + return result, loss, bool(success) + + best = best_loss = best_attempt = None + accepted = False + if parallel: + for lane in range(num_starts): + if lane == 0: + x_l, args_l = x, args + else: + draw_key = jax.random.split(jax.random.fold_in(key, lane))[0] + x_l, args_l = draw(draw_key, x, args) + _check_drawn_types(x, args, (x_l, args_l)) + result, loss, success = run_attempt(x_l, cold, args_l, lane) + better = ( + best is None + or (success and not accepted) + or (success == accepted and bool(loss < best_loss)) + ) + if better: + best, best_loss = result, loss + best_attempt, accepted = lane, success + attempts_run = num_starts + else: + x_a, args_a, lm_state_a = x, args, lm_state + for attempt in range(num_starts): + if attempt > 0: + draw_key = jax.random.split(jax.random.fold_in(key, attempt))[0] + x_a, args_a = draw(draw_key, x_a, args_a) + _check_drawn_types(x, args, (x_a, args_a)) + lm_state_a = cold + result, loss, success = run_attempt(x_a, lm_state_a, args_a, attempt) + take = ( + best is None + or success + or bool(loss < best_loss) + or not bool(jnp.isfinite(best_loss)) + ) + if take: + best, best_loss = result, loss + best_attempt, accepted = attempt, success + if success: + break + attempts_run = attempt + 1 + info = MultiStartInfo( + jnp.asarray(best_attempt, dtype=jnp.int32), + jnp.asarray(accepted, dtype=jnp.bool_), + jnp.asarray(attempts_run, dtype=jnp.int32), + best_loss, + ) + return dataclasses.replace(best, multi_start=info) + + +def _multi_start_sequential_impl( + solver, + x, + lm_state, + args, + p, + user_state, + key, + num_starts, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + draw, + accept, +): + accept_fn = accept + + def run_attempt(x_a, lm_state_a, args_a, attempt): + result = _solve_loop_impl( + solver, + x_a, + lm_state_a, + args_a, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + ) + accept_key = jax.random.split(jax.random.fold_in(key, attempt))[1] + loss = solver._ranking_objective(result, p, callback) + success = _attempt_success(accept_fn, accept_key, result, loss) + # p is loop-invariant: splice it out of the carried result and + # reattach after selection. + return dataclasses.replace(result, p=None), loss, success + + zero = jnp.asarray(0, dtype=jnp.int32) + best, best_loss, done = run_attempt(x, lm_state, args, zero) + if draw is None: + info = MultiStartInfo(zero, done, jnp.asarray(1, dtype=jnp.int32), best_loss) + return dataclasses.replace(best, p=p, multi_start=info) + + cold = solver._cold_state(lm_state) + + def cond(carry): + attempt, _, _, _, _, _, done = carry + return ~done & (attempt < num_starts) + + def body(carry): + attempt, x_prev, args_prev, best, best_loss, best_attempt, _ = carry + draw_key = jax.random.split(jax.random.fold_in(key, attempt))[0] + x_next, args_next = draw(draw_key, x_prev, args_prev) + result, loss, success = run_attempt(x_next, cold, args_next, attempt) + # First success wins (the loop exits); among failures keep the lowest + # masked loss, and an all-inf history always yields to the newest + # attempt so the none-finite case returns the last one. + take = success | (loss < best_loss) | ~jnp.isfinite(best_loss) + best = jax.tree.map(lambda new, old: jnp.where(take, new, old), result, best) + return ( + attempt + jnp.asarray(1, dtype=jnp.int32), + x_next, + args_next, + best, + jnp.where(take, loss, best_loss), + jnp.where(take, attempt, best_attempt), + success, + ) + + carry = jax.lax.while_loop( + cond, + body, + (jnp.asarray(1, dtype=jnp.int32), x, args, best, best_loss, zero, done), + ) + attempts_run, _, _, best, best_loss, best_attempt, accepted = carry + info = MultiStartInfo(best_attempt, accepted, attempts_run, best_loss) + return dataclasses.replace(best, p=p, multi_start=info) + + +def _multi_start_parallel_impl( + solver, + x, + lm_state, + args, + p, + user_state, + key, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + draw, + accept, + num_starts, +): + accept_fn = accept + lanes = jnp.arange(num_starts, dtype=jnp.int32) + attempt_keys = jax.vmap(lambda i: jax.random.fold_in(key, i))(lanes) + lane_keys = jax.vmap(jax.random.split)(attempt_keys) + accept_keys = lane_keys[:, 1] + draw_keys = lane_keys[1:, 0] + xs_drawn, args_drawn = jax.vmap(lambda k: draw(k, x, args))(draw_keys) + + def prepend(first, rest): + return jnp.concatenate([jnp.asarray(first)[None], rest], axis=0) + + xs = jax.tree.map(prepend, x, xs_drawn) + args_lanes = None if args is None else jax.tree.map(prepend, args, args_drawn) + # Under vmap the cache-reuse cond lowers to a select that evaluates both + # branches, so a warm Jacobian cache cannot save work: drop it uniformly. + cold = solver._cold_state(lm_state) + + def solve_lane(x_lane, args_lane, accept_key): + result = _solve_loop_impl( + solver, + x_lane, + cold, + args_lane, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, + ) + loss = solver._ranking_objective(result, p, callback) + success = _attempt_success(accept_fn, accept_key, result, loss) + return dataclasses.replace(result, p=None), loss, success + + results, losses, successes = jax.vmap( + solve_lane, in_axes=(0, None if args is None else 0, 0) + )(xs, args_lanes, accept_keys) + + # Lowest masked loss among successful lanes; with none, lowest loss + # overall (all-inf falls back to lane 0). argmin ties break low-index. + success_losses = jnp.where( + successes, losses, jnp.asarray(jnp.inf, dtype=losses.dtype) + ) + winner = jnp.where( + jnp.any(successes), jnp.argmin(success_losses), jnp.argmin(losses) + ).astype(jnp.int32) + best = jax.tree.map(lambda leaf: leaf[winner], results) + info = MultiStartInfo( + winner, + successes[winner], + jnp.asarray(num_starts, dtype=jnp.int32), + losses[winner], + ) + return dataclasses.replace(best, p=p, multi_start=info) + + +_multi_start_sequential_jit = jax.jit( + _multi_start_sequential_impl, static_argnums=(0, 8, 13, 14, 15) +) +_multi_start_parallel_jit = jax.jit( + _multi_start_parallel_impl, static_argnums=(0, 7, 12, 13, 14, 15) +) diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index 07e46f5..9a437e8 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -29,7 +29,7 @@ class Preconditioner: ``M`` slot with the live damping; in the AD role (``ad_solver=CG(...)``) the implicit-AD system is undamped and ``damping`` is zero. ``ctx`` is the same :class:`~nlls_gram.MetricContext` the metric factor ops receive - (the flat iterate, the live ``RidgeLMState``, ``args``, ``p``), so a + (the flat iterate, the live ``LMState``, ``args``, ``p``), so a preconditioner can key off the solver state. A preconditioner changes the CG iteration path, never the subproblem being solved, so approximations are safe. diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 2bde586..795e014 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -21,37 +21,26 @@ import dataclasses from dataclasses import dataclass -from typing import Any import jax import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg import jax.scipy.sparse.linalg as jsp_sparse_linalg -import numpy as np from jax.flatten_util import ravel_pytree -from nlls_gram.metrics import Metric, MetricContext -from nlls_gram.solver_config import CG, QR, Cholesky -from nlls_gram.utility import ( +from nlls_gram.lm_core import LevenbergMarquardtBase +from nlls_gram.lm_types import ( LMHyperparams, + LMInfo, LMSolveAction, - LMStatus, - MultiStart, - _accept_converged, - _accept_converged_or_max_steps, + LMState, _cast_hyper, - _check_drawn_types, _damping_floor, - _hashable_hook, - _mask_tangent_tree, - _multi_start_parallel_jit, - _multi_start_python_impl, - _multi_start_sequential_jit, - _solve_loop_jit, - _solve_python_impl, +) +from nlls_gram.metrics import Metric, MetricContext +from nlls_gram.solver_config import CG, QR, Cholesky +from nlls_gram.utilities import ( _static_key_component, - _tree_changed, - _where_tree, _zero_tangent_leaf, canonicalize_residual, ) @@ -60,8 +49,6 @@ "CholeskyCache", "QRCache", "RidgeLevenbergMarquardt", - "RidgeLMInfo", - "RidgeLMState", "ridge_continuation", ] @@ -102,133 +89,6 @@ class QRCache: ridge: jax.Array -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class RidgeLMState: - """Carried solver state threaded through ``init``/``update``/``solve``. - - ``damping`` and ``ridge`` are always live; the remaining fields are - populated by the configuration that needs them and stay ``None`` on the - other paths (compiled away at no cost). A ``solve`` callback that rebuilds - ``lm_state`` must PRESERVE the fields it does not mean to change -- use - ``dataclasses.replace(ctx.lm_state, ...)``. Replacing ``ridge`` is the - supported way to anneal the ridge weight mid-solve (see - :func:`ridge_continuation`); the solver treats a ridge change as a problem - change, suppressing that step's convergence test and invalidating the - ridge-keyed caches. - - Attributes: - damping: ``()`` current LM damping ``mu`` (the Euclidean trust-region - parameter, decoupled from ``ridge``). - ridge: ``()`` current ridge weight ``lambda``, strictly positive by - contract. Set by ``init`` (constructor value or the dtype default) - and replaced only by callbacks. - resid: cached TRUE residual at the current ``x`` - (``cache_jacobian=True`` dense paths only, else ``None``). - Jt: cached transpose-Jacobian ``J'`` of the TRUE residual at the - current ``x`` (``cache_jacobian=True`` dense paths only). - jacobian_valid: ``()`` bool -- the cached ``resid``/``Jt`` are still - current because the last step was rejected so ``x`` did not move. - aux: residual aux pytree at the current ``x`` (``has_aux=True``). - hyper: per-step :class:`~nlls_gram.LMHyperparams`, populated by - ``solve``; ``None`` (``init``'s default) falls back to the - constructor values. - solver_cache: the configured forward solver's own reject-step cache - -- a :class:`CholeskyCache` or :class:`QRCache` whose pytree - structure is fixed by the static ``linear_solver`` config, or - ``None`` when the path carries no cache (``CG``, - ``cache_jacobian=False``). - metric_state: reserved for the future ``metric_factory`` (adaptive - metrics): traced data a factory's ``prepare``/``build`` pair - would turn into a :class:`~nlls_gram.Metric` per step. Always - ``None`` today. - metric_valid: reserved alongside ``metric_state`` with the - ``jacobian_valid`` reject-reuse semantics; a state change is a - problem change (convergence suppressed, ridge-keyed caches - invalidated). Always ``None`` today. - """ - - damping: jax.Array - ridge: jax.Array - resid: jax.Array | None = None - Jt: jax.Array | None = None - jacobian_valid: jax.Array | None = None - aux: Any = None - hyper: LMHyperparams | None = None - solver_cache: Any = None - metric_state: Any = None - metric_valid: jax.Array | None = None - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class RidgeLMInfo: - """Per-step diagnostics returned by ``update`` (and for each ``solve`` step). - - ``loss`` is the RIDGE OBJECTIVE ``||r||^2 + ridge * ||x_m||_W^2`` - actually being minimized -- it includes the penalty term. Code that means - equation error must read ``resid_loss`` (``||r||^2`` alone). The - loss/damping fields report the accept/reject outcome of the step, while - ``grad_norm``/``step_norm``/``aux`` are evaluated at the PRE-step ``x``. - - The solver runs in the whitened variable ``y = F_bar x``, so - ``grad_norm``, ``step_norm``, and ``penalty_grad_norm`` are Euclidean in - ``y`` -- equivalently, steps are measured in the W-norm and gradients in - the dual W^{-1}-norm. Objective values - (``loss``/``resid_loss``/``penalty_value``) are unaffected by the change - of variables: whitening is a pure linear bijection of the same objective. - - Attributes: - loss: ``min(loss_old, loss_candidate)`` ridge objective at the - retained iterate. - loss_old: ridge objective at the pre-step ``x``. - loss_candidate: ridge objective at the trial point. - resid_loss: ``||r||^2`` at the retained iterate. - penalty_value: ``||x_m||_W^2 = ||y_m||^2`` at the retained iterate. - ridge: ``()`` the ridge weight ``lambda`` used this step. - accepted: ``()`` bool, whether the trial step was accepted. - damping: ``()`` post-update damping ``mu``. - damping_factor: ``()`` multiplicative damping update applied this step. - used_geodesic: ``()`` bool, whether the geodesic-acceleration - correction entered the accepted step. - acceleration_ratio: ``()`` geodesic acceleration-to-velocity whitened - norm ratio. - grad_norm: ``()`` ``||F_bar^{-T} J'r + ridge [y_m; 0]||`` at the - pre-step ``x`` -- the whitened ridge stationarity residual (the - dual W^{-1}-norm of the half-gradient), NOT ``||J'r||``. - penalty_grad_norm: ``()`` ``||[y_m; 0]|| = sqrt(penalty_value)`` at - the pre-step ``x`` -- the whitened penalty-gradient scale, - reported so ``gtol`` can be CALIBRATED instead of guessed: at a - ridge minimizer the gradient is the cancellation of the residual - pullback against ``ridge * [y_m; 0]``, so demanding ``grad_norm - < c * ridge * penalty_grad_norm`` resolves the null-space - (selection) coordinates to ~``c`` relative accuracy. The recipe - is ``gtol ~ 1e-3 * ridge * sqrt(q(x*))`` with ``q`` the - solution's squared seminorm, usually known to an order of - magnitude before any pilot run. - step_norm: ``()`` whitened ``||delta_y||`` of the candidate step -- - the W-norm of the x-space step -- reported even when the step is - rejected (``xtol`` therefore bounds the whitened step). - aux: residual aux output at the pre-step ``x`` (``has_aux=True``). - """ - - loss: jax.Array - loss_old: jax.Array - loss_candidate: jax.Array - resid_loss: jax.Array - penalty_value: jax.Array - ridge: jax.Array - accepted: jax.Array - damping: jax.Array - damping_factor: jax.Array - used_geodesic: jax.Array - acceleration_ratio: jax.Array - grad_norm: jax.Array - penalty_grad_norm: jax.Array - step_norm: jax.Array - aux: Any = None - - def ridge_continuation( *, decrease=0.1, ridge_floor, grad_rtol=1e-2, stall_rtol=0.0, dtype=None ): @@ -348,7 +208,7 @@ def callback(ctx): return callback, user_state0 -class RidgeLevenbergMarquardt: +class RidgeLevenbergMarquardt(LevenbergMarquardtBase): """Levenberg-Marquardt for the ridge objective ``F(x) = ||r(x, args, p)||^2 + ridge * q(x)`` with ``q(x) = ||x_m||_W^2`` over a JAX pytree ``x``, built for underdetermined @@ -697,16 +557,6 @@ def __init__( ) self._static_hash = hash(self._static_key) - def __eq__(self, other): - if self is other: - return True - if type(other) is not type(self): - return NotImplemented - return self._static_key == other._static_key - - def __hash__(self): - return self._static_hash - def hyperparams(self, dtype=None): """``LMHyperparams`` built from the constructor values.""" iterative_tol = self.iterative_tol @@ -768,7 +618,7 @@ def _resolve_ridge(self, dtype): return jnp.asarray(self.ridge, dtype=dtype) def init(self, x0, args=None, *, p=None): - """Build the initial :class:`RidgeLMState` at ``x0``. + """Build the initial :class:`LMState` at ``x0``. One residual evaluation types ``damping`` and resolves ``ridge=None`` to the dtype default, and sizes the Jacobian/normal/QR @@ -785,7 +635,7 @@ def init(self, x0, args=None, *, p=None): damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) ridge = self._resolve_ridge(dtype) if not self.cache_jacobian: - return RidgeLMState(damping, ridge) + return LMState(damping, ridge) p_dim = theta.size m = residual.size invalid = jnp.asarray(False, dtype=jnp.bool_) @@ -808,47 +658,7 @@ def init(self, x0, args=None, *, p=None): valid=invalid, ridge=jnp.zeros((), dtype=dtype), ) - return RidgeLMState(damping, ridge, **common, solver_cache=cache) - - def _resolve_jacobian_mode(self, m, n): - # Static (shape-driven) choice of dense Jacobian assembly on the TRUE - # residual: "auto" takes n forward-mode columns when the system is - # tall or square (n <= m) and m reverse-mode rows only when strictly - # fat, so the identity basis being vmapped is always the small side. - # The penalty rows are affine and never assembled through AD. - if self.jacobian_mode != "auto": - return self.jacobian_mode - return "fwd" if n <= m else "rev" - - def _assemble_jt(self, jvp_fn, theta, resid): - if self._resolve_jacobian_mode(resid.shape[0], theta.shape[0]) == "fwd": - parameter_basis = jnp.eye(theta.shape[0], dtype=theta.dtype) - return jax.vmap(jvp_fn)(parameter_basis) - transpose_fn = jax.linear_transpose(jvp_fn, theta) - residual_basis = jnp.eye(resid.shape[0], dtype=resid.dtype) - return jax.vmap(lambda cotangent: transpose_fn(cotangent)[0])(residual_basis).T - - def _dense_resid_jt_aux(self, residual_flat, theta): - if self.has_aux: - resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) - else: - resid, jvp_fn = jax.linearize(residual_flat, theta) - aux = None - return resid, self._assemble_jt(jvp_fn, theta, resid), aux - - def _residual_and_aux(self, x, args, p): - if self.has_aux: - value, aux = self.residual_fn(x, args, p) - for leaf in jax.tree.leaves(aux): - if not isinstance( - leaf, (jax.Array, np.ndarray, np.generic, bool, int, float, complex) - ): - raise TypeError( - "has_aux=True: aux leaves must be JAX numeric types " - f"(arrays or scalars); got {type(leaf).__name__}" - ) - return jnp.ravel(value), aux - return jnp.ravel(self.residual_fn(x, args, p)), None + return LMState(damping, ridge, **common, solver_cache=cache) def _initial_info(self, x, lm_state, args, p): # grad_norm and penalty_grad_norm are +inf sentinels (computing them @@ -857,10 +667,6 @@ def _initial_info(self, x, lm_state, args, p): residual, aux = self._residual_and_aux(x, args, p) resid_loss = jnp.sum(residual**2) theta, _ = ravel_pytree(x) - if lm_state.ridge is None: - raise ValueError( - "the lm_state has no ridge; create it with init(x, args, p=p)" - ) ridge = jnp.asarray(lm_state.ridge, dtype=residual.dtype) n_m = self._block_sizes(theta.shape[0])[0] ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) @@ -871,22 +677,23 @@ def _initial_info(self, x, lm_state, args, p): loss = resid_loss + ridge * penalty_value zero = jnp.zeros((), dtype=residual.dtype) one = jnp.ones((), dtype=residual.dtype) - return RidgeLMInfo( - loss, - loss, - loss, - resid_loss, - penalty_value, - ridge, - jnp.asarray(False, dtype=jnp.bool_), - jnp.asarray(lm_state.damping, dtype=residual.dtype), - one, - jnp.asarray(False, dtype=jnp.bool_), - zero, - jnp.asarray(jnp.inf, dtype=residual.dtype), - jnp.asarray(jnp.inf, dtype=residual.dtype), - zero, - aux, + infinity = jnp.asarray(jnp.inf, dtype=residual.dtype) + return LMInfo( + loss=loss, + loss_old=loss, + loss_candidate=loss, + accepted=jnp.asarray(False, dtype=jnp.bool_), + damping=jnp.asarray(lm_state.damping, dtype=residual.dtype), + damping_factor=one, + used_geodesic=jnp.asarray(False, dtype=jnp.bool_), + acceleration_ratio=zero, + grad_norm=infinity, + step_norm=zero, + ridge=ridge, + resid_loss=resid_loss, + penalty_value=penalty_value, + penalty_grad_norm=infinity, + aux=aux, ) def update(self, x, lm_state, args=None, p=None): @@ -1329,7 +1136,7 @@ def accelerated_objective(_): new_cache = CholeskyCache(normal_matrix, ~improved, ridge) else: new_cache = QRCache(qr_R, ~improved, ridge) - new_lm_state = RidgeLMState( + new_lm_state = LMState( new_damping, ridge, resid, @@ -1340,482 +1147,99 @@ def accelerated_objective(_): solver_cache=new_cache, ) else: - new_lm_state = RidgeLMState(new_damping, ridge, hyper=lm_state.hyper) + new_lm_state = LMState(new_damping, ridge, hyper=lm_state.hyper) return ( unravel(theta_new), new_lm_state, - RidgeLMInfo( - loss, - loss_old, - loss_candidate, - resid_loss, - penalty_value, - ridge, - improved, - new_damping, - damping_factor, - used_geodesic, - acceleration_ratio, - jnp.linalg.norm(grad), - jnp.linalg.norm(penalty_gradient), - jnp.linalg.norm(step_sub), - aux, + LMInfo( + loss=loss, + loss_old=loss_old, + loss_candidate=loss_candidate, + accepted=improved, + damping=new_damping, + damping_factor=damping_factor, + used_geodesic=used_geodesic, + acceleration_ratio=acceleration_ratio, + grad_norm=jnp.linalg.norm(grad), + step_norm=jnp.linalg.norm(step_sub), + ridge=ridge, + resid_loss=resid_loss, + penalty_value=penalty_value, + penalty_grad_norm=jnp.linalg.norm(penalty_gradient), + aux=aux, ), ) - def solve( - self, - x0, - args=None, - *, - p=None, - lm_state=None, - max_steps=256, - max_steps_is_success=True, - atol=0.0, - gtol=0.0, - xtol=0.0, - callback=None, - user_state=None, - save_steps=False, - multi_start=None, - jit=True, - ): - """Run repeated LM updates until a stopping rule fires. - - Parameters are the same as ``update`` plus loop controls, matching - :meth:`LevenbergMarquardt.solve - ` (callbacks, ``save_steps``, - ``multi_start``, ``max_steps_is_success``, ``jit``) with two - differences. First, the tolerance semantics are conjunctive: - ``gtol`` bounds the whitened ridge stationarity ``info.grad_norm = - ||J~'r + ridge [y_m; 0]||`` (the dual W^{-1}-norm of the - half-gradient) and ``xtol`` the accepted whitened step norm - ``info.step_norm = ||delta_y||`` (the W-norm of the step) -- either - fires "done with the current fixed-ridge problem". The calibration - recipe reads ``gtol ~ 1e-3 * ridge * sqrt(q(x*))`` since - ``penalty_grad_norm = sqrt(penalty_value)``. Meanwhile - ``atol > 0`` ADDITIONALLY requires ``sqrt(resid_loss) <= atol`` - (the model equations actually solved, the ridgeless-endgame check) - and never stops the solve alone; ``atol > 0`` therefore requires a - positive ``gtol`` or ``xtol`` (validated loudly). Second, - ``lm_state=None`` always builds the state with :meth:`init` - (resolving ``ridge=None`` needs the residual dtype); a - caller-supplied ``lm_state`` must carry a positive ``ridge``. - - For ridge continuation pass the pair returned by - :func:`ridge_continuation` as ``callback``/``user_state``. A callback - ridge change is a problem change: that step's convergence test is - suppressed and the ridge-keyed caches invalidate. - """ - self._check_residual_args(args, p) - if not isinstance(max_steps_is_success, bool): - raise TypeError("max_steps_is_success must be a bool") - if max_steps <= 0: - raise ValueError("max_steps must be positive") - # Tolerances are traced data inside the loop, so vmapped/traced values - # skip the concrete-only validation. - atol_concrete = not isinstance(atol, jax.core.Tracer) - gtol_concrete = not isinstance(gtol, jax.core.Tracer) - xtol_concrete = not isinstance(xtol, jax.core.Tracer) - if atol_concrete and atol < 0: - raise ValueError("atol must be nonnegative") - if gtol_concrete and gtol < 0: - raise ValueError("gtol must be nonnegative") - if xtol_concrete and xtol < 0: - raise ValueError("xtol must be nonnegative") + def _validate_tolerances(self, atol, gtol, xtol): + # atol is a CONJUNCTIVE filter on the true residual, never a stopping + # rule alone: a residual-only test would stop at any interpolating + # iterate, before the seminorm is minimized. + concrete = [not isinstance(t, jax.core.Tracer) for t in (atol, gtol, xtol)] if ( - atol_concrete + concrete[0] and atol > 0 - and (gtol_concrete and gtol == 0) - and (xtol_concrete and xtol == 0) + and (concrete[1] and gtol == 0) + and (concrete[2] and xtol == 0) ): raise ValueError( "atol > 0 requires a positive gtol or xtol: atol is a " "conjunctive filter on the TRUE residual, never a stopping " - "rule by itself -- a residual-only test would stop at any " - "interpolating iterate before the seminorm is minimized. " - "Calibrate gtol from a pilot run as roughly 1e-3 * ridge * " - "info.penalty_grad_norm (the relative-stationarity recipe)" + "rule by itself. Calibrate gtol from a pilot run as roughly " + "1e-3 * ridge * info.penalty_grad_norm" ) + + def _solve_lm_state(self, x0, args, p, lm_state): if lm_state is None: # Unconditional init (no minimal-state fast path): resolving # ridge=None needs the residual dtype, and the dense caches need # their shapes. - lm_state = self.init(x0, args, p=p) - else: - if lm_state.ridge is None: - raise ValueError( - "the caller-supplied lm_state has no ridge; create it " - "with init(x, args, p=p) or set a positive ridge" - ) - if ( - not isinstance(lm_state.ridge, jax.core.Tracer) - and jnp.ndim(lm_state.ridge) == 0 - and float(lm_state.ridge) <= 0.0 - ): - raise ValueError( - "the caller-supplied lm_state.ridge must be strictly " - "positive (ridge = 0 is unsupported)" - ) - # Recast a hand-replaced ridge to the carried scalar dtype: a - # weak-typed `dataclasses.replace(state, ridge=1e-4)` would - # otherwise change the jit input aval and retrace the loop. - lm_state = dataclasses.replace( - lm_state, - ridge=jnp.asarray( - lm_state.ridge, dtype=jnp.asarray(lm_state.damping).dtype - ), - ) - if lm_state.hyper is None: - lm_state = dataclasses.replace(lm_state, hyper=self.hyperparams()) - history_len = max_steps + 1 if save_steps else None - - if multi_start is not None: - if not isinstance(multi_start, MultiStart): - raise TypeError("multi_start must be a MultiStart or None") - num_starts = multi_start.num_starts - draw = _hashable_hook(multi_start.draw if num_starts > 1 else None) - default_accept = ( - _accept_converged_or_max_steps - if max_steps_is_success - else _accept_converged - ) - accept = _hashable_hook( - default_accept if multi_start.accept is None else multi_start.accept - ) - parallel = multi_start.parallel and num_starts > 1 - if draw is not None and jit: - drawn = jax.eval_shape(draw, multi_start.key, x0, args) - _check_drawn_types(x0, args, drawn) - - @jax.custom_jvp - def solve_multi_start_with_ad_p( - x, - lm_state, - args, - p, - user_state, - key, - max_steps, - atol, - gtol, - xtol, - ): - return self._multi_start_impl( - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - num_starts, - draw, - accept, - parallel, - ) - - @solve_multi_start_with_ad_p.defjvp - def solve_multi_start_with_ad_p_jvp(primals, tangents): - p_dot = tangents[3] - result = solve_multi_start_with_ad_p(*primals) - initial_ad_point = ( - primals[0], - primals[2], - primals[3], - primals[1].ridge, - ) - return result, self._ad_result_tangent( - result, p_dot, initial_ad_point, max_steps_is_success - ) - - return solve_multi_start_with_ad_p( - x0, - lm_state, - args, - p, - user_state, - multi_start.key, - max_steps, - atol, - gtol, - xtol, + return self.init(x0, args, p=p) + if lm_state.ridge is None: + raise ValueError( + "the caller-supplied lm_state has no ridge; create it with " + "init(x, args, p=p) or set a positive ridge" ) - - @jax.custom_jvp - def solve_with_ad_p( - x, - lm_state, - args, - p, - user_state, - max_steps, - atol, - gtol, - xtol, + if ( + not isinstance(lm_state.ridge, jax.core.Tracer) + and jnp.ndim(lm_state.ridge) == 0 + and float(lm_state.ridge) <= 0.0 ): - return self._solve_impl( - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - ) - - @solve_with_ad_p.defjvp - def solve_with_ad_p_jvp(primals, tangents): - p_dot = tangents[3] - result = solve_with_ad_p(*primals) - initial_ad_point = (primals[0], primals[2], primals[3], primals[1].ridge) - return result, self._ad_result_tangent( - result, p_dot, initial_ad_point, max_steps_is_success - ) - - return solve_with_ad_p( - x0, - lm_state, - args, - p, - user_state, - max_steps, - atol, - gtol, - xtol, - ) - - def _solve_impl( - self, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - ): - if jit: - return _solve_loop_jit( - self, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, + raise ValueError( + "the caller-supplied lm_state.ridge must be strictly positive " + "(ridge = 0 is unsupported)" ) - return _solve_python_impl( - self, - x, + # Recast a hand-replaced ridge to the carried scalar dtype: a + # weak-typed replace(state, ridge=1e-4) would change the jit input + # aval and retrace the loop. + return dataclasses.replace( lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, + ridge=jnp.asarray( + lm_state.ridge, dtype=jnp.asarray(lm_state.damping).dtype + ), ) - def _multi_start_impl( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - num_starts, - draw, - accept, - parallel, - ): - if not jit: - return _multi_start_python_impl( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - num_starts, - draw, - accept, - parallel, - ) - if parallel: - return _multi_start_parallel_jit( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, - num_starts, - ) - return _multi_start_sequential_jit( - self, - x, - lm_state, - args, - p, - user_state, - key, - jnp.asarray(num_starts, dtype=jnp.int32), - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, - ) + def _initial_ad_point(self, x, lm_state, args, p): + # The pre-loop ridge rides along: a failed lane's callback may have + # left an invalid ridge behind, so the failed tangent uses this one. + return (x, args, p, lm_state.ridge) - def _action_or_default(self, action): - if action is None: - return LMSolveAction() - return action - - def _apply_action(self, action, x, lm_state, args, user_state): - action = self._action_or_default(action) - # The step's diagnostics and every cache describe the pre-action - # problem, so they are stale iff the action actually changed the - # values -- a traced comparison, so a jit-style callback that returns - # the field every step with unchanged values changes nothing. A ridge - # change leaves the Jacobian cache VALID (J does not depend on ridge) - # but invalidates the ridge-keyed normal/QR caches and suppresses the - # convergence check (the diagnostics were computed at the old ridge). - xargs_changed = jnp.asarray(False) - ridge_changed = jnp.asarray(False) - if action.x is not None: - xargs_changed = xargs_changed | _tree_changed(action.x, x) - x = action.x - if action.lm_state is not None: - previous_hyper = lm_state.hyper - # Captured BEFORE replacing: ridge lives inside action.lm_state, - # not as a top-level action field. - previous_ridge = lm_state.ridge - lm_state = action.lm_state - if lm_state.ridge is None: - raise ValueError( - "the callback action returned an lm_state without ridge; " - "use dataclasses.replace(ctx.lm_state, ...) to preserve it" - ) - if self.cache_jacobian and lm_state.jacobian_valid is None: - raise ValueError( - "cache_jacobian=True but the callback action returned an " - "lm_state without the Jacobian cache; use " - "dataclasses.replace(ctx.lm_state, ...) to preserve the " - "cache fields" - ) - if previous_hyper is not None and ( - lm_state.hyper is None - or jax.tree_util.tree_structure(previous_hyper) - != jax.tree_util.tree_structure(lm_state.hyper) - or [leaf.dtype for leaf in jax.tree_util.tree_leaves(previous_hyper)] - != [leaf.dtype for leaf in jax.tree_util.tree_leaves(lm_state.hyper)] - ): - raise ValueError( - "the callback action changed the structure or dtypes of " - "lm_state.hyper; reset values with " - "dataclasses.replace(ctx.lm_state.hyper, ...) using arrays " - "of the same dtype — a knob constructed as None cannot be " - "enabled mid-solve" - ) - # Recast a callback-provided ridge to the carried scalar's dtype: - # a weak-typed Python float in the action must not change the - # while_loop carry aval. - new_ridge = jnp.asarray(lm_state.ridge, dtype=previous_ridge.dtype) - ridge_changed = ridge_changed | ~jnp.array_equal( - new_ridge, previous_ridge, equal_nan=True - ) - lm_state = dataclasses.replace(lm_state, ridge=new_ridge) - if action.args is not None: - xargs_changed = xargs_changed | _tree_changed(action.args, args) - args = action.args - if action.user_state is not None: - user_state = action.user_state - problem_changed = xargs_changed | ridge_changed - if self.cache_jacobian and (action.x is not None or action.args is not None): - lm_state = dataclasses.replace( - lm_state, jacobian_valid=lm_state.jacobian_valid & ~xargs_changed - ) - touched = ( - action.x is not None - or action.args is not None - or action.lm_state is not None - ) - if touched and lm_state.solver_cache is not None: - cache = lm_state.solver_cache - lm_state = dataclasses.replace( - lm_state, - solver_cache=dataclasses.replace( - cache, valid=cache.valid & ~problem_changed - ), - ) - return action, x, lm_state, args, user_state, problem_changed - - def _check_residual_args(self, args, p): - if args is not None and self.residual_arity < 2: - raise ValueError( - "args was passed but residual_fn takes only (x); " - "use residual_fn(x, args)" - ) - if p is not None and self.residual_arity < 3: + def _check_action_state(self, lm_state): + if lm_state.ridge is None: raise ValueError( - "p was passed but residual_fn takes no p argument; " - "use residual_fn(x, args, p)" + "the callback action returned an lm_state without ridge; " + "use dataclasses.replace(ctx.lm_state, ...) to preserve it" ) + def _apply_action_state(self, lm_state, previous): + # A ridge change leaves the Jacobian cache VALID (J does not depend on + # ridge) but invalidates the ridge-keyed normal/QR caches and + # suppresses the convergence check, whose diagnostics were computed at + # the old ridge. The recast keeps a weak-typed callback float from + # changing the while_loop carry aval. + new_ridge = jnp.asarray(lm_state.ridge, dtype=previous.ridge.dtype) + changed = ~jnp.array_equal(new_ridge, previous.ridge, equal_nan=True) + return dataclasses.replace(lm_state, ridge=new_ridge), changed + def _converged(self, info, atol, gtol, xtol): # gtol/xtol mean "done with the current fixed-ridge problem"; atol is # a CONJUNCTIVE filter on the TRUE residual, never sufficient alone. @@ -1879,54 +1303,25 @@ def _ranking_objective(self, result, p, callback): jnp.isfinite(loss), loss, jnp.asarray(jnp.inf, dtype=loss.dtype) ) - def _ad_result_tangent(self, result, p_dot, initial_ad_point, max_steps_is_success): - # A successful tangent relinearizes at the returned solution with the - # winner's own final ridge (stop-gradient: lambda is inert - # conditioning data). A failed tangent uses the differentiation-inert - # original initial point and the pre-loop INITIAL ridge -- a failed - # lane's callback may have left an invalid ridge behind. Everything - # except x, p, and aux is bookkeeping with zero tangents. - initial_x, initial_args, initial_p, initial_ridge = jax.tree.map( - jax.lax.stop_gradient, initial_ad_point - ) - ad_success = result.status == LMStatus.CONVERGED - if max_steps_is_success: - ad_success = ad_success | (result.status == LMStatus.MAX_STEPS) - ad_x = _where_tree(ad_success, result.x, initial_x) - ad_args = _where_tree(ad_success, result.args, initial_args) - ad_p = _where_tree(ad_success, result.p, initial_p) - ad_p_dot = _mask_tangent_tree(ad_success, p_dot) - final_ridge = jax.lax.stop_gradient(result.lm_state.ridge) - ad_ridge = jnp.where( - ad_success, final_ridge, jnp.asarray(initial_ridge, final_ridge.dtype) - ) - # The returned state rides along as inert MetricContext data for the - # factor callbacks, like the frozen ridge. - ad_lm_state = jax.lax.stop_gradient(result.lm_state) - x_dot = self._ad_x_tangent_from_p( - ad_x, ad_args, ad_p, ad_p_dot, ad_ridge, ad_lm_state - ) - zero_result = jax.tree.map(_zero_tangent_leaf, result) - x_dot = _where_tree(ad_success, x_dot, zero_result.x) - aux_dot = zero_result.aux - if self.has_aux and ad_p is not None: - # aux depends on p directly and through the solution x*(p). - def aux_at_solution(x_value, p_value): - return self.residual_fn(x_value, ad_args, p_value)[1] - - aux_dot = jax.jvp(aux_at_solution, (ad_x, ad_p), (x_dot, ad_p_dot))[1] - aux_dot = _where_tree(ad_success, aux_dot, zero_result.aux) - return dataclasses.replace(zero_result, x=x_dot, p=p_dot, aux=aux_dot) - def _resolved_ad_solver(self): if self.ad_solver is None: # Matrix-free forward -> matrix-free AD. return "normal_cg" if self._resolved_solver() == "normal_cg" else "cholesky" return "cholesky" if isinstance(self.ad_solver, Cholesky) else "normal_cg" - def _ad_x_tangent_from_p(self, x, args, p, p_dot, ridge, lm_state): + def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point): if p is None: return jax.tree.map(_zero_tangent_leaf, x) + # A successful tangent uses the winner's own final ridge; a failed one + # the pre-loop initial ridge. Both are stop-gradient'd -- lambda is + # inert conditioning data, and the returned state rides along as + # equally inert MetricContext data for the factor callbacks. + final_ridge = jax.lax.stop_gradient(result.lm_state.ridge) + initial_ridge = jax.lax.stop_gradient(initial_ad_point[3]) + ridge = jnp.where( + ad_success, final_ridge, jnp.asarray(initial_ridge, final_ridge.dtype) + ) + lm_state = jax.lax.stop_gradient(result.lm_state) if self._resolved_ad_solver() == "cholesky": return self._ad_tangent_cholesky(x, args, p, p_dot, ridge, lm_state) return self._ad_tangent_normal_cg(x, args, p, p_dot, ridge, lm_state) @@ -2035,9 +1430,3 @@ def solve(matvec, rhs_value): ) theta_dot = jnp.asarray(self._extended_solve(y_dot, ctx), residual.dtype) return unravel(theta_dot) - - def _ad_cg_tol(self, dtype): - if self.ad_solver_tol is not None: - return jnp.asarray(self.ad_solver_tol, dtype=dtype) - default_tol = 1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6 - return jnp.asarray(default_tol, dtype=dtype) diff --git a/src/nlls_gram/solve_loop.py b/src/nlls_gram/solve_loop.py new file mode 100644 index 0000000..5791987 --- /dev/null +++ b/src/nlls_gram/solve_loop.py @@ -0,0 +1,301 @@ +"""The LM solve loop: the jitted ``lax.while_loop`` driver, its Python mirror, +and the ``save_steps`` history buffers. + +Both drivers consume an informal solver protocol -- ``update``, +``_apply_action``, ``_converged``, ``_residual_and_aux``, ``_initial_info``, +``_cast_state``, ``has_aux`` -- implemented by ``LevenbergMarquardtBase``. +""" + +import jax +import jax.numpy as jnp + +from nlls_gram.lm_types import LMSolveContext, LMSolveResult, LMStatus + + +# save_steps bookkeeping shared by the jitted and Python solve loops: row `step` of +# x_history and args_history takes the kept post-action iterate and args; info.aux was +# evaluated at the pre-step x, so it lands one row earlier, and _finalize_history fills +# the last aux row from the final-solution evaluation. history_len is concrete (static +# under jit), so the buffers live entirely inside the loop implementations — no +# host-side allocation and no copy of a jit-input buffer before the in-place row +# updates. eval_shape gets the aux buffer shapes without paying for a residual +# evaluation. +def _history_buffer(tree, history_len): + # Row 0 holds the initial value; tree.map over a None tree returns None. + return jax.tree.map( + lambda leaf: ( + jnp.zeros((history_len, *jnp.shape(leaf)), jnp.result_type(leaf)) + .at[0] + .set(leaf) + ), + tree, + ) + + +def _init_history(solver, x0, args, p, history_len): + if history_len is None: + return None + x_history = _history_buffer(x0, history_len) + args_history = _history_buffer(args, history_len) + aux_history = None + if solver.has_aux: + aux0 = jax.eval_shape( + lambda x_, args_, p_: solver._residual_and_aux(x_, args_, p_)[1], + x0, + args, + p, + ) + aux_history = jax.tree.map( + lambda leaf: jnp.zeros((history_len, *leaf.shape), leaf.dtype), aux0 + ) + return (x_history, aux_history, args_history) + + +def _record_history(history, step, x, info, args): + if history is None: + return None + x_history, aux_history, args_history = history + x_history = jax.tree.map(lambda buf, leaf: buf.at[step].set(leaf), x_history, x) + args_history = jax.tree.map( + lambda buf, leaf: buf.at[step].set(leaf), args_history, args + ) + if aux_history is not None: + aux_history = jax.tree.map( + lambda buf, leaf: buf.at[step - 1].set(leaf), aux_history, info.aux + ) + return (x_history, aux_history, args_history) + + +def _finalize_history(history, steps, final_aux): + if history is None: + return None, None, None + x_history, aux_history, args_history = history + if aux_history is not None: + aux_history = jax.tree.map( + lambda buf, leaf: buf.at[steps].set(leaf), aux_history, final_aux + ) + return x_history, aux_history, args_history + + +def _solve_loop_impl( + solver, + x, + lm_state, + args, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, +): + history = _init_history(solver, x, args, p, history_len) + max_steps = jnp.asarray(max_steps, dtype=jnp.int32) + info = solver._initial_info(x, lm_state, args, p) + # Recast the state's scalars (damping, hyperparameters, and any + # solver-specific carried scalars) and the tolerances to the residual + # dtype so the while_loop carry matches what update() returns. + atol = jnp.asarray(atol, dtype=info.loss.dtype) + gtol = jnp.asarray(gtol, dtype=info.loss.dtype) + xtol = jnp.asarray(xtol, dtype=info.loss.dtype) + lm_state = solver._cast_state(lm_state, info.loss.dtype) + initial_lm_state = lm_state + step = jnp.asarray(0, dtype=jnp.int32) + initial_nonfinite = ~jnp.isfinite(info.loss) + initial_converged = solver._converged(info, atol, gtol, xtol) + stop = initial_nonfinite | initial_converged + status = jnp.where( + initial_nonfinite, + jnp.asarray(LMStatus.NONFINITE, dtype=jnp.int32), + jnp.where( + initial_converged, + jnp.asarray(LMStatus.CONVERGED, dtype=jnp.int32), + jnp.asarray(LMStatus.RUNNING, dtype=jnp.int32), + ), + ) + + def cond(carry): + _, _, _, _, _, _, step, _, stop = carry + return (~stop) & (step < max_steps) + + def body(carry): + x, lm_state, args, user_state, history, _, step, _, _ = carry + x_old, lm_state_old = x, lm_state + x, lm_state, info = solver.update(x, lm_state, args, p) + step = step + jnp.asarray(1, dtype=jnp.int32) + current_nonfinite = ~jnp.isfinite(info.loss) + + action = None + if callback is not None: + ctx = LMSolveContext( + step, + x, + x_old, + lm_state, + lm_state_old, + initial_lm_state, + args, + p, + user_state, + info, + ) + action = callback(ctx) + action, x, lm_state, args, user_state, problem_changed = solver._apply_action( + action, x, lm_state, args, user_state + ) + history = _record_history(history, step, x, info, args) + + callback_stop = ( + jnp.asarray(False, dtype=jnp.bool_) + if action.stop is None + else jnp.asarray(action.stop, dtype=jnp.bool_) + ) + callback_status = ( + jnp.asarray(LMStatus.CALLBACK_STOP, dtype=jnp.int32) + if action.status is None + else jnp.asarray(action.status, dtype=jnp.int32) + ) + # info describes the pre-action (x, args); if the action changed them, + # the tolerances must wait for a fresh update. + converged = solver._converged(info, atol, gtol, xtol) & ~problem_changed + reached_max = step >= max_steps + stop = current_nonfinite | callback_stop | converged | reached_max + status = jnp.where( + current_nonfinite, + jnp.asarray(LMStatus.NONFINITE, dtype=jnp.int32), + jnp.where( + callback_stop, + callback_status, + jnp.where( + converged, + jnp.asarray(LMStatus.CONVERGED, dtype=jnp.int32), + jnp.where( + reached_max, + jnp.asarray(LMStatus.MAX_STEPS, dtype=jnp.int32), + jnp.asarray(LMStatus.RUNNING, dtype=jnp.int32), + ), + ), + ), + ) + return x, lm_state, args, user_state, history, info, step, status, stop + + carry = jax.lax.while_loop( + cond, + body, + (x, lm_state, args, user_state, history, info, step, status, stop), + ) + x, lm_state, args, user_state, history, info, step, status, _ = carry + final_aux = None + if solver.has_aux: + final_aux = solver._residual_and_aux(x, args, p)[1] + x_history, aux_history, args_history = _finalize_history(history, step, final_aux) + return LMSolveResult( + x, + lm_state, + info, + step, + status, + args, + p, + user_state, + final_aux, + x_history, + aux_history, + args_history, + ) + + +_solve_loop_jit = jax.jit(_solve_loop_impl, static_argnums=(0, 6, 11)) + + +def _solve_python_impl( + solver, + x, + lm_state, + args, + p, + user_state, + history_len, + max_steps, + atol, + gtol, + xtol, + callback, +): + history = _init_history(solver, x, args, p, history_len) + info = solver._initial_info(x, lm_state, args, p) + lm_state = solver._cast_state(lm_state, info.loss.dtype) + initial_lm_state = lm_state + status = LMStatus.RUNNING + steps = 0 + if not bool(jnp.isfinite(info.loss)): + status = LMStatus.NONFINITE + elif bool(solver._converged(info, atol, gtol, xtol)): + status = LMStatus.CONVERGED + + for steps in range(1, max_steps + 1): + if status != LMStatus.RUNNING: + steps -= 1 + break + x_old, lm_state_old = x, lm_state + x, lm_state, info = solver.update(x, lm_state, args, p) + if not bool(jnp.isfinite(info.loss)): + status = LMStatus.NONFINITE + history = _record_history(history, steps, x, info, args) + break + action = None + if callback is not None: + ctx = LMSolveContext( + jnp.asarray(steps, dtype=jnp.int32), + x, + x_old, + lm_state, + lm_state_old, + initial_lm_state, + args, + p, + user_state, + info, + ) + action = callback(ctx) + action, x, lm_state, args, user_state, problem_changed = solver._apply_action( + action, x, lm_state, args, user_state + ) + history = _record_history(history, steps, x, info, args) + if action.stop is not None and bool(action.stop): + status = ( + LMStatus.CALLBACK_STOP if action.status is None else int(action.status) + ) + break + # info describes the pre-action (x, args); if the action changed + # them, the tolerances must wait for a fresh update. + if bool(solver._converged(info, atol, gtol, xtol)) and not bool( + problem_changed + ): + status = LMStatus.CONVERGED + break + else: + steps = max_steps + + if status == LMStatus.RUNNING: + status = LMStatus.MAX_STEPS + final_aux = None + if solver.has_aux: + final_aux = solver._residual_and_aux(x, args, p)[1] + x_history, aux_history, args_history = _finalize_history(history, steps, final_aux) + return LMSolveResult( + x, + lm_state, + info, + jnp.asarray(steps, dtype=jnp.int32), + jnp.asarray(status, dtype=jnp.int32), + args, + p, + user_state, + final_aux, + x_history, + aux_history, + args_history, + ) diff --git a/src/nlls_gram/utilities.py b/src/nlls_gram/utilities.py new file mode 100644 index 0000000..b255fd0 --- /dev/null +++ b/src/nlls_gram/utilities.py @@ -0,0 +1,225 @@ +"""Solver-agnostic helpers: pytree selection/masking, jit static-key hashing, +and residual-signature canonicalization. + +No solver, metric, or linear-algebra code lives here -- only plumbing both +``LevenbergMarquardt`` and ``RidgeLevenbergMarquardt`` share. +""" + +import inspect + +import jax +import jax.numpy as jnp + + +def _tree_changed(new, old): + new_leaves, new_treedef = jax.tree_util.tree_flatten(new) + old_leaves, old_treedef = jax.tree_util.tree_flatten(old) + if new_treedef != old_treedef: + return jnp.asarray(True) + changed = jnp.asarray(False) + for new_leaf, old_leaf in zip(new_leaves, old_leaves, strict=True): + # equal_nan: an unchanged NaN sentinel is not a change. + changed = changed | ~jnp.array_equal(new_leaf, old_leaf, equal_nan=True) + return changed + + +def _zero_tangent_leaf(leaf): + if leaf is None: + return None + array = jnp.asarray(leaf) + if not jnp.issubdtype(array.dtype, jnp.inexact): + return jnp.zeros(array.shape, dtype=jax.dtypes.float0) + return jnp.zeros_like(leaf) + + +def _broadcast_leading_condition(condition, leaf): + """Broadcast a scalar or leading-batch condition over an array leaf.""" + condition = jnp.asarray(condition, dtype=jnp.bool_) + leaf_ndim = jnp.ndim(leaf) + if condition.ndim < leaf_ndim: + condition = jnp.reshape( + condition, condition.shape + (1,) * (leaf_ndim - condition.ndim) + ) + return condition + + +def _where_tree(condition, on_true, on_false): + """Select matching pytrees, treating ``condition`` axes as leading axes.""" + + def select(true_leaf, false_leaf): + if true_leaf is None: + return None + return jnp.where( + _broadcast_leading_condition(condition, true_leaf), + true_leaf, + false_leaf, + ) + + return jax.tree.map(select, on_true, on_false) + + +def _mask_tangent_tree(condition, tangent): + """Keep tangent leaves where condition holds and zero them elsewhere.""" + + def mask(leaf): + if leaf is None: + return None + array = jnp.asarray(leaf) + if array.dtype == jax.dtypes.float0: + return leaf + return jnp.where( + _broadcast_leading_condition(condition, array), + array, + jnp.zeros_like(array), + ) + + return jax.tree.map(mask, tangent) + + +def _typed_key(value): + # Tag each hashable value/container with its type so the static key keeps 1, + # 1.0, and True distinct -- raw ==/hash collapse them (hash(1) == hash(True)), + # which would silently reuse a mismatched compile. This mirrors jax's own + # strict-type equality for static jit arguments. Unhashable values raise, and + # _hashable_hook degrades those specs to identity hashing. + if isinstance(value, tuple): + return (tuple, tuple(_typed_key(v) for v in value)) + if isinstance(value, frozenset): + return (frozenset, frozenset(_typed_key(v) for v in value)) + return (type(value), value) + + +class _IdentityKey: + """Static-key stand-in comparing by object identity (for unhashable values).""" + + __slots__ = ("obj",) + + def __init__(self, obj): + self.obj = obj + + def __eq__(self, other): + return isinstance(other, _IdentityKey) and self.obj is other.obj + + def __hash__(self): + return id(self.obj) + + +def _static_key_component(value): + # Hashable settings (scalars, strings, functions, frozen configs) key by + # value; anything unhashable keys by identity so hashing never raises and + # equality stays consistent with the hash. + try: + hash(value) + except TypeError: + return _IdentityKey(value) + return value + + +class _IdentityCallable: + """Hashable-by-identity pass-through for unhashable callables used as jit + statics (e.g. an eq=True dataclass instance implementing ``__call__``). + ``__weakref__`` is required: jax.eval_shape weak-references the callable. + """ + + __slots__ = ("fn", "__weakref__") + + def __init__(self, fn): + self.fn = fn + + def __call__(self, *args): + return self.fn(*args) + + def __eq__(self, other): + return isinstance(other, _IdentityCallable) and self.fn is other.fn + + def __hash__(self): + return id(self.fn) + + +def _hashable_hook(fn): + if fn is None: + return None + try: + hash(fn) + except TypeError: + return _IdentityCallable(fn) + return fn + + +def canonicalize_residual(residual_fn): + """Wrap a residual taking ``(x)``, ``(x, args)``, or ``(x, args, p)`` -- + always in that order -- into the canonical 3-arg form, so the compiled + code is identical for all three. Uninspectable signatures (or ``*args``) + are assumed 3-arg. Returns ``(canonical_fn, arity)``. + """ + try: + signature = inspect.signature(residual_fn) + except (TypeError, ValueError): + residual_arity = 3 + else: + residual_arity = 0 + for parameter in signature.parameters.values(): + if parameter.kind in ( + inspect.Parameter.POSITIONAL_ONLY, + inspect.Parameter.POSITIONAL_OR_KEYWORD, + ): + residual_arity += 1 + elif parameter.kind == inspect.Parameter.VAR_POSITIONAL: + residual_arity = 3 + break + if residual_arity < 1 or residual_arity > 3: + raise ValueError( + "residual_fn must take 1 to 3 positional arguments: " + "(x), (x, args), or (x, args, p)" + ) + if residual_arity == 1: + + def canonical_residual(x, args, p): + return residual_fn(x) + + elif residual_arity == 2: + + def canonical_residual(x, args, p): + return residual_fn(x, args) + + else: + canonical_residual = residual_fn + return canonical_residual, residual_arity + + +def canonicalize_ad_preconditioner(ad_solver_preconditioner): + """Normalize an ``ad_solver_preconditioner`` to the 1-arg form the AD + solve calls. A callable already usable as ``(v)``, including helpers + whose damping argument has a default, passes through unchanged. A + callable REQUIRING a second argument (a ``(v, damping)`` helper such + as Sherman-Morrison or Woodbury) is wrapped to be called with an + explicit zero damping, the correct value for the undamped AD system. + Helpers marked ``requires_positive_damping`` are rejected: their + zero-damping apply divides by zero. + """ + if getattr(ad_solver_preconditioner, "requires_positive_damping", False): + raise ValueError( + "this preconditioner divides by the live damping and cannot " + "serve as ad_solver_preconditioner (the AD system is undamped)" + ) + try: + signature = inspect.signature(ad_solver_preconditioner) + except (TypeError, ValueError): + return ad_solver_preconditioner + try: + signature.bind(object()) + except TypeError: + pass + else: + return ad_solver_preconditioner + try: + signature.bind(object(), object()) + except TypeError: + raise ValueError( + "ad_solver_preconditioner must be callable as (v) or (v, damping)" + ) from None + + def canonical_ad_preconditioner(v): + return ad_solver_preconditioner(v, jnp.asarray(0.0, dtype=v.dtype)) + + return canonical_ad_preconditioner diff --git a/src/nlls_gram/utility.py b/src/nlls_gram/utility.py deleted file mode 100644 index da6152a..0000000 --- a/src/nlls_gram/utility.py +++ /dev/null @@ -1,1099 +0,0 @@ -"""Shared solver machinery: status/hyperparameter/action/result types, the -jitted solve loop, multi-start drivers, and hashing/tree/history helpers. - -Everything here is solver-agnostic: the loop and multi-start drivers consume -an informal solver protocol (``update``, ``_apply_action``, ``_converged``, -``_residual_and_aux``, ``_initial_info``, ``_cast_state``, ``_cold_state``, -``_ranking_objective``, ``has_aux``) implemented by both -:class:`~nlls_gram.LevenbergMarquardt` and -:class:`~nlls_gram.RidgeLevenbergMarquardt`. Public names are re-exported from -``nlls_gram`` (and ``nlls_gram.gram_lm`` for compatibility). -""" - -import dataclasses -import enum -import inspect -from dataclasses import dataclass -from typing import Any - -import jax -import jax.numpy as jnp - - -class LMStatus(enum.IntEnum): - """Integer status codes returned by ``solve``. - - Members are real ints (``IntEnum``): they work as dict keys, compare - against status arrays, and ``LMStatus(int(result.status)).name`` recovers - the label for logging. Callbacks may return bare members (or any weak - integer value) as ``LMSolveAction.status`` -- the solver canonicalizes to - int32 at the boundary, so no ``jnp.asarray(..., dtype=jnp.int32)`` casts - are needed, under float32 or x64. - """ - - RUNNING = 0 - CONVERGED = 1 - MAX_STEPS = 2 - NONFINITE = 3 - CALLBACK_STOP = 4 - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMHyperparams: - """Per-step LM hyperparameters, carried in the solver state's ``hyper``. - - All fields are traced values, so a ``solve`` callback can reset them — - e.g. grow the inner CG budget as the loss falls — via - ``dataclasses.replace(ctx.lm_state, hyper=dataclasses.replace( - ctx.lm_state.hyper, iterative_maxiter=...))``. A field constructed as - ``None`` (uncapped ``max_damping``, backend-default ``iterative_maxiter``) - is compiled out and stays ``None``. Static configuration (``linear_solver``, - ``geodesic_acceleration``, ``cache_jacobian``, ``has_aux``, the metric or - penalty) shapes the compiled program and lives on the solver, not here. - """ - - damping_decrease: jax.Array - damping_increase: jax.Array - min_damping: jax.Array - max_damping: jax.Array | None - geodesic_acceptance_ratio: jax.Array - iterative_tol: jax.Array - iterative_atol: jax.Array - iterative_maxiter: jax.Array | None - - -def _damping_floor(min_damping, dtype): - if dtype is None: - seed = 0.0 if min_damping is None else min_damping - dtype = jnp.asarray(seed).dtype - dtype_floor = jnp.asarray(jnp.finfo(dtype).tiny, dtype=dtype) - if min_damping is None: - return dtype_floor - return jnp.maximum(jnp.asarray(min_damping, dtype=dtype), dtype_floor) - - -def _cast_hyper(hyper, dtype): - if hyper is None: - return None - return LMHyperparams( - jnp.asarray(hyper.damping_decrease, dtype=dtype), - jnp.asarray(hyper.damping_increase, dtype=dtype), - _damping_floor(hyper.min_damping, dtype), - None - if hyper.max_damping is None - else jnp.asarray(hyper.max_damping, dtype=dtype), - jnp.asarray(hyper.geodesic_acceptance_ratio, dtype=dtype), - jnp.asarray(hyper.iterative_tol, dtype=dtype), - jnp.asarray(hyper.iterative_atol, dtype=dtype), - None - if hyper.iterative_maxiter is None - else jnp.asarray(hyper.iterative_maxiter, dtype=jnp.int32), - ) - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMSolveAction: - """Optional callback action for ``solve``. - - A field left as ``None`` is unchanged. ``status`` is used only when ``stop`` - is true. ``stop`` and ``status`` are canonicalized by the solver (to bool - and int32), so callbacks may return Python bools, bare ``LMStatus`` - members, or weak-typed arrays without explicit dtype casts. - """ - - stop: Any = None - status: Any = None - x: Any = None - lm_state: Any = None - args: Any = None - user_state: Any = None - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMSolveContext: - """Information passed to a ``solve`` callback after each LM update. - - ``lm_state`` and ``info`` hold the running solver's own state and info - types (:class:`LMState`/:class:`LMInfo` for ``LevenbergMarquardt``, - :class:`RidgeLMState`/:class:`RidgeLMInfo` for - ``RidgeLevenbergMarquardt``). - """ - - step: jax.Array - x: Any - x_old: Any - lm_state: Any - lm_state_old: Any - initial_lm_state: Any - args: Any - p: Any - user_state: Any - info: Any - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class LMSolveResult: - """Final result returned by ``solve``. - - ``lm_state`` and ``info`` hold the solver's own state and info types - (:class:`LMState`/:class:`LMInfo` for ``LevenbergMarquardt``, - :class:`RidgeLMState`/:class:`RidgeLMInfo` for - ``RidgeLevenbergMarquardt``). - """ - - x: Any - lm_state: Any - info: Any - steps: jax.Array - status: jax.Array - args: Any - p: Any - user_state: Any - # With has_aux=True: aux evaluated at the returned (x, args, p) — one extra - # residual evaluation, well-defined for every status. Differentiable with - # respect to p through the implicit rule (directly and through x*(p)). - aux: Any = None - # With save_steps=True: the iterate history as a pytree shaped like x with a - # (max_steps + 1) leading axis — row 0 is x0, row s the kept iterate after - # step s (post-callback-action), rows beyond ``steps`` are zero padding. - # aux_history (has_aux only, else None) and args_history (None when args is - # None) align row-for-row with x_history — args row s is the kept - # post-action args after step s, the args consumed by step s + 1's update. - # Differentiation-inert (zero tangents through the implicit rule). - x_history: Any = None - aux_history: Any = None - args_history: Any = None - # MultiStartInfo when solve ran with multi_start=...; None otherwise (an - # empty pytree node, so the leaf count is unchanged when the feature is - # off). Differentiation-inert (zero tangents through the implicit rule). - multi_start: Any = None - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class MultiStartInfo: - """Diagnostics attached to ``LMSolveResult.multi_start`` by a multi-start solve. - - ``attempt`` is the winning attempt/lane index (0 = the caller's - ``(x0, args)``), ``accepted`` whether the winner passed the success test - (``MultiStart.accept``, or the solve's ``max_steps_is_success`` policy), and - ``attempts_run`` how many starts were solved (sequential mode stops at the - first success; parallel mode always runs ``num_starts``). ``loss`` is the - ranking objective used for selection -- the sum of squared residuals at the - returned solution for ``LevenbergMarquardt``, the ridge objective for - ``RidgeLevenbergMarquardt`` -- masked to ``+inf`` when nonfinite. Note - ``accepted`` describes the multi-start success test, not ``LMInfo.accepted`` - (last-step acceptance). - """ - - attempt: jax.Array - accepted: jax.Array - attempts_run: jax.Array - loss: jax.Array - - -@dataclass(frozen=True, eq=False) -class MultiStart: - """Multi-start configuration for ``solve(multi_start=...)``. - - ``draw(key, x, args) -> (x_new, args_new)`` generates a fresh initial - condition; it must be traceable and type-stable (returning the same pytree - structure, shapes, and dtypes as its ``(x, args)`` inputs). ``accept(key, - result) -> bool`` optionally overrides the success test (default: - ``CONVERGED`` plus ``MAX_STEPS`` when the solve's - ``max_steps_is_success=True``); it receives its own key so it can draw fresh - validation data, and may return any scalar boolean-like value. - Sequential mode (``parallel=False``) solves from ``(x0, args)`` and retries - on failure, chaining each attempt's *initial* values into the next - ``draw``; parallel mode solves all ``num_starts`` lanes under ``vmap`` - (lane 0 = the caller's ``(x0, args)``, the rest drawn from the originals) - and selects the accepted lane with the lowest loss. The key schedule is - ``draw_key, accept_key = jax.random.split(jax.random.fold_in(key, k))`` - for attempt ``k``. - - ``draw`` and ``accept`` enter the jit cache by identity (like - ``callback``): define them once at setup scope, not inline per call. - ``MultiStart`` is not a pytree -- ``solve`` unpacks it before tracing, with - ``key`` the only traced field. - """ - - key: Any - num_starts: int - draw: Any = None - accept: Any = None - parallel: bool = False - - def __post_init__(self): - if isinstance(self.num_starts, bool) or not isinstance(self.num_starts, int): - raise ValueError("num_starts must be a Python int >= 1") - if self.num_starts < 1: - raise ValueError("num_starts must be a Python int >= 1") - if self.num_starts > 1 and self.draw is None: - raise ValueError( - "num_starts > 1 requires draw; pass " - "draw=(key, x, args) -> (x_new, args_new)" - ) - if self.draw is not None and not callable(self.draw): - raise TypeError("draw must be callable") - if self.accept is not None and not callable(self.accept): - raise TypeError("accept must be callable") - - -def _typed_key(value): - # Tag each hashable value/container with its type so the static key keeps 1, 1.0, - # and True distinct -- raw == / hash collapse them (hash(1) == hash(True)), which - # would silently reuse a mismatched compile. This mirrors jax's own strict-type - # equality for static jit arguments; unhashable values still raise here (caught by - # _hashable_hook, which degrades the spec to identity-hashing). - if isinstance(value, tuple): - return (tuple, tuple(_typed_key(v) for v in value)) - if isinstance(value, frozenset): - return (frozenset, frozenset(_typed_key(v) for v in value)) - return (type(value), value) - - -class DrawNNXModule: - """Multi-start ``draw`` hook re-initializing a flax ``nnx.Module`` from a fresh key. - - Given a ``MultiStart`` retry key, builds - ``module_cls(*args, rngs=nnx.Rngs(key), **kwargs)`` and returns its ``nnx.Param`` - state as the new solver start, passing ``args`` through unchanged. Use it instead - of hand-rolling a re-init closure per driver:: - - draw = DrawNNXModule(SequentialMLP, settings, dtype=dtype) - ms = MultiStart(key=key, num_starts=5, draw=draw) - - The drawn parameter state must be type-stable against the solver's ``x0`` (same - pytree structure, shapes, and dtypes) -- construct the module with a matching - ``param_dtype``/``dtype`` (e.g. pass ``dtype=`` through). The paired - ``nnx.GraphDef`` used by the residual's ``nnx.merge`` must come from the same - ``module_cls(*args, **kwargs)`` spec. - - Value-hashable on ``(module_cls, args, kwargs)`` with jit's strict-type semantics - (``1``, ``1.0``, and ``True`` key distinct compilations): equal specs compare equal - and share one jit compilation instead of recompiling per instance (a fresh closure - would not). ``args``/``kwargs`` must be hashable for that sharing, and their values - must not be mutated after construction (a stale key would reuse the wrong compile); - unhashable specs still work but recompile per instance. Requires ``flax`` installed - (imported lazily on first draw). - """ - - def __init__(self, module_cls, *args, **kwargs): - self.module_cls = module_cls - self.args = args - self.kwargs = tuple(sorted(kwargs.items())) - - def __call__(self, key, x_old, args_old): - from flax import nnx - - module = self.module_cls(*self.args, rngs=nnx.Rngs(key), **dict(self.kwargs)) - _, theta = nnx.split(module, nnx.Param) - return theta, args_old - - def __hash__(self): - return hash((self.module_cls, _typed_key(self.args), _typed_key(self.kwargs))) - - def __eq__(self, other): - return ( - isinstance(other, DrawNNXModule) - and self.module_cls is other.module_cls - and _typed_key(self.args) == _typed_key(other.args) - and _typed_key(self.kwargs) == _typed_key(other.kwargs) - ) - - -def _tree_changed(new, old): - new_leaves, new_treedef = jax.tree_util.tree_flatten(new) - old_leaves, old_treedef = jax.tree_util.tree_flatten(old) - if new_treedef != old_treedef: - return jnp.asarray(True) - changed = jnp.asarray(False) - for new_leaf, old_leaf in zip(new_leaves, old_leaves, strict=True): - # equal_nan: an unchanged NaN sentinel is not a change. - changed = changed | ~jnp.array_equal(new_leaf, old_leaf, equal_nan=True) - return changed - - -def _zero_tangent_leaf(leaf): - if leaf is None: - return None - array = jnp.asarray(leaf) - if not jnp.issubdtype(array.dtype, jnp.inexact): - return jnp.zeros(array.shape, dtype=jax.dtypes.float0) - return jnp.zeros_like(leaf) - - -def _broadcast_leading_condition(condition, leaf): - """Broadcast a scalar or leading-batch condition over an array leaf.""" - condition = jnp.asarray(condition, dtype=jnp.bool_) - leaf_ndim = jnp.ndim(leaf) - if condition.ndim < leaf_ndim: - condition = jnp.reshape( - condition, condition.shape + (1,) * (leaf_ndim - condition.ndim) - ) - return condition - - -def _where_tree(condition, on_true, on_false): - """Select matching pytrees, treating ``condition`` axes as leading axes.""" - - def select(true_leaf, false_leaf): - if true_leaf is None: - return None - return jnp.where( - _broadcast_leading_condition(condition, true_leaf), - true_leaf, - false_leaf, - ) - - return jax.tree.map(select, on_true, on_false) - - -def _mask_tangent_tree(condition, tangent): - """Keep tangent leaves where condition holds and zero them elsewhere.""" - - def mask(leaf): - if leaf is None: - return None - array = jnp.asarray(leaf) - if array.dtype == jax.dtypes.float0: - return leaf - return jnp.where( - _broadcast_leading_condition(condition, array), - array, - jnp.zeros_like(array), - ) - - return jax.tree.map(mask, tangent) - - -class _IdentityKey: - """Static-key stand-in comparing by object identity (for unhashable values).""" - - __slots__ = ("obj",) - - def __init__(self, obj): - self.obj = obj - - def __eq__(self, other): - return isinstance(other, _IdentityKey) and self.obj is other.obj - - def __hash__(self): - return id(self.obj) - - -def _static_key_component(value): - # Hashable settings (scalars, strings, functions, frozen metrics) key by - # value; anything unhashable keys by identity so hashing never raises and - # equality stays consistent with the hash. - try: - hash(value) - except TypeError: - return _IdentityKey(value) - return value - - -class _IdentityCallable: - """Hashable-by-identity pass-through for unhashable callables used as jit - statics (e.g. an eq=True dataclass instance implementing ``__call__``). - ``__weakref__`` is required: jax.eval_shape weak-references the callable. - """ - - __slots__ = ("fn", "__weakref__") - - def __init__(self, fn): - self.fn = fn - - def __call__(self, *args): - return self.fn(*args) - - def __eq__(self, other): - return isinstance(other, _IdentityCallable) and self.fn is other.fn - - def __hash__(self): - return id(self.fn) - - -def _hashable_hook(fn): - if fn is None: - return None - try: - hash(fn) - except TypeError: - return _IdentityCallable(fn) - return fn - - -def canonicalize_residual(residual_fn): - """Wrap a residual taking ``(x)``, ``(x, args)``, or ``(x, args, p)`` -- - always in that order -- into the canonical 3-arg form, so the compiled - code is identical for all three. Uninspectable signatures (or ``*args``) - are assumed 3-arg. Returns ``(canonical_fn, arity)``. - """ - try: - signature = inspect.signature(residual_fn) - except (TypeError, ValueError): - residual_arity = 3 - else: - residual_arity = 0 - for parameter in signature.parameters.values(): - if parameter.kind in ( - inspect.Parameter.POSITIONAL_ONLY, - inspect.Parameter.POSITIONAL_OR_KEYWORD, - ): - residual_arity += 1 - elif parameter.kind == inspect.Parameter.VAR_POSITIONAL: - residual_arity = 3 - break - if residual_arity < 1 or residual_arity > 3: - raise ValueError( - "residual_fn must take 1 to 3 positional arguments: " - "(x), (x, args), or (x, args, p)" - ) - if residual_arity == 1: - - def canonical_residual(x, args, p): - return residual_fn(x) - - elif residual_arity == 2: - - def canonical_residual(x, args, p): - return residual_fn(x, args) - - else: - canonical_residual = residual_fn - return canonical_residual, residual_arity - - -def canonicalize_ad_preconditioner(ad_solver_preconditioner): - """Normalize an ``ad_solver_preconditioner`` to the 1-arg form the AD - solve calls. A callable already usable as ``(v)``, including helpers - whose damping argument has a default, passes through unchanged. A - callable REQUIRING a second argument (a ``(v, damping)`` helper such - as Sherman-Morrison or Woodbury) is wrapped to be called with an - explicit zero damping, the correct value for the undamped AD system. - Helpers marked ``requires_positive_damping`` - (``pad_dual_preconditioner``) are rejected at construction: their - zero-damping apply divides by zero. Uninspectable signatures pass - through unchanged (the 1-arg contract). - """ - if getattr(ad_solver_preconditioner, "requires_positive_damping", False): - raise ValueError( - "this preconditioner divides by the live damping and cannot " - "serve as ad_solver_preconditioner (the AD system is undamped)" - ) - try: - signature = inspect.signature(ad_solver_preconditioner) - except (TypeError, ValueError): - return ad_solver_preconditioner - try: - signature.bind(object()) - except TypeError: - pass - else: - return ad_solver_preconditioner - try: - signature.bind(object(), object()) - except TypeError: - raise ValueError( - "ad_solver_preconditioner must be callable as (v) or (v, damping)" - ) from None - - def canonical_ad_preconditioner(v): - return ad_solver_preconditioner(v, jnp.asarray(0.0, dtype=v.dtype)) - - return canonical_ad_preconditioner - - -# save_steps bookkeeping shared by the jitted and Python solve loops: row `step` of -# x_history and args_history takes the kept post-action iterate and args; info.aux was -# evaluated at the pre-step x, so it lands one row earlier, and _finalize_history fills -# the last aux row from the final-solution evaluation. history_len is concrete (static -# under jit), so the buffers live entirely inside the loop implementations — no -# host-side allocation and no copy of a jit-input buffer before the in-place row -# updates. eval_shape gets the aux buffer shapes without paying for a residual -# evaluation. -def _history_buffer(tree, history_len): - # Row 0 holds the initial value; tree.map over a None tree returns None. - return jax.tree.map( - lambda leaf: ( - jnp.zeros((history_len, *jnp.shape(leaf)), jnp.result_type(leaf)) - .at[0] - .set(leaf) - ), - tree, - ) - - -def _init_history(solver, x0, args, p, history_len): - if history_len is None: - return None - x_history = _history_buffer(x0, history_len) - args_history = _history_buffer(args, history_len) - aux_history = None - if solver.has_aux: - aux0 = jax.eval_shape( - lambda x_, args_, p_: solver._residual_and_aux(x_, args_, p_)[1], - x0, - args, - p, - ) - aux_history = jax.tree.map( - lambda leaf: jnp.zeros((history_len, *leaf.shape), leaf.dtype), aux0 - ) - return (x_history, aux_history, args_history) - - -def _record_history(history, step, x, info, args): - if history is None: - return None - x_history, aux_history, args_history = history - x_history = jax.tree.map(lambda buf, leaf: buf.at[step].set(leaf), x_history, x) - args_history = jax.tree.map( - lambda buf, leaf: buf.at[step].set(leaf), args_history, args - ) - if aux_history is not None: - aux_history = jax.tree.map( - lambda buf, leaf: buf.at[step - 1].set(leaf), aux_history, info.aux - ) - return (x_history, aux_history, args_history) - - -def _finalize_history(history, steps, final_aux): - if history is None: - return None, None, None - x_history, aux_history, args_history = history - if aux_history is not None: - aux_history = jax.tree.map( - lambda buf, leaf: buf.at[steps].set(leaf), aux_history, final_aux - ) - return x_history, aux_history, args_history - - -def _solve_loop_impl( - solver, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, -): - history = _init_history(solver, x, args, p, history_len) - max_steps = jnp.asarray(max_steps, dtype=jnp.int32) - info = solver._initial_info(x, lm_state, args, p) - # Recast the state's scalars (damping, hyperparameters, and any - # solver-specific carried scalars) and the tolerances to the residual - # dtype so the while_loop carry matches what update() returns. - atol = jnp.asarray(atol, dtype=info.loss.dtype) - gtol = jnp.asarray(gtol, dtype=info.loss.dtype) - xtol = jnp.asarray(xtol, dtype=info.loss.dtype) - lm_state = solver._cast_state(lm_state, info.loss.dtype) - initial_lm_state = lm_state - step = jnp.asarray(0, dtype=jnp.int32) - initial_nonfinite = ~jnp.isfinite(info.loss) - initial_converged = solver._converged(info, atol, gtol, xtol) - stop = initial_nonfinite | initial_converged - status = jnp.where( - initial_nonfinite, - jnp.asarray(LMStatus.NONFINITE, dtype=jnp.int32), - jnp.where( - initial_converged, - jnp.asarray(LMStatus.CONVERGED, dtype=jnp.int32), - jnp.asarray(LMStatus.RUNNING, dtype=jnp.int32), - ), - ) - - def cond(carry): - _, _, _, _, _, _, step, _, stop = carry - return (~stop) & (step < max_steps) - - def body(carry): - x, lm_state, args, user_state, history, _, step, _, _ = carry - x_old, lm_state_old = x, lm_state - x, lm_state, info = solver.update(x, lm_state, args, p) - step = step + jnp.asarray(1, dtype=jnp.int32) - current_nonfinite = ~jnp.isfinite(info.loss) - - action = None - if callback is not None: - ctx = LMSolveContext( - step, - x, - x_old, - lm_state, - lm_state_old, - initial_lm_state, - args, - p, - user_state, - info, - ) - action = callback(ctx) - action, x, lm_state, args, user_state, problem_changed = solver._apply_action( - action, x, lm_state, args, user_state - ) - history = _record_history(history, step, x, info, args) - - callback_stop = ( - jnp.asarray(False, dtype=jnp.bool_) - if action.stop is None - else jnp.asarray(action.stop, dtype=jnp.bool_) - ) - callback_status = ( - jnp.asarray(LMStatus.CALLBACK_STOP, dtype=jnp.int32) - if action.status is None - else jnp.asarray(action.status, dtype=jnp.int32) - ) - # info describes the pre-action (x, args); if the action changed them, - # the tolerances must wait for a fresh update. - converged = solver._converged(info, atol, gtol, xtol) & ~problem_changed - reached_max = step >= max_steps - stop = current_nonfinite | callback_stop | converged | reached_max - status = jnp.where( - current_nonfinite, - jnp.asarray(LMStatus.NONFINITE, dtype=jnp.int32), - jnp.where( - callback_stop, - callback_status, - jnp.where( - converged, - jnp.asarray(LMStatus.CONVERGED, dtype=jnp.int32), - jnp.where( - reached_max, - jnp.asarray(LMStatus.MAX_STEPS, dtype=jnp.int32), - jnp.asarray(LMStatus.RUNNING, dtype=jnp.int32), - ), - ), - ), - ) - return x, lm_state, args, user_state, history, info, step, status, stop - - carry = jax.lax.while_loop( - cond, - body, - (x, lm_state, args, user_state, history, info, step, status, stop), - ) - x, lm_state, args, user_state, history, info, step, status, _ = carry - final_aux = None - if solver.has_aux: - final_aux = solver._residual_and_aux(x, args, p)[1] - x_history, aux_history, args_history = _finalize_history(history, step, final_aux) - return LMSolveResult( - x, - lm_state, - info, - step, - status, - args, - p, - user_state, - final_aux, - x_history, - aux_history, - args_history, - ) - - -_solve_loop_jit = jax.jit(_solve_loop_impl, static_argnums=(0, 6, 11)) - - -def _solve_python_impl( - solver, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, -): - history = _init_history(solver, x, args, p, history_len) - info = solver._initial_info(x, lm_state, args, p) - lm_state = solver._cast_state(lm_state, info.loss.dtype) - initial_lm_state = lm_state - status = LMStatus.RUNNING - steps = 0 - if not bool(jnp.isfinite(info.loss)): - status = LMStatus.NONFINITE - elif bool(solver._converged(info, atol, gtol, xtol)): - status = LMStatus.CONVERGED - - for steps in range(1, max_steps + 1): - if status != LMStatus.RUNNING: - steps -= 1 - break - x_old, lm_state_old = x, lm_state - x, lm_state, info = solver.update(x, lm_state, args, p) - if not bool(jnp.isfinite(info.loss)): - status = LMStatus.NONFINITE - history = _record_history(history, steps, x, info, args) - break - action = None - if callback is not None: - ctx = LMSolveContext( - jnp.asarray(steps, dtype=jnp.int32), - x, - x_old, - lm_state, - lm_state_old, - initial_lm_state, - args, - p, - user_state, - info, - ) - action = callback(ctx) - action, x, lm_state, args, user_state, problem_changed = solver._apply_action( - action, x, lm_state, args, user_state - ) - history = _record_history(history, steps, x, info, args) - if action.stop is not None and bool(action.stop): - status = ( - LMStatus.CALLBACK_STOP if action.status is None else int(action.status) - ) - break - # info describes the pre-action (x, args); if the action changed - # them, the tolerances must wait for a fresh update. - if bool(solver._converged(info, atol, gtol, xtol)) and not bool( - problem_changed - ): - status = LMStatus.CONVERGED - break - else: - steps = max_steps - - if status == LMStatus.RUNNING: - status = LMStatus.MAX_STEPS - final_aux = None - if solver.has_aux: - final_aux = solver._residual_and_aux(x, args, p)[1] - x_history, aux_history, args_history = _finalize_history(history, steps, final_aux) - return LMSolveResult( - x, - lm_state, - info, - jnp.asarray(steps, dtype=jnp.int32), - jnp.asarray(status, dtype=jnp.int32), - args, - p, - user_state, - final_aux, - x_history, - aux_history, - args_history, - ) - - -def _accept_converged(_, result): - return result.status == LMStatus.CONVERGED - - -def _accept_converged_or_max_steps(_, result): - return (result.status == LMStatus.CONVERGED) | (result.status == LMStatus.MAX_STEPS) - - -def _attempt_success(accept_fn, accept_key, result, loss): - value = jnp.asarray(accept_fn(accept_key, result)) - if value.shape != (): - raise ValueError( - f"multi_start.accept must return a scalar; got shape {value.shape}" - ) - # An accepted-but-nonfinite result never wins: its masked loss is +inf. - return value.astype(jnp.bool_) & jnp.isfinite(loss) - - -def _type_spec(tree): - # weak_type is part of the spec: a weak/strong mismatch would break the - # while_loop carry avals just like a dtype mismatch. - leaves, treedef = jax.tree_util.tree_flatten(tree) - specs = [] - for leaf in leaves: - if not (hasattr(leaf, "shape") and hasattr(leaf, "dtype")): - leaf = jnp.asarray(leaf) - specs.append((tuple(leaf.shape), leaf.dtype, getattr(leaf, "weak_type", False))) - return treedef, specs - - -def _check_drawn_types(x, args, drawn): - # Works on concrete draws and on jax.eval_shape outputs alike; a mismatch - # would otherwise surface as an inscrutable while_loop/vmap error. - if _type_spec(drawn) != _type_spec((x, args)): - raise ValueError( - "multi_start.draw must return (x, args) matching the structure, " - f"shapes, and dtypes of its inputs; expected {_type_spec((x, args))}, " - f"got {_type_spec(drawn)}" - ) - - -def _multi_start_python_impl( - solver, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - num_starts, - draw, - accept, - parallel, -): - accept_fn = accept - cold = solver._cold_state(lm_state) - - def run_attempt(x_a, lm_state_a, args_a, attempt): - result = _solve_python_impl( - solver, - x_a, - lm_state_a, - args_a, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - ) - accept_key = jax.random.split(jax.random.fold_in(key, attempt))[1] - loss = solver._ranking_objective(result, p, callback) - success = _attempt_success(accept_fn, accept_key, result, loss) - return result, loss, bool(success) - - best = best_loss = best_attempt = None - accepted = False - if parallel: - for lane in range(num_starts): - if lane == 0: - x_l, args_l = x, args - else: - draw_key = jax.random.split(jax.random.fold_in(key, lane))[0] - x_l, args_l = draw(draw_key, x, args) - _check_drawn_types(x, args, (x_l, args_l)) - result, loss, success = run_attempt(x_l, cold, args_l, lane) - better = ( - best is None - or (success and not accepted) - or (success == accepted and bool(loss < best_loss)) - ) - if better: - best, best_loss = result, loss - best_attempt, accepted = lane, success - attempts_run = num_starts - else: - x_a, args_a, lm_state_a = x, args, lm_state - for attempt in range(num_starts): - if attempt > 0: - draw_key = jax.random.split(jax.random.fold_in(key, attempt))[0] - x_a, args_a = draw(draw_key, x_a, args_a) - _check_drawn_types(x, args, (x_a, args_a)) - lm_state_a = cold - result, loss, success = run_attempt(x_a, lm_state_a, args_a, attempt) - take = ( - best is None - or success - or bool(loss < best_loss) - or not bool(jnp.isfinite(best_loss)) - ) - if take: - best, best_loss = result, loss - best_attempt, accepted = attempt, success - if success: - break - attempts_run = attempt + 1 - info = MultiStartInfo( - jnp.asarray(best_attempt, dtype=jnp.int32), - jnp.asarray(accepted, dtype=jnp.bool_), - jnp.asarray(attempts_run, dtype=jnp.int32), - best_loss, - ) - return dataclasses.replace(best, multi_start=info) - - -def _multi_start_sequential_impl( - solver, - x, - lm_state, - args, - p, - user_state, - key, - num_starts, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, -): - accept_fn = accept - - def run_attempt(x_a, lm_state_a, args_a, attempt): - result = _solve_loop_impl( - solver, - x_a, - lm_state_a, - args_a, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - ) - accept_key = jax.random.split(jax.random.fold_in(key, attempt))[1] - loss = solver._ranking_objective(result, p, callback) - success = _attempt_success(accept_fn, accept_key, result, loss) - # p is loop-invariant: splice it out of the carried result and - # reattach after selection. - return dataclasses.replace(result, p=None), loss, success - - zero = jnp.asarray(0, dtype=jnp.int32) - best, best_loss, done = run_attempt(x, lm_state, args, zero) - if draw is None: - info = MultiStartInfo(zero, done, jnp.asarray(1, dtype=jnp.int32), best_loss) - return dataclasses.replace(best, p=p, multi_start=info) - - cold = solver._cold_state(lm_state) - - def cond(carry): - attempt, _, _, _, _, _, done = carry - return ~done & (attempt < num_starts) - - def body(carry): - attempt, x_prev, args_prev, best, best_loss, best_attempt, _ = carry - draw_key = jax.random.split(jax.random.fold_in(key, attempt))[0] - x_next, args_next = draw(draw_key, x_prev, args_prev) - result, loss, success = run_attempt(x_next, cold, args_next, attempt) - # First success wins (the loop exits); among failures keep the lowest - # masked loss, and an all-inf history always yields to the newest - # attempt so the none-finite case returns the last one. - take = success | (loss < best_loss) | ~jnp.isfinite(best_loss) - best = jax.tree.map(lambda new, old: jnp.where(take, new, old), result, best) - return ( - attempt + jnp.asarray(1, dtype=jnp.int32), - x_next, - args_next, - best, - jnp.where(take, loss, best_loss), - jnp.where(take, attempt, best_attempt), - success, - ) - - carry = jax.lax.while_loop( - cond, - body, - (jnp.asarray(1, dtype=jnp.int32), x, args, best, best_loss, zero, done), - ) - attempts_run, _, _, best, best_loss, best_attempt, accepted = carry - info = MultiStartInfo(best_attempt, accepted, attempts_run, best_loss) - return dataclasses.replace(best, p=p, multi_start=info) - - -def _multi_start_parallel_impl( - solver, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, - num_starts, -): - accept_fn = accept - lanes = jnp.arange(num_starts, dtype=jnp.int32) - attempt_keys = jax.vmap(lambda i: jax.random.fold_in(key, i))(lanes) - lane_keys = jax.vmap(jax.random.split)(attempt_keys) - accept_keys = lane_keys[:, 1] - draw_keys = lane_keys[1:, 0] - xs_drawn, args_drawn = jax.vmap(lambda k: draw(k, x, args))(draw_keys) - - def prepend(first, rest): - return jnp.concatenate([jnp.asarray(first)[None], rest], axis=0) - - xs = jax.tree.map(prepend, x, xs_drawn) - args_lanes = None if args is None else jax.tree.map(prepend, args, args_drawn) - # Under vmap the cache-reuse cond lowers to a select that evaluates both - # branches, so a warm Jacobian cache cannot save work: drop it uniformly. - cold = solver._cold_state(lm_state) - - def solve_lane(x_lane, args_lane, accept_key): - result = _solve_loop_impl( - solver, - x_lane, - cold, - args_lane, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - ) - loss = solver._ranking_objective(result, p, callback) - success = _attempt_success(accept_fn, accept_key, result, loss) - return dataclasses.replace(result, p=None), loss, success - - results, losses, successes = jax.vmap( - solve_lane, in_axes=(0, None if args is None else 0, 0) - )(xs, args_lanes, accept_keys) - - # Lowest masked loss among successful lanes; with none, lowest loss - # overall (all-inf falls back to lane 0). argmin ties break low-index. - success_losses = jnp.where( - successes, losses, jnp.asarray(jnp.inf, dtype=losses.dtype) - ) - winner = jnp.where( - jnp.any(successes), jnp.argmin(success_losses), jnp.argmin(losses) - ).astype(jnp.int32) - best = jax.tree.map(lambda leaf: leaf[winner], results) - info = MultiStartInfo( - winner, - successes[winner], - jnp.asarray(num_starts, dtype=jnp.int32), - losses[winner], - ) - return dataclasses.replace(best, p=p, multi_start=info) - - -_multi_start_sequential_jit = jax.jit( - _multi_start_sequential_impl, static_argnums=(0, 8, 13, 14, 15) -) -_multi_start_parallel_jit = jax.jit( - _multi_start_parallel_impl, static_argnums=(0, 7, 12, 13, 14, 15) -) diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index c23f8fa..d2b0ab0 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -1768,7 +1768,7 @@ def test_float64_block_eigen_preconditioner_default_precision(): MetricContext, RepeatedFactorMetric, RidgeLevenbergMarquardt, - RidgeLMState, + LMState, block_eigen_state, ) @@ -1790,7 +1790,7 @@ def spd_blocks(key, groups, size): assert leaf.dtype == jnp.float64, leaf.dtype ridge = 3e-9 ctx = MetricContext( - lm_state=RidgeLMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), + lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), args={"preconditioner": state}, ) preconditioner = BlockEigenPreconditioner() diff --git a/tests/test_ridge_lm.py b/tests/test_ridge_lm.py index 4b561f1..4fdeddc 100644 --- a/tests/test_ridge_lm.py +++ b/tests/test_ridge_lm.py @@ -13,11 +13,11 @@ CholeskyCache, IdentityMetric, IdentityPreconditioner, + LMState, Preconditioner, QRCache, RepeatedFactorMetric, RidgeLevenbergMarquardt, - RidgeLMState, ) # Analytic linear-Gaussian testbed: r(theta) = A theta - b with m < p, the @@ -299,12 +299,12 @@ def test_constructor_and_state_validation(): bare = RidgeLevenbergMarquardt( linear_residual, metric=make_metric(), ridge=1e-3, cache_jacobian=False ) - bad = RidgeLMState(jnp.asarray(1e-3), None) + bad = LMState(jnp.asarray(1e-3), None) with pytest.raises(ValueError, match="ridge"): bare.update(jnp.zeros(P_DIM), bad) with pytest.raises(ValueError, match="ridge"): bare.solve(jnp.zeros(P_DIM), lm_state=bad, gtol=1e-5) - zero_ridge = RidgeLMState(jnp.asarray(1e-3), jnp.asarray(0.0)) + zero_ridge = LMState(jnp.asarray(1e-3), jnp.asarray(0.0)) with pytest.raises(ValueError, match="strictly positive"): bare.solve(jnp.zeros(P_DIM), lm_state=zero_ridge, gtol=1e-5) diff --git a/tests/test_ridge_metrics.py b/tests/test_ridge_metrics.py index 64d13f3..a92dc79 100644 --- a/tests/test_ridge_metrics.py +++ b/tests/test_ridge_metrics.py @@ -109,7 +109,7 @@ def test_constructor_and_input_validation(): def test_solver_passes_live_context_to_the_factor_ops(): # Every factor op receives a MetricContext carrying the flat iterate and - # the live RidgeLMState (recorded at trace time -- the fields are + # the live LMState (recorded at trace time -- the fields are # tracers, their presence and shapes are static). seen = [] diff --git a/tests/test_ridge_preconditioners.py b/tests/test_ridge_preconditioners.py index 47b457f..f360e3c 100644 --- a/tests/test_ridge_preconditioners.py +++ b/tests/test_ridge_preconditioners.py @@ -15,11 +15,11 @@ BlockEigenPreconditioner, Cholesky, LMSolveAction, + LMState, LMStatus, MetricContext, RepeatedFactorMetric, RidgeLevenbergMarquardt, - RidgeLMState, block_eigen_state, ) @@ -53,7 +53,7 @@ def test_apply_matches_dense_inverse(damping): state, dense_permuted, ridge_mask, permutation = packed_state(jax.random.key(0)) ridge = 0.05 ctx = MetricContext( - lm_state=RidgeLMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), + lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), args={"preconditioner": state}, ) preconditioner = BlockEigenPreconditioner() @@ -80,7 +80,7 @@ def test_value_hashing_and_config_equality(): def test_missing_state_and_bad_builder_inputs(): preconditioner = BlockEigenPreconditioner() ctx = MetricContext( - lm_state=RidgeLMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(1e-3)), + lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(1e-3)), args={"other": 1.0}, ) with pytest.raises(ValueError, match="ctx.args"): @@ -253,7 +253,7 @@ def test_state_dataclass_survives_jit_boundary(): def apply(v, damping, ridge, state): traces.append(None) ctx = MetricContext( - lm_state=RidgeLMState(damping=damping, ridge=ridge), + lm_state=LMState(damping=damping, ridge=ridge), args={"preconditioner": state}, ) return preconditioner.apply(v, damping, ctx) From b4c0c7f8d506de9a745fbf654f11016d5092ae3a Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 00:55:22 -0700 Subject: [PATCH 02/22] refactor: linear solvers own their cache and their solve solver_config.py becomes linear_solvers.py and grows the contract the configs were missing. Each config now supplies: new_cache(m, n, n_m, dtype) -> the reject-step cache pytree, or None prepare(Subproblem) -> StepSolver(grad, velocity, solve, accel_rhs, make_cache) so init() no longer branches on a solver-name string to allocate a cache, and update() no longer carries three parallel if/elif blocks that each redefine solve_step/accel_rhs. The QR path's extra machinery -- its backward-stable Q2 velocity route and the corrected semi-normal refinement -- lives behind StepSolver.velocity instead of a fourth closure the other branches lacked. CholeskyCache/QRCache move alongside the configs that build them, and _resolved_solver() (the string the branches keyed on) is gone. Dispatch still happens once at trace time, so the compiled program is unchanged; Subproblem pins metric-callback outputs to the residual dtype in one place rather than at eleven call sites. Constructor validation drops the isinstance checks on user-supplied types and the reserved metric_factory stub, keeping the mathematical invariants (ridge > 0, the damping schedule, a CG stopping rule) and the size checks. The ridge solver still rejects a None ridge in update() -- with the merged LMState that is now a legal state for the metric solver, so it is a real contract check rather than defensive noise. ridge_lm.py: 2043 -> 1114 lines. 596 passed, 12 skipped, unchanged. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/__init__.py | 13 +- src/nlls_gram/linear_solvers.py | 401 +++++++++++++++++++++++++++ src/nlls_gram/ridge_lm.py | 468 +++++--------------------------- src/nlls_gram/solver_config.py | 102 ------- tests/test_ridge_lm.py | 18 +- 5 files changed, 479 insertions(+), 523 deletions(-) create mode 100644 src/nlls_gram/linear_solvers.py delete mode 100644 src/nlls_gram/solver_config.py diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index 3411e83..aa837f5 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -49,6 +49,7 @@ PreconditionerFactory, WhitenedPreconditioner, ) +from nlls_gram.linear_solvers import CG, QR, Cholesky, CholeskyCache, QRCache from nlls_gram.lm_types import ( LMHyperparams, LMInfo, @@ -92,17 +93,7 @@ deflated_pcg, recycled_cg, ) -from nlls_gram.ridge_lm import ( - CholeskyCache, - QRCache, - RidgeLevenbergMarquardt, - ridge_continuation, -) -from nlls_gram.solver_config import ( - CG, - QR, - Cholesky, -) +from nlls_gram.ridge_lm import RidgeLevenbergMarquardt, ridge_continuation __all__ = [ "BlockEigenPreconditioner", diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py new file mode 100644 index 0000000..9940f45 --- /dev/null +++ b/src/nlls_gram/linear_solvers.py @@ -0,0 +1,401 @@ +"""Typed linear-solver configs, and the contract they implement. + +A config selects the algebra for the LM subproblem (``linear_solver``) or the +implicit-AD solve (``ad_solver``) and carries that method's own knobs as +fields, so an option that exists for only one method cannot be passed with +another. Configs compare and hash by value, so equal configs key the same +compiled solve loop; construct them inline freely. + +Each config owns two things the solver used to branch on by name: + +- ``new_cache(sub_shapes)`` builds its reject-step cache, so ``init`` never + asks "which solver am I". +- ``prepare(sub)`` receives a :class:`Subproblem` and returns a + :class:`StepSolver` -- the gradient, a velocity solve, a general solve for + the geodesic correction, and a cache constructor. Dispatch happens once at + trace time, so the compiled program is identical to a hand-written branch. + +The menu: + +- :class:`Cholesky` (the default): dense normal equations. +- :class:`QR`: MINPACK-structured damping-row QR, stable at tiny + ridge/damping where forming a normal matrix squares the condition number. +- :class:`CG`: matrix-free preconditioned CG on the normal operator. +""" + +from dataclasses import dataclass +from typing import Any, NamedTuple + +import jax +import jax.numpy as jnp +import jax.scipy.linalg as jsp_linalg +import jax.scipy.sparse.linalg as jsp_sparse_linalg + +from nlls_gram.preconditioners import Preconditioner + +__all__ = [ + "CG", + "QR", + "Cholesky", + "CholeskyCache", + "QRCache", + "StepSolver", + "Subproblem", +] + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class CholeskyCache: + """Per-``(x, ridge)`` cache carried by the :class:`Cholesky` path. + + ``G`` is the assembled whitened normal matrix ``J~'J~ + ridge E`` + (``J~ = J F_bar^{-1}``, ``E`` the metric-block diagonal pad; pre-damping), + so a rejected step re-factors without re-assembling. ``valid`` marks it + current for the state's ``x``; ``ridge`` is the weight it was assembled + with -- a callback ridge change invalidates through this key. + """ + + G: jax.Array + valid: jax.Array + ridge: jax.Array + + @property + def payload(self): + return self.G + + +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class QRCache: + """Per-``(x, ridge)`` cache carried by the :class:`QR` path. + + ``R`` is the R factor of the augmented whitened stack + ``[J~; sqrt(ridge) [I 0] | b~]`` -- its first ``n`` columns are the R + factor of the stack and its last column carries ``Q'b``, so the velocity + solve is backward stable with no normal equations. ``valid``/``ridge`` + have the :class:`CholeskyCache` semantics. + """ + + R: jax.Array + valid: jax.Array + ridge: jax.Array + + @property + def payload(self): + return self.R + + +@dataclass(frozen=True) +class Subproblem: + """One LM step's linearized data, posed in the whitened variable. + + The solver builds this once per ``update`` and hands it to + ``linear_solver.prepare``. ``whiten``/``whiten_transpose`` apply + ``F_bar^{-1}`` and ``F_bar^{-T}`` (vectors or leading-axis-batched + matrices), already closed over the metric context; ``Jt`` is the dense + ``J'`` for the direct paths and ``jvp_fn``/``JT`` the matrix-free pair. + """ + + resid: jax.Array + theta: jax.Array + Jt: Any + jvp_fn: Any + JT: Any + whiten: Any + whiten_transpose: Any + y_m: jax.Array + penalty_gradient: jax.Array + ridge: jax.Array + damping: jax.Array + n_m: int + n_f: int + cache: Any + cache_enabled: bool + hyper: Any + ctx: Any + + @property + def dtype(self): + return self.resid.dtype + + @property + def n(self): + return self.theta.shape[0] + + @property + def m(self): + return self.resid.shape[0] + + def whitened(self, v): + """``F_bar^{-1} v`` pinned to the residual dtype. + + A wider-typed metric (float64 kernel data under a float32 residual) + must not promote the gradient and break the loop-carry dtypes. + """ + return jnp.asarray(self.whiten(v), dtype=self.dtype) + + def whitened_transpose(self, v): + """``F_bar^{-T} v`` pinned to the residual dtype.""" + return jnp.asarray(self.whiten_transpose(v), dtype=self.dtype) + + def cached(self, assemble): + """The cache payload when it is current for ``(x, ridge)``, else a + fresh ``assemble()``.""" + if not self.cache_enabled: + return assemble() + cache = self.cache + return jax.lax.cond( + cache.valid & (cache.ridge == self.ridge), + lambda _: cache.payload, + lambda _: assemble(), + operand=None, + ) + + +class StepSolver(NamedTuple): + """What a linear solver returns for one LM step. + + ``grad`` is the whitened half-gradient; ``velocity()`` the first-order + step in the whitened variable; ``solve(rhs)`` the same damped system + against an arbitrary right-hand side (the geodesic correction); + ``accel_rhs(f_vv)`` the correction's right-hand side; and + ``make_cache(valid)`` the pytree to carry, or ``None``. + """ + + grad: jax.Array + velocity: Any + solve: Any + accel_rhs: Any + make_cache: Any + + +class LinearSolver: + """Base class for the typed configs. ``materializes_jacobian`` drives the + dense ``J'`` assembly and its reject-step reuse.""" + + materializes_jacobian = True + + def new_cache(self, m, n, n_m, dtype): + """The reject-step cache pytree at ``init``, or ``None``.""" + return None + + def prepare(self, sub): + raise NotImplementedError + + +@dataclass(frozen=True) +class Cholesky(LinearSolver): + """Dense normal equations. + + Assembles ``G = J~'J~ + ridge E`` -- cached across rejected steps, where + only the damping changed, so a reject pays the ``n^3/3`` refactor without + the GEMM and without re-materializing ``J~'`` -- and factors + ``G + damping I`` per step. No knobs. + """ + + def new_cache(self, m, n, n_m, dtype): + return CholeskyCache( + G=jnp.zeros((n, n), dtype=dtype), + valid=jnp.asarray(False, dtype=jnp.bool_), + ridge=jnp.zeros((), dtype=dtype), + ) + + def prepare(self, sub): + n_m, ridge, dtype = sub.n_m, sub.ridge, sub.dtype + grad = sub.whitened_transpose(sub.Jt @ sub.resid) + ridge * sub.penalty_gradient + + def assemble(): + Jt_sub = sub.whitened_transpose(sub.Jt) + diagonal = jnp.arange(n_m) + return (Jt_sub @ Jt_sub.T).at[diagonal, diagonal].add(ridge) + + normal_matrix = sub.cached(assemble) + shifted = normal_matrix + sub.damping * jnp.eye(sub.n, dtype=dtype) + factor = jsp_linalg.cho_factor(shifted) + + def solve(rhs): + return -jsp_linalg.cho_solve(factor, rhs) + + return StepSolver( + grad=grad, + velocity=lambda: solve(grad), + solve=solve, + accel_rhs=lambda f_vv: sub.whitened_transpose(sub.Jt @ f_vv), + make_cache=lambda valid: CholeskyCache(normal_matrix, valid, ridge), + ) + + +@dataclass(frozen=True) +class QR(LinearSolver): + """Damping-row QR of the augmented whitened stack. + + One QR of ``[J~; sqrt(ridge) [I 0] | b~]`` with ``b~ = [r; sqrt(ridge) + y_m]`` is cached per ``(x, ridge)``: its leading columns are the stack's R + factor and its last column carries ``Q'b``, so the velocity is a + backward-stable least-squares solve with NO normal equations -- More + 1978's damping-row structure, accurate at ``cond(A)`` rather than + ``cond(A)^2``. Each step re-factors only the damping rows. No knobs. + """ + + def new_cache(self, m, n, n_m, dtype): + return QRCache( + R=jnp.zeros((min(m + n_m, n + 1), n + 1), dtype=dtype), + valid=jnp.asarray(False, dtype=jnp.bool_), + ridge=jnp.zeros((), dtype=dtype), + ) + + def prepare(self, sub): + n, n_m, ridge, dtype = sub.n, sub.n_m, sub.ridge, sub.dtype + sqrt_ridge = jnp.sqrt(ridge) + grad = sub.whitened_transpose(sub.Jt @ sub.resid) + ridge * sub.penalty_gradient + + def assemble(): + Jt_sub = sub.whitened_transpose(sub.Jt) + stacked = jnp.concatenate( + [Jt_sub.T, sqrt_ridge * jnp.eye(n_m, n, dtype=dtype)], axis=0 + ) + b_stacked = jnp.concatenate([sub.resid, sqrt_ridge * sub.y_m]) + return jnp.linalg.qr( + jnp.concatenate([stacked, b_stacked[:, None]], axis=1), mode="r" + ) + + qr_R = sub.cached(assemble) + r_factor, transformed_rhs = qr_R[:, :-1], qr_R[:, -1] + # Per-step damping-row refactor: [R; sqrt(damping) I] = Q2 R2 with + # R2'R2 = A'A + damping I. When m + n_m < n the cached R is upper + # trapezoidal and these rows are what make the system full rank. Q2 is + # retained to transform the velocity right-hand side stably. + damped_stack = jnp.concatenate( + [r_factor, jnp.sqrt(sub.damping) * jnp.eye(n, dtype=dtype)], axis=0 + ) + Q_mu, R_mu = jnp.linalg.qr(damped_stack, mode="reduced") + + def damped_normal_matvec(v): + gauss_newton = sub.whitened_transpose(sub.Jt @ (sub.Jt.T @ sub.whitened(v))) + metric_shift = jnp.concatenate([v[:n_m], jnp.zeros(sub.n_f, dtype=dtype)]) + return gauss_newton + ridge * metric_shift + sub.damping * v + + def solve(rhs): + # Corrected semi-normal equations (Bjorck 1987) for the geodesic + # right-hand side: triangular solves against R_mu, then ONE fixed + # iterative-refinement pass through matvecs (Bjorck 1996 Sec. + # 6.6.5). The second-order correction tolerates the squared + # conditioning; accept/reject guards it. + b = -rhs + half = jsp_linalg.solve_triangular(R_mu.T, b, lower=True) + delta = jsp_linalg.solve_triangular(R_mu, half, lower=False) + correction_rhs = b - damped_normal_matvec(delta) + half = jsp_linalg.solve_triangular(R_mu.T, correction_rhs, lower=True) + return delta + jsp_linalg.solve_triangular(R_mu, half, lower=False) + + def velocity(): + # min ||[R; sqrt(damping) I] delta + [Q'b; 0]||^2 solved through + # Q2: exact and backward stable at cond(A), never cond(A)^2. + rhs = jnp.concatenate([transformed_rhs, jnp.zeros(n, dtype=dtype)]) + return -jsp_linalg.solve_triangular(R_mu, Q_mu.T @ rhs, lower=False) + + return StepSolver( + grad=grad, + velocity=velocity, + solve=solve, + accel_rhs=lambda f_vv: sub.whitened_transpose(sub.Jt @ f_vv), + make_cache=lambda valid: QRCache(qr_R, valid, ridge), + ) + + +@dataclass(frozen=True) +class CG(LinearSolver): + """Matrix-free preconditioned CG on the whitened normal operator. + + As ``linear_solver`` it solves the damped forward subproblem + ``(J~'J~ + ridge E + damping I) delta_y = -g`` -- the same SPD system + :class:`Cholesky` factors -- with the ``preconditioner`` in CG's ``M`` + slot at the live damping. As ``ad_solver`` it solves the undamped + implicit-AD system ``J~'J~ + ridge E``, with the preconditioner applied at + zero damping (subclasses marked ``requires_positive_damping`` are rejected + for that role). + + ``preconditioner`` is REQUIRED in both roles -- nobody should run Krylov + methods without a preconditioning decision, so + :class:`~nlls_gram.IdentityPreconditioner` is the explicit opt-out and a + custom one is a small subclass implementing ``apply(v, damping, ctx)``. + ``tol=None`` resolves to a dtype default (``1e-10`` in float64, ``1e-6`` + in float32); ``maxiter`` must be set when both tolerances are explicitly + zero, since an uncapped zero-tolerance CG loop has no stopping rule. + """ + + preconditioner: Preconditioner + tol: float | None = None + atol: float = 0.0 + maxiter: int | None = None + + materializes_jacobian = False + + def __post_init__(self): + if self.tol is not None and self.tol < 0: + raise ValueError("CG.tol must be nonnegative or None") + if self.atol < 0: + raise ValueError("CG.atol must be nonnegative") + if self.maxiter is not None and self.maxiter <= 0: + raise ValueError("CG.maxiter must be positive or None") + if self.tol == 0 and self.atol == 0 and self.maxiter is None: + raise ValueError("CG.maxiter must be set when both tolerances are zero") + + def prepare(self, sub): + n_m, n_f, ridge, dtype = sub.n_m, sub.n_f, sub.ridge, sub.dtype + m, damping, ctx = sub.m, sub.damping, sub.ctx + sqrt_ridge = jnp.sqrt(ridge) + + # Whitened operator J~ = J F_bar^{-1}: products route through the + # metric's factor callbacks. + def J_sub(u): + return sub.jvp_fn(sub.whitened(u)) + + def JT_sub(w): + return sub.whitened_transpose(sub.JT(w)) + + grad = JT_sub(sub.resid) + ridge * sub.penalty_gradient + + # Augmented operator A = [J~; sqrt(ridge) [I 0]]: the penalty rows are + # the constant metric-block identity on y. + def A_matvec(u): + return jnp.concatenate([J_sub(u), sqrt_ridge * u[:n_m]]) + + def At_matvec(w): + pullback = sqrt_ridge * jnp.concatenate( + [w[m:], jnp.zeros(n_f, dtype=dtype)] + ) + return JT_sub(w[:m]) + pullback + + # N = A'A + damping I, the preconditioner-free SPD operator that + # custom_linear_solve differentiates through, posed on u. + def N_matvec(u): + return At_matvec(A_matvec(u)) + damping * u + + def apply_M(v): + return self.preconditioner.apply(v, damping, ctx) + + def solve_N(_, c): + solution, _ = jsp_sparse_linalg.cg( + N_matvec, + c, + tol=jnp.asarray(sub.hyper.iterative_tol, dtype=dtype), + atol=jnp.asarray(sub.hyper.iterative_atol, dtype=dtype), + maxiter=sub.hyper.iterative_maxiter, + M=apply_M, + ) + return solution + + def solve(rhs): + return jax.lax.custom_linear_solve( + N_matvec, -rhs, solve=solve_N, transpose_solve=solve_N, symmetric=True + ) + + return StepSolver( + grad=grad, + velocity=lambda: solve(grad), + solve=solve, + accel_rhs=JT_sub, + make_cache=lambda valid: None, + ) diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 795e014..c317399 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -20,7 +20,6 @@ """ import dataclasses -from dataclasses import dataclass import jax import jax.numpy as jnp @@ -28,6 +27,13 @@ import jax.scipy.sparse.linalg as jsp_sparse_linalg from jax.flatten_util import ravel_pytree +from nlls_gram.linear_solvers import ( + CG, + Cholesky, + CholeskyCache, + QRCache, + Subproblem, +) from nlls_gram.lm_core import LevenbergMarquardtBase from nlls_gram.lm_types import ( LMHyperparams, @@ -37,8 +43,7 @@ _cast_hyper, _damping_floor, ) -from nlls_gram.metrics import Metric, MetricContext -from nlls_gram.solver_config import CG, QR, Cholesky +from nlls_gram.metrics import MetricContext from nlls_gram.utilities import ( _static_key_component, _zero_tangent_leaf, @@ -53,42 +58,6 @@ ] -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class CholeskyCache: - """Per-``(x, ridge)`` cache carried by the ``Cholesky`` forward path. - - ``G`` is the assembled whitened normal matrix ``J~'J~ + ridge E`` - (``J~ = J F_bar^{-1}``, ``E`` the metric-block diagonal pad; - pre-damping), so a rejected step re-factors without re-assembling; - ``valid`` marks it current for the state's ``x``; ``ridge`` is the weight - it was assembled with -- a callback ridge change invalidates through this - key. - """ - - G: jax.Array - valid: jax.Array - ridge: jax.Array - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class QRCache: - """Per-``(x, ridge)`` cache carried by the ``QR`` forward path. - - ``R`` is the R factor of the augmented whitened stack - ``[J~, sqrt(ridge) [I 0] | b~]`` -- the first ``p`` columns are the R - factor of ``[J~; sqrt(ridge) [I 0]]`` and the last column carries the - ``Q``-transformed residual, so the velocity solve is backward stable with - no normal equations. ``valid``/``ridge`` have the :class:`CholeskyCache` - semantics. - """ - - R: jax.Array - valid: jax.Array - ridge: jax.Array - - def ridge_continuation( *, decrease=0.1, ridge_floor, grad_rtol=1e-2, stall_rtol=0.0, dtype=None ): @@ -382,7 +351,6 @@ def __init__( residual_fn, *, metric, - metric_factory=None, ridge=None, init_damping=1e-3, damping_decrease=0.5, @@ -398,68 +366,24 @@ def __init__( geodesic_acceptance_ratio=0.75, ): canonical_residual, residual_arity = canonicalize_residual(residual_fn) - if metric_factory is not None: - raise NotImplementedError( - "metric_factory is reserved for a future release: its " - "documented contract is a prepare/build pair producing a " - "Metric from traced, differentiation-inert metric_state " - "(with metric_valid reject-step reuse, and a state change " - "treated as a problem change -- the same " - "convergence-suppression/cache-invalidation machinery as a " - "callback ridge change); pass a fixed metric" - ) - if not isinstance(metric, Metric): - raise TypeError("metric must be a Metric") - if not isinstance(linear_solver, (Cholesky, QR, CG)): - raise TypeError( - "linear_solver must be a solver config -- Cholesky(), QR(), " - f"or CG(preconditioner, ...); got {linear_solver!r}" - ) - if ad_solver is not None and not isinstance(ad_solver, (Cholesky, CG)): - raise TypeError( - "ad_solver must be None (match the forward path), Cholesky(), " - f"or CG(...); got {ad_solver!r}" - ) - if jacobian_mode not in ("auto", "fwd", "rev"): - raise ValueError(f"unknown jacobian_mode: {jacobian_mode}") - if ridge is not None: - if jnp.ndim(ridge) != 0: - raise ValueError("ridge must be a scalar or None") - if ( - not isinstance(ridge, (jax.Array, jax.core.Tracer)) - and float(ridge) <= 0.0 - ): - raise ValueError( - "ridge must be strictly positive (ridge = 0 is unsupported: " - "use ridge_continuation with a positive ridge_floor to " - "approach the ridgeless limit)" - ) - if init_damping <= 0: - raise ValueError("init_damping must be positive") - if damping_decrease <= 0: - raise ValueError("damping_decrease must be positive") - if damping_increase <= 0: - raise ValueError("damping_increase must be positive") - if min_damping is not None and min_damping <= 0: - raise ValueError("min_damping must be positive or None") - if min_damping is not None and min_damping > init_damping: - raise ValueError("min_damping must not exceed init_damping") - if max_damping is not None and max_damping < init_damping: - raise ValueError("max_damping must be at least init_damping") - # jacobian_mode is consumed by the dense forward paths and the - # cholesky AD method; a matrix-free normal_cg forward with a cg AD - # rule never materializes J, so a forced mode is a construction - # error there. if ( - jacobian_mode != "auto" - and isinstance(linear_solver, CG) - and not isinstance(ad_solver, Cholesky) + ridge is not None + and not isinstance(ridge, (jax.Array, jax.core.Tracer)) + and float(ridge) <= 0.0 ): raise ValueError( - "jacobian_mode controls dense Jacobian assembly, but neither " - "a matrix-free CG forward solver nor its cg-resolved " - "ad_solver ever consumes it" + "ridge must be strictly positive (ridge = 0 is unsupported: " + "use ridge_continuation with a positive ridge_floor to " + "approach the ridgeless limit)" + ) + if init_damping <= 0 or damping_decrease <= 0 or damping_increase <= 0: + raise ValueError( + "init_damping, damping_decrease, and damping_increase must be positive" ) + if min_damping is not None and not 0 < min_damping <= init_damping: + raise ValueError("min_damping must be positive and at most init_damping") + if max_damping is not None and max_damping < init_damping: + raise ValueError("max_damping must be at least init_damping") self.residual_fn = canonical_residual self.residual_arity = residual_arity self.metric = metric @@ -579,11 +503,6 @@ def hyperparams(self, dtype=None): else jnp.asarray(self.iterative_maxiter, dtype=jnp.int32), ) - def _resolved_solver(self): - if isinstance(self.linear_solver, Cholesky): - return "cholesky" - return "qr" if isinstance(self.linear_solver, QR) else "normal_cg" - def _block_sizes(self, theta_size): # The free-block size is inferred from the flattened iterate: the # metric covers the leading metric.size coordinates, the rest is free. @@ -645,20 +564,12 @@ def init(self, x0, args=None, *, p=None): jacobian_valid=invalid, aux=jax.tree.map(jnp.zeros_like, aux), ) - if self._resolved_solver() == "cholesky": - cache = CholeskyCache( - G=jnp.zeros((p_dim, p_dim), dtype=dtype), - valid=invalid, - ridge=jnp.zeros((), dtype=dtype), - ) - else: - r_rows = min(m + n_m, p_dim + 1) - cache = QRCache( - R=jnp.zeros((r_rows, p_dim + 1), dtype=dtype), - valid=invalid, - ridge=jnp.zeros((), dtype=dtype), - ) - return LMState(damping, ridge, **common, solver_cache=cache) + return LMState( + damping, + ridge, + **common, + solver_cache=self.linear_solver.new_cache(m, p_dim, n_m, dtype), + ) def _initial_info(self, x, lm_state, args, p): # grad_norm and penalty_grad_norm are +inf sentinels (computing them @@ -717,32 +628,26 @@ def residual_flat(th): residual_value = residual_flat - # TRUE-residual linearization: matrix-free closures for normal_cg, - # dense J' (reused from the cache after a rejected step) otherwise. - resolved_solver = self._resolved_solver() - if resolved_solver == "normal_cg": + # TRUE-residual linearization: matrix-free closures when the linear + # solver never materializes J, dense J' (reused from the cache after a + # rejected step) otherwise. + jvp_fn = JT = Jt = None + if not self.linear_solver.materializes_jacobian: if self.has_aux: resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) else: resid, jvp_fn = jax.linearize(residual_flat, theta) aux = None - elif self.cache_jacobian: - if lm_state.jacobian_valid is None: - raise ValueError( - "cache_jacobian=True but the lm_state has no Jacobian cache; " - "create the lm_state with init(x, args, p=p)" - ) - - def compute_resid_and_jt(_): - return self._dense_resid_jt_aux(residual_flat, theta) + transpose_fn = jax.linear_transpose(jvp_fn, theta) - def reuse_resid_and_jt(_): - return lm_state.resid, lm_state.Jt, lm_state.aux + def JT(cotangent): + return transpose_fn(cotangent)[0] + elif self.cache_jacobian: resid, Jt, aux = jax.lax.cond( lm_state.jacobian_valid, - reuse_resid_and_jt, - compute_resid_and_jt, + lambda _: (lm_state.resid, lm_state.Jt, lm_state.aux), + lambda _: self._dense_resid_jt_aux(residual_flat, theta), operand=None, ) else: @@ -760,273 +665,54 @@ def reuse_resid_and_jt(_): jnp.asarray(lm_state.damping, dtype=resid.dtype), min_damping ) if lm_state.ridge is None: + # A None ridge is a legal LMState (the metric solver leaves it + # unset); this solver needs one. raise ValueError( "the lm_state has no ridge; create it with init(x, args, p=p)" ) ridge = jnp.asarray(lm_state.ridge, dtype=resid.dtype) # The subproblem is posed on the whitened variable y = F_bar x, where - # the penalty rows are the constant [I_{n_m} | 0]: the half-gradient - # is g = F_bar^{-T} J'r + ridge [y_m; 0] (grad F = 2 g; the factor - # cancels in the LM equations), and every gradient/step quantity - # below (including the reported norms) is the whitened one. y_m is - # reused for the pre-step penalty value ||y_m||^2. Metric callback - # outputs are pinned to the residual dtype so a wider-typed metric - # (e.g. float64 kernel data under a float32 residual) cannot promote - # the gradient and break the loop-carry dtypes. + # the penalty rows are the constant [I_{n_m} | 0]: the half-gradient is + # g = F_bar^{-T} J'r + ridge [y_m; 0] (grad F = 2 g; the factor cancels + # in the LM equations), and every gradient/step quantity below -- + # including the reported norms -- is the whitened one. y_m doubles as + # the pre-step penalty value ||y_m||^2. n_m, n_f = self._block_sizes(theta.shape[0]) ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) y_m = jnp.asarray(self.metric.factor_apply(theta[:n_m], ctx), dtype=resid.dtype) penalty_value_old = jnp.sum(y_m**2) penalty_gradient = jnp.concatenate([y_m, jnp.zeros(n_f, dtype=resid.dtype)]) - if resolved_solver == "normal_cg": - transpose_fn = jax.linear_transpose(jvp_fn, theta) - - def JT(cotangent): - return transpose_fn(cotangent)[0] - - # Whitened operator J~ = J F_bar^{-1}: products route through the - # metric's factor callbacks. - def J_sub(u): - return jvp_fn(jnp.asarray(self._extended_solve(u, ctx), resid.dtype)) - - def JT_sub(w): - return jnp.asarray( - self._extended_solve_transpose(JT(w), ctx), dtype=resid.dtype - ) - - grad = JT_sub(resid) + ridge * penalty_gradient - inner_tol = jnp.asarray(hyper.iterative_tol, dtype=resid.dtype) - inner_atol = jnp.asarray(hyper.iterative_atol, dtype=resid.dtype) - sqrt_ridge = jnp.sqrt(ridge) - m = resid.shape[0] - - # Augmented operator A = [J~; sqrt(ridge) [I 0]]: the penalty - # rows are the constant metric-block identity on y. - def A_matvec(u): - return jnp.concatenate([J_sub(u), sqrt_ridge * u[:n_m]]) - - def At_matvec(w): - penalty_pullback = sqrt_ridge * jnp.concatenate( - [w[m:], jnp.zeros(n_f, dtype=resid.dtype)] - ) - return JT_sub(w[:m]) + penalty_pullback - - # N = A'A + damping I, the preconditioner-free SPD operator that - # custom_linear_solve differentiates through, posed on u (not z). - def N_matvec(u): - return At_matvec(A_matvec(u)) + damping * u - - # Preconditioned CG on N itself -- the same damped SPD system - # the cholesky path factors, applied matrix-free. The typed - # Preconditioner sits in CG's M slot: an SPD approximation of - # N^{-1} at the live damping, with the solver context along. - def apply_M(v): - return self.normal_cg_preconditioner.apply(v, damping, ctx) - - def solve_N(_, c): - solution, _ = jsp_sparse_linalg.cg( - N_matvec, - c, - tol=inner_tol, - atol=inner_atol, - maxiter=hyper.iterative_maxiter, - M=apply_M, - ) - return solution - - def solve_step(rhs): - return jax.lax.custom_linear_solve( - N_matvec, - -rhs, - solve=solve_N, - transpose_solve=solve_N, - symmetric=True, - ) - - def accel_rhs(f_vv): - return JT_sub(f_vv) - - elif resolved_solver == "cholesky": - # The assembled G = J~'J~ + ridge E is cached across rejected - # steps -- only mu changed, so the reject pays the p^3/3 refactor - # without the GEMM; the J~' materialization (a batched factor - # solve through the metric) is likewise skipped on reject, and - # the per-step gradient and acceleration RHS only ever pull - # vectors back through factor_solve_transpose. A callback ridge - # change invalidates through the cache's ridge key. - grad = ( - jnp.asarray( - self._extended_solve_transpose(Jt @ resid, ctx), - dtype=resid.dtype, - ) - + ridge * penalty_gradient - ) - - def assemble_normal(_): - Jt_sub = jnp.asarray( - self._extended_solve_transpose(Jt, ctx), dtype=resid.dtype - ) - diag = jnp.arange(n_m) - return (Jt_sub @ Jt_sub.T).at[diag, diag].add(ridge) - - if self.cache_jacobian: - cache = lm_state.solver_cache - if not isinstance(cache, CholeskyCache): - raise ValueError( - "the lm_state has no normal-matrix cache for the " - "cholesky path; create the lm_state with " - "init(x, args, p=p)" - ) - normal_matrix = jax.lax.cond( - cache.valid & (cache.ridge == ridge), - lambda _: cache.G, - assemble_normal, - operand=None, - ) - else: - normal_matrix = assemble_normal(None) - shifted = normal_matrix + damping * jnp.eye( - theta.shape[0], dtype=resid.dtype - ) - factor = jsp_linalg.cho_factor(shifted) - - def solve_step(rhs): - return -jsp_linalg.cho_solve(factor, rhs) - - def accel_rhs(f_vv): - return jnp.asarray( - self._extended_solve_transpose(Jt @ f_vv, ctx), - dtype=resid.dtype, - ) - - else: # qr - # One QR of the AUGMENTED whitened stack - # [J~; sqrt(ridge) [I 0] | b~] with b~ = [r; sqrt(ridge) y_m], - # cached per (x, ridge): its first p columns are the stack's R - # factor and its last column carries Q'b, so the velocity can be - # solved as a backward-stable least-squares problem with NO - # normal equations anywhere -- More 1978's actual damping-row - # structure. (An extra residual-norm row appears when - # m + n_m > p; it is a constant in the least-squares objective - # and harmless.) The semi-normal route (R'R delta = -g) squares - # the stack's condition number, which loses the Gauss-Newton - # step accuracy exactly in the tiny-ridge regime this path - # exists for. J~ is materialized only when the cache refreshes. - grad = ( - jnp.asarray( - self._extended_solve_transpose(Jt @ resid, ctx), - dtype=resid.dtype, - ) - + ridge * penalty_gradient - ) - - def assemble_r(_): - Jt_sub = jnp.asarray( - self._extended_solve_transpose(Jt, ctx), dtype=resid.dtype - ) - stacked = jnp.concatenate( - [ - Jt_sub.T, - jnp.sqrt(ridge) - * jnp.eye(n_m, theta.shape[0], dtype=resid.dtype), - ], - axis=0, - ) - b_stacked = jnp.concatenate([resid, jnp.sqrt(ridge) * y_m]) - augmented = jnp.concatenate([stacked, b_stacked[:, None]], axis=1) - return jnp.linalg.qr(augmented, mode="r") - - if self.cache_jacobian: - cache = lm_state.solver_cache - if not isinstance(cache, QRCache): - raise ValueError( - "the lm_state has no QR cache for the qr path; create " - "the lm_state with init(x, args, p=p)" - ) - qr_R = jax.lax.cond( - cache.valid & (cache.ridge == ridge), - lambda _: cache.R, - assemble_r, - operand=None, - ) - else: - qr_R = assemble_r(None) - r_factor = qr_R[:, :-1] - transformed_rhs = qr_R[:, -1] - # Per-update damping-row refactor: [R; sqrt(damping) I] = Q2 R2 - # with R2'R2 = A'A + damping I. When m + k < p the cached R is - # upper trapezoidal and these damping rows are what make the - # final system full rank. Q2 is retained to transform the - # velocity RHS stably. - damped_stack = jnp.concatenate( - [ - r_factor, - jnp.sqrt(damping) * jnp.eye(theta.shape[0], dtype=resid.dtype), - ], - axis=0, + step_solver = self.linear_solver.prepare( + Subproblem( + resid=resid, + theta=theta, + Jt=Jt, + jvp_fn=jvp_fn, + JT=JT, + whiten=lambda v: self._extended_solve(v, ctx), + whiten_transpose=lambda v: self._extended_solve_transpose(v, ctx), + y_m=y_m, + penalty_gradient=penalty_gradient, + ridge=ridge, + damping=damping, + n_m=n_m, + n_f=n_f, + cache=lm_state.solver_cache, + cache_enabled=self.cache_jacobian, + hyper=hyper, + ctx=ctx, ) - Q_mu, R_mu = jnp.linalg.qr(damped_stack, mode="reduced") - - def damped_normal_matvec(v): - gauss_newton = jnp.asarray( - self._extended_solve_transpose( - Jt - @ ( - Jt.T - @ jnp.asarray(self._extended_solve(v, ctx), resid.dtype) - ), - ctx, - ), - dtype=resid.dtype, - ) - metric_shift = jnp.concatenate( - [v[:n_m], jnp.zeros(n_f, dtype=resid.dtype)] - ) - return gauss_newton + ridge * metric_shift + damping * v - - def solve_step(rhs): - # Corrected semi-normal equations (Bjorck 1987) for the - # geodesic-acceleration RHS: triangular solves against R_mu, - # then ONE fixed iterative-refinement pass through matvecs - # (Bjorck 1996 Sec. 6.6.5). The second-order correction - # tolerates the squared conditioning; accept/reject guards it. - b = -rhs - half = jsp_linalg.solve_triangular(R_mu.T, b, lower=True) - delta = jsp_linalg.solve_triangular(R_mu, half, lower=False) - correction_rhs = b - damped_normal_matvec(delta) - half = jsp_linalg.solve_triangular(R_mu.T, correction_rhs, lower=True) - delta = delta + jsp_linalg.solve_triangular(R_mu, half, lower=False) - return delta - - def solve_velocity(): - # min ||[R; sqrt(damping) I] delta + [Q'b; 0]||^2 solved - # through Q2: exact and backward stable at cond(A), never - # cond(A)^2. - rhs_aug = jnp.concatenate( - [ - transformed_rhs, - jnp.zeros(theta.shape[0], dtype=resid.dtype), - ] - ) - return -jsp_linalg.solve_triangular(R_mu, Q_mu.T @ rhs_aug, lower=False) - - def accel_rhs(f_vv): - return jnp.asarray( - self._extended_solve_transpose(Jt @ f_vv, ctx), - dtype=resid.dtype, - ) + ) + grad = step_solver.grad # First-order step (velocity) and its ridge objective. The solves - # produce the whitened step delta_y: the x-space step maps back - # through the factor solve, and the trial penalty uses the linearity - # of the change of variables -- F_bar(theta + step) = y + delta_y, so - # no second factor application is ever needed. - if resolved_solver == "qr": - velocity_sub = solve_velocity() - else: - velocity_sub = solve_step(grad) + # produce the whitened step delta_y: the x-space step maps back through + # the factor solve, and the trial penalty uses the linearity of the + # change of variables -- F_bar(theta + step) = y + delta_y, so no + # second factor application is ever needed. + velocity_sub = step_solver.velocity() velocity = jnp.asarray(self._extended_solve(velocity_sub, ctx), resid.dtype) def trial_penalty(step_sub): @@ -1056,7 +742,7 @@ def first_jvp(th): ] f_vv = jax.jvp(first_jvp, (theta,), (velocity,))[1] - acceleration_sub = solve_step(accel_rhs(f_vv)) + acceleration_sub = step_solver.solve(step_solver.accel_rhs(f_vv)) acceleration = jnp.asarray( self._extended_solve(acceleration_sub, ctx), dtype=resid.dtype ) @@ -1132,10 +818,6 @@ def accelerated_objective(_): # init() and callbacks set it. The input hyper (not the fallback) # passes through so the loop carry structure is stable. if self.cache_jacobian: - if resolved_solver == "cholesky": - new_cache = CholeskyCache(normal_matrix, ~improved, ridge) - else: - new_cache = QRCache(qr_R, ~improved, ridge) new_lm_state = LMState( new_damping, ridge, @@ -1144,7 +826,7 @@ def accelerated_objective(_): ~improved, aux, lm_state.hyper, - solver_cache=new_cache, + solver_cache=step_solver.make_cache(~improved), ) else: new_lm_state = LMState(new_damping, ridge, hyper=lm_state.hyper) @@ -1306,7 +988,7 @@ def _ranking_objective(self, result, p, callback): def _resolved_ad_solver(self): if self.ad_solver is None: # Matrix-free forward -> matrix-free AD. - return "normal_cg" if self._resolved_solver() == "normal_cg" else "cholesky" + return "normal_cg" if isinstance(self.linear_solver, CG) else "cholesky" return "cholesky" if isinstance(self.ad_solver, Cholesky) else "normal_cg" def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point): diff --git a/src/nlls_gram/solver_config.py b/src/nlls_gram/solver_config.py deleted file mode 100644 index c508e17..0000000 --- a/src/nlls_gram/solver_config.py +++ /dev/null @@ -1,102 +0,0 @@ -"""Typed linear-solver configuration for ``RidgeLevenbergMarquardt``. - -Each config is a small frozen dataclass selecting the algebra for the LM -subproblem (``linear_solver``) or the implicit-AD solve (``ad_solver``), -carrying that solver's own knobs as fields -- so an option that only exists -for one method cannot be passed with another. Instances compare and hash by -value (standard frozen-dataclass semantics), so equal configs key the same -compiled solve loop; construct them inline freely. - -- ``Cholesky()`` (the default): dense normal equations (forward) or the - assembled dense implicit-AD solve. -- ``QR()``: MINPACK-structured damping-row QR, stable at tiny ridge/damping. -- ``CG(preconditioner, ...)``: matrix-free preconditioned CG on the normal - operator -- as ``linear_solver`` the damped forward subproblem, as - ``ad_solver`` the undamped implicit-AD solve. ``preconditioner`` is - required in both roles; ``identity_preconditioner()`` opts out. - -``ad_solver=None`` (the default) matches the forward path's family: -``Cholesky`` for the dense forwards, ``CG`` under a ``CG`` forward -- with -the forward's preconditioner inherited into the undamped solve (applied at -zero damping; ``requires_positive_damping`` hooks fall back to -unpreconditioned) and the AD-default tolerance and budget. -``LevenbergMarquardt`` (the metric solver) keeps its string-named solver menu -for now; these types are the configuration surface the solvers are converging -on. -""" - -from dataclasses import dataclass - -from nlls_gram.preconditioners import Preconditioner - -__all__ = ["Cholesky", "CG", "QR"] - - -@dataclass(frozen=True) -class Cholesky: - """Dense normal-equations solve. - - Forward: assemble ``G = J'J + ridge L'L`` (cached across rejected steps) - and factor ``G + damping I`` per step. AD: assemble and factor the - undamped ``J'J + ridge L'L`` once. No knobs. - """ - - -@dataclass(frozen=True) -class QR: - """Damping-row QR of the augmented stack ``[J; sqrt(ridge) L]``. - - Backward stable at ``cond(A)`` rather than ``cond(A)^2``, the choice for - tiny ridge/damping where forming the normal matrix squares the condition - number. One QR per ``(x, ridge)`` is cached; each step re-factors only the - damping rows. No knobs. - """ - - -@dataclass(frozen=True) -class CG: - """Matrix-free preconditioned CG on the whitened normal operator, in both - roles. - - As ``linear_solver`` it solves the damped forward subproblem - ``(J~'J~ + ridge E + damping I) delta_y = -g`` -- the same SPD system the - :class:`Cholesky` path factors, matrix-free, with the ``ridge`` spectral - floor on the metric block. The ``preconditioner`` is applied in CG's - ``M`` slot with the live damping. - - As ``ad_solver`` it solves the undamped implicit-AD system - ``J~'J~ + ridge E``; the preconditioner is applied with zero damping - (subclasses marked ``requires_positive_damping`` are rejected for this - role). - - ``preconditioner`` is REQUIRED in both roles and must be a - :class:`~nlls_gram.Preconditioner` -- nobody should run Krylov methods - without a preconditioning decision, so - :class:`~nlls_gram.IdentityPreconditioner` is the explicit opt-out and a - custom preconditioner is a small subclass implementing - ``apply(v, damping, ctx)``. ``tol=None`` resolves to a dtype default - (``1e-10`` in float64, ``1e-6`` in float32); ``maxiter`` must be set when - both tolerances are explicitly zero, since an uncapped zero-tolerance CG - loop has no stopping rule. - """ - - preconditioner: Preconditioner - tol: float | None = None - atol: float = 0.0 - maxiter: int | None = None - - def __post_init__(self): - if not isinstance(self.preconditioner, Preconditioner): - raise TypeError( - "CG.preconditioner must be a Preconditioner subclass " - "instance; pass IdentityPreconditioner() to run " - "unpreconditioned CG" - ) - if self.tol is not None and self.tol < 0: - raise ValueError("CG.tol must be nonnegative or None") - if self.atol < 0: - raise ValueError("CG.atol must be nonnegative") - if self.maxiter is not None and self.maxiter <= 0: - raise ValueError("CG.maxiter must be positive or None") - if self.tol == 0 and self.atol == 0 and self.maxiter is None: - raise ValueError("CG.maxiter must be set when both tolerances are zero") diff --git a/tests/test_ridge_lm.py b/tests/test_ridge_lm.py index 4fdeddc..437bf7c 100644 --- a/tests/test_ridge_lm.py +++ b/tests/test_ridge_lm.py @@ -260,27 +260,11 @@ def test_atol_is_conjunctive_an_interpolating_start_does_not_stop(): def test_constructor_and_state_validation(): metric = make_metric() - with pytest.raises(TypeError, match="Metric"): - RidgeLevenbergMarquardt(linear_residual, metric=object()) with pytest.raises(ValueError, match="strictly positive"): RidgeLevenbergMarquardt(linear_residual, metric=metric, ridge=0.0) with pytest.raises(ValueError, match="strictly positive"): RidgeLevenbergMarquardt(linear_residual, metric=metric, ridge=-1e-3) - # String solver names are gone: the typed configs are the only spelling. - with pytest.raises(TypeError, match="solver config"): - RidgeLevenbergMarquardt( - linear_residual, metric=metric, linear_solver="cholesky" - ) - with pytest.raises(TypeError, match="ad_solver must be None"): - RidgeLevenbergMarquardt(linear_residual, metric=metric, ad_solver="auto") - with pytest.raises(NotImplementedError, match="metric_factory"): - RidgeLevenbergMarquardt(linear_residual, metric=metric, metric_factory=object()) - # Each config validates its own fields at construction; the CG - # preconditioner is a required typed Preconditioner in both roles. - with pytest.raises(TypeError): - CG(maxiter=100) - with pytest.raises(TypeError, match="Preconditioner"): - CG(preconditioner=lambda v, damping: v) + # An uncapped zero-tolerance CG loop has no stopping rule. with pytest.raises(ValueError, match="maxiter"): CG(IdentityPreconditioner(), tol=0.0) # The metric must cover no more than the flattened iterate. From 70cfcda27bd39e9c214f0a152c1ed590c4c8010c Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 01:07:08 -0700 Subject: [PATCH 03/22] refactor: metrics and preconditioners own their adaptive state Both hook base classes gain the same optional pair: prepare(theta, ctx) -> traced state pytree, or None (the default) rebuild(ctx) -> traced predicate gating a rebuild, True by default The output rides on lm_state (metric_state/precond) and comes back as ctx.metric_state / ctx.preconditioner_state, rebuilt on accepted steps and reused across rejected ones. Whether a hook is stateful is a static property of its class, so the slots and their lax.cond compile away entirely for the stateless default. BlockEigenPreconditioner stops reading ctx.args[args_key]: it holds blocks_fn + permutation and eigendecomposes in prepare, so its state is no longer threaded through the residual args and rebuilt by hand from a solve callback. rebuild() is the knob for declining a refresh -- a stale preconditioner only changes the CG iteration path, never the converged step. MetricContext becomes SolverContext and moves to lm_types: it now serves the metric, the preconditioner, AND the linear solver, and carries the two new state slots. Under implicit AD the hooks are prepared once at the returned solution and not differentiated, the documented freeze contract. 594 passed, 12 skipped (four BlockEigenPreconditioner tests for the old args-threading contract replaced by two for the new one). Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/ridge_lm.md | 6 +- src/nlls_gram/__init__.py | 4 +- src/nlls_gram/lm_types.py | 31 ++++ src/nlls_gram/metrics.py | 52 +++--- src/nlls_gram/preconditioners.py | 101 +++++++----- src/nlls_gram/ridge_lm.py | 137 +++++++++++++--- tests/test_float64_subprocess.py | 49 ++---- tests/test_ridge_lm.py | 2 +- tests/test_ridge_metrics.py | 6 +- tests/test_ridge_preconditioners.py | 246 ++++++++++------------------ 10 files changed, 345 insertions(+), 289 deletions(-) diff --git a/docs/ridge_lm.md b/docs/ridge_lm.md index 0c86ada..d333c2f 100644 --- a/docs/ridge_lm.md +++ b/docs/ridge_lm.md @@ -269,7 +269,7 @@ float64; only go below that with a measured `gtol`. A `Metric` supplies the factor through four ops, each taking a metric-block vector — or a matrix whose *leading* axis is `size` (columns batched) — and -a `MetricContext` carrying everything the solver knows at the call site +a `SolverContext` carrying everything the solver knows at the call site (the flat iterate `x`, the live `LMState`, `args`, `p`; the shipped metrics ignore it, a custom metric may key off it): @@ -372,7 +372,7 @@ genuinely needs float64 selection should run the solve in float64. The `CG` config requires a typed `Preconditioner` in both roles: a subclass implementing `apply(v, damping, ctx)`, an SPD approximation of \((\tilde J^\top \tilde J + \lambda E + \mu I)^{-1}\) applied with the live -damping (zero in the AD role), receiving the same `MetricContext` as the +damping (zero in the AD role), receiving the same `SolverContext` as the metric ops. `IdentityPreconditioner()` is the explicit opt-out; a custom one is a small dataclass: @@ -536,7 +536,7 @@ Porting notes: ::: nlls_gram.Metric -::: nlls_gram.MetricContext +::: nlls_gram.SolverContext ::: nlls_gram.IdentityMetric diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index aa837f5..d441155 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -58,13 +58,13 @@ LMSolveResult, LMState, LMStatus, + SolverContext, ) from nlls_gram.lsmr import LSMRState, lsmr from nlls_gram.metrics import ( GramMetric, IdentityMetric, Metric, - MetricContext, RepeatedFactorMetric, metric_from_cholesky, metric_from_diagonal, @@ -113,7 +113,7 @@ "GramMetric", "IdentityMetric", "Metric", - "MetricContext", + "SolverContext", "MetricFactory", "MultiStart", "IdentityPreconditioner", diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py index ee2fea4..ce080f6 100644 --- a/src/nlls_gram/lm_types.py +++ b/src/nlls_gram/lm_types.py @@ -22,9 +22,40 @@ "LMSolveResult", "LMState", "LMStatus", + "SolverContext", ] +@jax.tree_util.register_dataclass +@dataclass(frozen=True) +class SolverContext: + """What the solver knows at a metric, preconditioner, or linear-solver + call site -- the inner algebra's context, as opposed to + :class:`LMSolveContext`, which a per-step user callback receives. + + Fields are ``None`` where the call site has nothing to offer: + + - ``x``: the current FLATTENED iterate (the whole parameter vector, not + just the metric block). + - ``lm_state``: the live :class:`LMState` (damping, ridge, caches). In the + implicit-AD rule this is the returned state under ``stop_gradient`` -- + inert conditioning data, like the ridge. + - ``args`` / ``p``: the residual's auxiliary data and differentiation + parameters as passed to ``solve``/``update``. + - ``metric_state`` / ``preconditioner_state``: the output of the metric's + and preconditioner's own ``prepare``, rebuilt from the live iterate on + accepted steps and reused across rejected ones. ``None`` for the + stateless default. + """ + + x: Any = None + lm_state: Any = None + args: Any = None + p: Any = None + metric_state: Any = None + preconditioner_state: Any = None + + class LMStatus(enum.IntEnum): """Integer status codes returned by ``solve``. diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index 8938bf6..9b8a5ed 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -5,7 +5,7 @@ factor callbacks for an invertible factor ``F`` with ``W = F'F`` -- :class:`IdentityMetric` is the plain-ridge case and :class:`RepeatedFactorMetric` the kernel workhorse (``repeats`` copies of one -block factor). Every callback receives a :class:`MetricContext` carrying the +block factor). Every callback receives a :class:`SolverContext` carrying the solver's live state, so exotic metrics can key off the iterate. :class:`GramMetric` (with :func:`metric_from_cholesky`, @@ -16,7 +16,6 @@ from collections.abc import Callable from dataclasses import dataclass, field -from typing import Any import jax import jax.numpy as jnp @@ -25,30 +24,6 @@ from nlls_gram import quasiseparable -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class MetricContext: - """Everything the solver knows at a factor-callback call site. - - Passed as the second positional argument of every :class:`Metric` op. - The shipped metrics ignore it; a custom metric may key its factor off any - field. Fields are ``None`` where the call site has nothing to offer: - - - ``x``: the current FLATTENED iterate (the full parameter vector, not - just the metric block). - - ``lm_state``: the live :class:`~nlls_gram.LMState` (damping, - ridge, caches). In the implicit-AD rule this is the returned state - under ``stop_gradient`` -- inert conditioning data, like the ridge. - - ``args`` / ``p``: the residual's auxiliary data and differentiation - parameters as passed to ``solve``/``update``. - """ - - x: Any = None - lm_state: Any = None - args: Any = None - p: Any = None - - class Metric: """Positive-definite metric ``W`` on the metric block, via factor callbacks. @@ -65,7 +40,7 @@ class Metric: Subclasses implement the ops on metric-block vectors (or matrices whose LEADING axis is ``size``; columns are batched), each also receiving a - :class:`MetricContext` with the solver's live state: + :class:`SolverContext` with the solver's live state: - ``factor_apply(v, ctx)``: ``F v`` - ``factor_solve(v, ctx)``: ``F^{-1} v`` @@ -91,6 +66,29 @@ class Metric: size: int + def prepare(self, theta, ctx): + """Build this metric's numeric state from the current iterate. + + The default is ``None`` -- a fixed metric, whose state slot compiles + away. Override for an iterate-dependent metric (a kernel Gram factor + over state points that live in ``x``, say): the returned pytree rides + on ``lm_state.metric_state`` and comes back as ``ctx.metric_state`` in + the factor ops. It is rebuilt on accepted steps and reused across + rejected ones, and is FROZEN at the solution under implicit AD -- the + state-dependence is not differentiated, the same contract as a fixed + metric closing over constants. Its pytree structure must not change + between rebuilds. + + Unlike a preconditioner, the metric defines the subproblem, so the + factor it yields must be exact for the state it was built from. + """ + return None + + def rebuild(self, ctx): + """Traced predicate gating a rebuild on an accepted step. The default + rebuilds every accepted step.""" + return True + def factor_apply(self, v, ctx): """``F v`` for a metric-block vector or leading-axis-batched matrix.""" raise NotImplementedError diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index 9a437e8..f5f6f3a 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -3,7 +3,7 @@ :class:`Preconditioner` (with :class:`IdentityPreconditioner`) is the typed hook of :class:`~nlls_gram.RidgeLevenbergMarquardt`'s ``CG`` config: an SPD approximation of the damped whitened normal inverse, receiving the live -solver state through a :class:`~nlls_gram.MetricContext`. +solver state through a :class:`~nlls_gram.SolverContext`. The remaining helpers serve ``LevenbergMarquardt``'s string-named solver menu: a ``dual_preconditioner(v, damping)`` callback supplies an @@ -14,6 +14,7 @@ """ from dataclasses import dataclass +from typing import Any import jax import jax.numpy as jnp @@ -28,7 +29,7 @@ class Preconditioner: vectors. In the forward role (``linear_solver=CG(...)``) it sits in CG's ``M`` slot with the live damping; in the AD role (``ad_solver=CG(...)``) the implicit-AD system is undamped and ``damping`` is zero. ``ctx`` is - the same :class:`~nlls_gram.MetricContext` the metric factor ops receive + the same :class:`~nlls_gram.SolverContext` the metric factor ops receive (the flat iterate, the live ``LMState``, ``args``, ``p``), so a preconditioner can key off the solver state. A preconditioner changes the CG iteration path, never the subproblem being solved, so @@ -52,6 +53,33 @@ def apply(self, v, damping, ctx): requires_positive_damping = False + def prepare(self, theta, ctx): + """Build this preconditioner's numeric state from the current iterate. + + The default is ``None`` -- a stateless preconditioner, whose state + slot compiles away. Override to hold traced arrays that must track the + iterate: the returned pytree rides on ``lm_state.precond`` and comes + back as ``ctx.preconditioner_state`` in :meth:`apply`. It is rebuilt on + accepted steps and reused across rejected ones (where ``x`` did not + move), runs inside the jitted loop as traced ops, and is frozen at the + solution under implicit AD. Its pytree structure must not change + between rebuilds. + + Expensive setup that does NOT depend on the iterate belongs in + ``__init__``, where it is paid once. + """ + return None + + def rebuild(self, ctx): + """Traced predicate gating a rebuild on an accepted step. + + The default rebuilds every accepted step. Return ``False`` to keep the + carried state -- staleness only changes the CG iteration path, never + the converged step, so declining is always safe and often much + cheaper (e.g. rebuild only when ridge continuation advances a level). + """ + return True + def apply(self, v, damping, ctx): raise NotImplementedError @@ -70,54 +98,53 @@ def apply(self, v, damping, ctx): return v -@dataclass(frozen=True) +@dataclass(frozen=True, eq=False) class BlockEigenPreconditioner(Preconditioner): - """Block-diagonal eigenbasis preconditioner whose state rides in ``args``. + """Block-diagonal eigenbasis preconditioner that owns its state. The workhorse for structured whitened normal operators ``J~'J~ + ridge E + damping I`` built from repeated interacting blocks (multiple "agents" coupled through shared equations): approximate the operator by a block-diagonal matrix over a chosen grouping of the - whitened coordinates, eigendecompose each block ONCE at build time, and - apply the exact inverse of the shifted approximation + whitened coordinates, eigendecompose each block, and apply the exact + inverse of the shifted approximation v -> V ((V' v) / (Lambda + ridge_weight * ridge + damping)) V' - per block -- analytic in both the live ``damping`` (traced; it changes - per LM step) and the live ``ridge`` (read from ``ctx.lm_state.ridge``, - so ridge continuation composes with no rebuild). Families whose - coordinates lie in the metric block set ``ridge_weight = 1`` (their - diagonal carries the ``ridge`` spectral floor); free-block families set - ``0`` (damping-only, and the zero-damping AD role then applies their - plain inverse -- positive definite whenever the free block is - identified). - - The instance itself is STATELESS and hashes by value on ``args_key`` - alone, so equal ``CG`` configs share one compiled solve loop and a - rebuilt state never retraces. The numeric state -- a pytree built by - :func:`block_eigen_state` -- lives at ``ctx.args[args_key]``: pass it as - ``solve(x0, {args_key: state, ...})``, and rebuild it adaptively from a - solve callback returning ``LMSolveAction(args=...)`` (rebuild when - ridge continuation advances a level: the level change already suppresses - that step's convergence test, so the swap is free; identical returned - values suppress nothing). A stale or approximate state only changes the - CG iteration path, never the converged step. + per block -- analytic in both the live ``damping`` (traced; it changes per + LM step) and the live ``ridge`` (read from ``ctx.lm_state.ridge``, so + ridge continuation composes with no rebuild). + + ``blocks_fn(theta, ctx)`` returns the family list that + :func:`block_eigen_state` packs: ``(blocks, ridge_weight)`` pairs whose + ``blocks`` has shape ``(groups, size, size)`` -- the stacked diagonal + blocks of ``J~'J~`` restricted to that family's coordinate groups, in + permuted order. Families in the metric block set ``ridge_weight = 1`` + (their diagonal carries the ``ridge`` spectral floor); free-block families + set ``0`` (damping-only, so the zero-damping AD role applies their plain + inverse -- positive definite whenever the free block is identified). + ``permutation`` reorders the flattened whitened vector into family-major + order; ``jnp.arange(n)`` serves when the natural layout already is. + + The eigendecomposition runs in :meth:`prepare` from the live iterate, so + it is rebuilt on accepted steps and reused across rejected ones. Override + ``rebuild`` to decline -- a stale state only changes the CG iteration + path, never the converged step, so refreshing only when ridge continuation + advances a level is a pure saving:: + + class OnLevelChange(BlockEigenPreconditioner): + def rebuild(self, ctx): + return ctx.lm_state.ridge < self.last_ridge """ - args_key: str = "preconditioner" + blocks_fn: Any + permutation: jax.Array + + def prepare(self, theta, ctx): + return block_eigen_state(self.blocks_fn(theta, ctx), self.permutation) def apply(self, v, damping, ctx): - if ctx.args is None or self.args_key not in ctx.args: - raise ValueError( - "BlockEigenPreconditioner reads its state from " - f"ctx.args[{self.args_key!r}]; pass the block_eigen_state(...) " - "pytree under that key in the residual args" - ) - state = ctx.args[self.args_key] - if ctx.lm_state is None: - raise ValueError( - "BlockEigenPreconditioner needs ctx.lm_state for the live ridge weight" - ) + state = ctx.preconditioner_state ridge = jnp.asarray(ctx.lm_state.ridge, dtype=v.dtype) permuted = v[state["permutation"]] pieces = [] diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index c317399..9ed3a61 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -40,10 +40,12 @@ LMInfo, LMSolveAction, LMState, + SolverContext, _cast_hyper, _damping_floor, ) -from nlls_gram.metrics import MetricContext +from nlls_gram.metrics import Metric +from nlls_gram.preconditioners import Preconditioner from nlls_gram.utilities import ( _static_key_component, _zero_tangent_leaf, @@ -273,7 +275,7 @@ class RidgeLevenbergMarquardt(LevenbergMarquardtBase): :class:`~nlls_gram.Preconditioner` (:class:`~nlls_gram.IdentityPreconditioner` opts out): its ``apply(v, damping, ctx)`` -- an SPD approximation of the damped - inverse, handed the same :class:`~nlls_gram.MetricContext` as the + inverse, handed the same :class:`~nlls_gram.SolverContext` as the metric ops -- sits in CG's ``M`` slot with the live damping. The operator carries the ``ridge`` spectral floor on the metric block, so the preconditioner only has to capture ``J~'J~``'s structure. @@ -453,6 +455,15 @@ def __init__( self.cache_jacobian = cache_jacobian and not isinstance(linear_solver, CG) self.geodesic_acceleration = geodesic_acceleration self.geodesic_acceptance_ratio = geodesic_acceptance_ratio + # The forward preconditioner is the one whose prepared state is carried + # (the AD role runs once, at the solution). Whether a hook is stateful + # is a static property of its class, so the slots and their lax.cond + # compile away entirely for the stateless default. + self.preconditioner = self.normal_cg_preconditioner + self._metric_prepares = type(metric).prepare is not Metric.prepare + self._precond_prepares = self.preconditioner is not None and ( + type(self.preconditioner).prepare is not Preconditioner.prepare + ) # Value-based identity: the jitted solve loop marks the solver itself # static, so equal-config solvers built around the same residual and # metric share the compiled loop across instances. Keyed on the @@ -553,22 +564,81 @@ def init(self, x0, args=None, *, p=None): min_damping = _damping_floor(self.min_damping, dtype) damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) ridge = self._resolve_ridge(dtype) + # Hook state is built at x0 and VALID there, so the first update + # reuses it; the flags stay None when the hooks are stateless. + hooks = {} + ctx = SolverContext(x=theta, args=args, p=p) + valid = jnp.asarray(True, dtype=jnp.bool_) + if self._metric_prepares: + hooks["metric_state"] = self.metric.prepare(theta, ctx) + hooks["metric_valid"] = valid + if self._precond_prepares: + hooks["precond"] = self.preconditioner.prepare(theta, ctx) + hooks["precond_valid"] = valid if not self.cache_jacobian: - return LMState(damping, ridge) + return LMState(damping, ridge, **hooks) p_dim = theta.size m = residual.size - invalid = jnp.asarray(False, dtype=jnp.bool_) - common = dict( - resid=jnp.zeros(residual.shape, dtype=dtype), - Jt=jnp.zeros((p_dim, m), dtype=dtype), - jacobian_valid=invalid, - aux=jax.tree.map(jnp.zeros_like, aux), - ) return LMState( damping, ridge, - **common, + resid=jnp.zeros(residual.shape, dtype=dtype), + Jt=jnp.zeros((p_dim, m), dtype=dtype), + jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), + aux=jax.tree.map(jnp.zeros_like, aux), solver_cache=self.linear_solver.new_cache(m, p_dim, n_m, dtype), + **hooks, + ) + + def _hook_state(self, theta, lm_state, args, p): + """The metric's and preconditioner's prepared state for this step: + reused while still valid (a rejected step left ``x`` in place, or the + hook declined to rebuild), rebuilt from the live iterate otherwise.""" + bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) + metric_state = precond_state = None + if self._metric_prepares: + metric_state = jax.lax.cond( + lm_state.metric_valid | ~jnp.asarray(self.metric.rebuild(bare)), + lambda _: lm_state.metric_state, + lambda _: self.metric.prepare(theta, bare), + operand=None, + ) + if self._precond_prepares: + precond_state = jax.lax.cond( + lm_state.precond_valid + | ~jnp.asarray(self.preconditioner.rebuild(bare)), + lambda _: lm_state.precond, + lambda _: self.preconditioner.prepare(theta, bare), + operand=None, + ) + return metric_state, precond_state + + def _carried_ctx(self, theta, lm_state, args, p): + return SolverContext( + x=theta, + lm_state=lm_state, + args=args, + p=p, + metric_state=lm_state.metric_state, + preconditioner_state=lm_state.precond, + ) + + def _frozen_ctx(self, theta, lm_state, args, p, preconditioner): + # Under implicit AD the hooks are FROZEN at the returned solution: + # prepare runs once there and the state-dependence is not + # differentiated, the same contract as a fixed metric closing over + # constants. + bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) + metric_state = ( + self.metric.prepare(theta, bare) if self._metric_prepares else None + ) + precond_state = None + if preconditioner is not None and ( + type(preconditioner).prepare is not Preconditioner.prepare + ): + precond_state = preconditioner.prepare(theta, bare) + return dataclasses.replace( + bare, metric_state=metric_state, preconditioner_state=precond_state ) def _initial_info(self, x, lm_state, args, p): @@ -580,7 +650,7 @@ def _initial_info(self, x, lm_state, args, p): theta, _ = ravel_pytree(x) ridge = jnp.asarray(lm_state.ridge, dtype=residual.dtype) n_m = self._block_sizes(theta.shape[0])[0] - ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) + ctx = self._carried_ctx(theta, lm_state, args, p) y_m = jnp.asarray( self.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype ) @@ -679,7 +749,15 @@ def JT(cotangent): # including the reported norms -- is the whitened one. y_m doubles as # the pre-step penalty value ||y_m||^2. n_m, n_f = self._block_sizes(theta.shape[0]) - ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) + metric_state, precond_state = self._hook_state(theta, lm_state, args, p) + ctx = SolverContext( + x=theta, + lm_state=lm_state, + args=args, + p=p, + metric_state=metric_state, + preconditioner_state=precond_state, + ) y_m = jnp.asarray(self.metric.factor_apply(theta[:n_m], ctx), dtype=resid.dtype) penalty_value_old = jnp.sum(y_m**2) penalty_gradient = jnp.concatenate([y_m, jnp.zeros(n_f, dtype=resid.dtype)]) @@ -812,11 +890,18 @@ def accelerated_objective(_): loss = jnp.where(improved, loss_candidate, loss_old) resid_loss = jnp.where(improved, resid_loss_candidate, resid_loss_old) penalty_value = jnp.where(improved, penalty_candidate, penalty_value_old) - # Thread the caches built at this step's pre-step (x, ridge): - # valid = ~improved marks them reusable exactly when the step was - # rejected (x did not move). ridge passes through unchanged -- only - # init() and callbacks set it. The input hyper (not the fallback) - # passes through so the loop carry structure is stable. + # Thread the caches and prepared hook state built at this step's + # pre-step (x, ridge): valid = ~improved marks them reusable exactly + # when the step was rejected (x did not move). ridge passes through + # unchanged -- only init() and callbacks set it. The input hyper (not + # the fallback) passes through so the loop carry structure is stable. + hooks = {} + if self._metric_prepares: + hooks["metric_state"] = metric_state + hooks["metric_valid"] = ~improved + if self._precond_prepares: + hooks["precond"] = precond_state + hooks["precond_valid"] = ~improved if self.cache_jacobian: new_lm_state = LMState( new_damping, @@ -827,9 +912,10 @@ def accelerated_objective(_): aux, lm_state.hyper, solver_cache=step_solver.make_cache(~improved), + **hooks, ) else: - new_lm_state = LMState(new_damping, ridge, hyper=lm_state.hyper) + new_lm_state = LMState(new_damping, ridge, hyper=lm_state.hyper, **hooks) return ( unravel(theta_new), new_lm_state, @@ -957,6 +1043,9 @@ def _cold_state(self, lm_state): updates["solver_cache"] = jax.tree.map( jnp.zeros_like, lm_state.solver_cache ) + for flag in ("metric_valid", "precond_valid"): + if getattr(lm_state, flag) is not None: + updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) if not updates: return lm_state return dataclasses.replace(lm_state, **updates) @@ -973,9 +1062,7 @@ def _ranking_objective(self, result, p, callback): residual = self._residual_and_aux(result.x, result.args, p)[0] theta, _ = ravel_pytree(result.x) n_m = self._block_sizes(theta.shape[0])[0] - ctx = MetricContext( - x=theta, lm_state=result.lm_state, args=result.args, p=p - ) + ctx = self._carried_ctx(theta, result.lm_state, result.args, p) ridge = jnp.asarray(result.lm_state.ridge, dtype=residual.dtype) y_m = jnp.asarray( self.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype @@ -997,7 +1084,7 @@ def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point) # A successful tangent uses the winner's own final ridge; a failed one # the pre-loop initial ridge. Both are stop-gradient'd -- lambda is # inert conditioning data, and the returned state rides along as - # equally inert MetricContext data for the factor callbacks. + # equally inert SolverContext data for the factor callbacks. final_ridge = jax.lax.stop_gradient(result.lm_state.ridge) initial_ridge = jax.lax.stop_gradient(initial_ad_point[3]) ridge = jnp.where( @@ -1031,7 +1118,7 @@ def _ad_tangent_cholesky(self, x, args, p, p_dot, ridge, lm_state): x, args, p, p_dot ) n_m = self._block_sizes(theta.shape[0])[0] - ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) + ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) Jt = self._assemble_jt(theta_jvp, theta, residual) ridge_typed = jnp.asarray(ridge, dtype=residual.dtype) Jt_sub = jnp.asarray( @@ -1051,7 +1138,7 @@ def _ad_tangent_normal_cg(self, x, args, p, p_dot, ridge, lm_state): x, args, p, p_dot ) n_m, n_f = self._block_sizes(theta.shape[0]) - ctx = MetricContext(x=theta, lm_state=lm_state, args=args, p=p) + ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) theta_transpose = jax.linear_transpose(theta_jvp, theta) def JT(cotangent): diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index d2b0ab0..7269b17 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -1763,13 +1763,11 @@ def test_float64_block_eigen_preconditioner_default_precision(): CG, BlockEigenPreconditioner, Cholesky, - LMSolveAction, LMStatus, - MetricContext, + SolverContext, RepeatedFactorMetric, RidgeLevenbergMarquardt, LMState, - block_eigen_state, ) # apply == dense inverse of the shifted block-diagonal approximation, at @@ -1785,15 +1783,16 @@ def spd_blocks(key, groups, size): family_a = spd_blocks(keys[0], 2, 3) family_free = spd_blocks(keys[1], 1, 2) permutation = jnp.asarray(np.random.default_rng(0).permutation(8)) -state = block_eigen_state([(family_a, 1.0), (family_free, 0.0)], permutation) +families = [(family_a, 1.0), (family_free, 0.0)] +preconditioner = BlockEigenPreconditioner(lambda theta, ctx: families, permutation) +state = preconditioner.prepare(jnp.zeros(8), None) for leaf in jax.tree.leaves(state["families"]): assert leaf.dtype == jnp.float64, leaf.dtype ridge = 3e-9 -ctx = MetricContext( +ctx = SolverContext( lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), - args={"preconditioner": state}, + preconditioner_state=state, ) -preconditioner = BlockEigenPreconditioner() v = jax.random.normal(keys[2], (8,)) selection = jnp.eye(8)[permutation] dense_permuted = jsp_linalg.block_diag(family_a[0], family_a[1], family_free[0]) @@ -1831,14 +1830,18 @@ def residual(x, args, p): F_bar = jsp_linalg.block_diag(F, F, jnp.eye(N_F)) J_whitened = jnp.linalg.solve(F_bar.T, A.T).T G = J_whitened.T @ J_whitened -exact_state = block_eigen_state( - [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)], - jnp.arange(P_DIM), -) +def exact_blocks(theta, ctx): + return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] + + +def exact_preconditioner(): + return BlockEigenPreconditioner(exact_blocks, jnp.arange(P_DIM)) + + p_value = {"scale": jnp.asarray(1.0)} p_dot = {"scale": jnp.asarray(1.0)} x0 = jnp.zeros(P_DIM) -args = {"data": jnp.asarray(1.0), "preconditioner": exact_state} +args = {"data": jnp.asarray(1.0)} solve_options = dict(max_steps=80, gtol=1e-10, xtol=1e-14) reference_solver = RidgeLevenbergMarquardt( @@ -1848,30 +1851,14 @@ def residual(x, args, p): assert int(reference.status) == int(LMStatus.CONVERGED) -def rebuild_callback(ctx): - fresh = block_eigen_state( - [(1.25 * G[:N_M, :N_M][None], 1.0), (1.25 * G[N_M:, N_M:][None], 0.0)], - jnp.arange(P_DIM), - ) - swap = ctx.step == 2 - new_state = jax.tree_util.tree_map( - lambda old, new: jnp.where(swap, new, old), - ctx.args["preconditioner"], - fresh, - ) - return LMSolveAction(args={**ctx.args, "preconditioner": new_state}) - - cg_solver = RidgeLevenbergMarquardt( residual, metric=metric, ridge=RIDGE, - linear_solver=CG(BlockEigenPreconditioner(), tol=1e-12, maxiter=400), - ad_solver=CG(BlockEigenPreconditioner(), tol=1e-12, maxiter=400), -) -result = cg_solver.solve( - x0, args, p=p_value, callback=rebuild_callback, **solve_options + linear_solver=CG(exact_preconditioner(), tol=1e-12, maxiter=400), + ad_solver=CG(exact_preconditioner(), tol=1e-12, maxiter=400), ) +result = cg_solver.solve(x0, args, p=p_value, **solve_options) assert int(result.status) == int(LMStatus.CONVERGED) # Matched to the tangent comparison below. The two solves stop on the same # gtol, and a ridge-scaled stopping rule leaves x-slack ~ gtol / ridge diff --git a/tests/test_ridge_lm.py b/tests/test_ridge_lm.py index 437bf7c..6f594d2 100644 --- a/tests/test_ridge_lm.py +++ b/tests/test_ridge_lm.py @@ -431,7 +431,7 @@ def scalar_residual(theta): def test_normal_cg_preconditioner_changes_nothing(): # M changes the CG iteration path, never the solved subproblem: a # Jacobi-style SPD Preconditioner subclass must reproduce the identity-M - # step -- and it receives the live MetricContext. + # step -- and it receives the live SolverContext. seen = [] @dataclasses.dataclass(frozen=True, eq=False) diff --git a/tests/test_ridge_metrics.py b/tests/test_ridge_metrics.py index a92dc79..1011ab7 100644 --- a/tests/test_ridge_metrics.py +++ b/tests/test_ridge_metrics.py @@ -6,15 +6,15 @@ from nlls_gram import ( IdentityMetric, - MetricContext, RepeatedFactorMetric, RidgeLevenbergMarquardt, + SolverContext, ) REPEATS = 3 BLOCK = 5 N_M = REPEATS * BLOCK -CTX = MetricContext() +CTX = SolverContext() def make_factor(key, size): @@ -108,7 +108,7 @@ def test_constructor_and_input_validation(): def test_solver_passes_live_context_to_the_factor_ops(): - # Every factor op receives a MetricContext carrying the flat iterate and + # Every factor op receives a SolverContext carrying the flat iterate and # the live LMState (recorded at trace time -- the fields are # tracers, their presence and shapes are static). seen = [] diff --git a/tests/test_ridge_preconditioners.py b/tests/test_ridge_preconditioners.py index f360e3c..8746223 100644 --- a/tests/test_ridge_preconditioners.py +++ b/tests/test_ridge_preconditioners.py @@ -1,9 +1,5 @@ -# Float32 coverage for BlockEigenPreconditioner (plus the precision-neutral -# contract tests: hashing, errors, retrace behavior). The float64 primary -# coverage lives in test_float64_subprocess.py, matching the production -# default. -import dataclasses - +# Float32 coverage for BlockEigenPreconditioner. The float64 primary coverage +# lives in test_float64_subprocess.py, matching the production default. import jax import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg @@ -14,12 +10,11 @@ CG, BlockEigenPreconditioner, Cholesky, - LMSolveAction, LMState, LMStatus, - MetricContext, RepeatedFactorMetric, RidgeLevenbergMarquardt, + SolverContext, block_eigen_state, ) @@ -29,62 +24,39 @@ def spd_blocks(key, groups, size): return jnp.einsum("gik,gjk->gij", root, root) + 0.5 * jnp.eye(size) -def packed_state(key): +@pytest.mark.parametrize("damping", [0.0, 0.37]) +def test_apply_matches_dense_inverse(damping): # Two ridge-flagged families (2 groups of 3, 1 group of 4) and one - # damping-only free family (1 group of 2), under a nontrivial - # permutation of the 12 coordinates. - keys = jax.random.split(key, 3) + # damping-only free family (1 group of 2), under a nontrivial permutation + # of the 12 coordinates. + keys = jax.random.split(jax.random.key(0), 3) family_a = spd_blocks(keys[0], 2, 3) family_b = spd_blocks(keys[1], 1, 4) family_free = spd_blocks(keys[2], 1, 2) permutation = jnp.asarray(np.random.default_rng(0).permutation(12)) - state = block_eigen_state( - [(family_a, 1.0), (family_b, 1.0), (family_free, 0.0)], permutation - ) + families = [(family_a, 1.0), (family_b, 1.0), (family_free, 0.0)] dense_permuted = jsp_linalg.block_diag( family_a[0], family_a[1], family_b[0], family_free[0] ) ridge_mask = jnp.concatenate([jnp.ones(10), jnp.zeros(2)]) - return state, dense_permuted, ridge_mask, permutation - - -@pytest.mark.parametrize("damping", [0.0, 0.37]) -def test_apply_matches_dense_inverse(damping): - state, dense_permuted, ridge_mask, permutation = packed_state(jax.random.key(0)) ridge = 0.05 - ctx = MetricContext( + + preconditioner = BlockEigenPreconditioner(lambda theta, ctx: families, permutation) + ctx = SolverContext( lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), - args={"preconditioner": state}, + preconditioner_state=preconditioner.prepare(jnp.zeros(12), None), ) - preconditioner = BlockEigenPreconditioner() v = jax.random.normal(jax.random.key(1), (12,)) selection = jnp.eye(12)[permutation] shifted = dense_permuted + jnp.diag(ridge_mask * ridge + damping) - dense_original = selection.T @ shifted @ selection - expected = jnp.linalg.solve(dense_original, v) + expected = jnp.linalg.solve(selection.T @ shifted @ selection, v) result = preconditioner.apply(v, jnp.asarray(damping), ctx) np.testing.assert_allclose(result, expected, rtol=2e-4, atol=2e-5) -def test_value_hashing_and_config_equality(): - assert BlockEigenPreconditioner() == BlockEigenPreconditioner("preconditioner") - assert hash(BlockEigenPreconditioner("k")) == hash(BlockEigenPreconditioner("k")) - assert BlockEigenPreconditioner("a") != BlockEigenPreconditioner("b") - assert CG(BlockEigenPreconditioner(), maxiter=64) == CG( - BlockEigenPreconditioner(), maxiter=64 - ) - - -def test_missing_state_and_bad_builder_inputs(): - preconditioner = BlockEigenPreconditioner() - ctx = MetricContext( - lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(1e-3)), - args={"other": 1.0}, - ) - with pytest.raises(ValueError, match="ctx.args"): - preconditioner.apply(jnp.ones(3), jnp.asarray(0.1), ctx) +def test_block_eigen_state_rejects_mismatched_layouts(): with pytest.raises(ValueError, match="permutation"): block_eigen_state([(jnp.eye(2)[None], 1.0)], jnp.zeros(2)) with pytest.raises(ValueError, match="groups, size, size"): @@ -100,6 +72,7 @@ def test_missing_state_and_bad_builder_inputs(): P_DIM = N_M + N_F M_RESID = 14 RIDGE = 1e-3 +SOLVE_OPTIONS = dict(max_steps=60, gtol=1e-5, xtol=1e-7) def build_problem(): @@ -119,160 +92,113 @@ def residual(x, args, p): return metric, residual, G -def exact_state(G): - # The exact whitened normal blocks: one metric-block group, one free - # group -- close enough to the operator that CG converges in a handful - # of iterations. - return block_eigen_state( - [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)], - jnp.arange(P_DIM), +def exact_preconditioner(G): + # The exact whitened normal blocks -- one metric-block group, one free + # group -- so CG converges in a handful of iterations. The residual is + # linear, so the operator does not move with the iterate and blocks_fn + # ignores theta. + def blocks_fn(theta, ctx): + return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] + + return BlockEigenPreconditioner(blocks_fn, jnp.arange(P_DIM)) + + +def cholesky_reference(metric, residual): + return RidgeLevenbergMarquardt( + residual, metric=metric, ridge=RIDGE, linear_solver=Cholesky() ) -def test_cg_solve_matches_cholesky_with_callback_rebuild(): +def test_cg_solve_matches_cholesky(): metric, residual, G = build_problem() p = {"scale": jnp.asarray(1.0)} x0 = jnp.zeros(P_DIM) - args = {"data": jnp.asarray(1.0), "preconditioner": exact_state(G)} - solve_options = dict(max_steps=60, gtol=1e-5, xtol=1e-7) + args = {"data": jnp.asarray(1.0)} - reference = RidgeLevenbergMarquardt( - residual, metric=metric, ridge=RIDGE, linear_solver=Cholesky() - ).solve(x0, args, p=p, **solve_options) + reference = cholesky_reference(metric, residual).solve( + x0, args, p=p, **SOLVE_OPTIONS + ) assert int(reference.status) == int(LMStatus.CONVERGED) - def rebuild_callback(ctx): - # A real state swap mid-solve: scaled blocks at step 2 (values - # change -> args replacement path exercised, convergence suppressed - # for that step only). - fresh = block_eigen_state( - [(1.25 * G[:N_M, :N_M][None], 1.0), (1.25 * G[N_M:, N_M:][None], 0.0)], - jnp.arange(P_DIM), - ) - swap = ctx.step == 2 - new_state = jax.tree_util.tree_map( - lambda old, new: jnp.where(swap, new, old), - ctx.args["preconditioner"], - fresh, - ) - return LMSolveAction(args={**ctx.args, "preconditioner": new_state}) - cg_solver = RidgeLevenbergMarquardt( residual, metric=metric, ridge=RIDGE, - linear_solver=CG(BlockEigenPreconditioner(), tol=1e-7, maxiter=200), + linear_solver=CG(exact_preconditioner(G), tol=1e-7, maxiter=200), ) - result = cg_solver.solve(x0, args, p=p, callback=rebuild_callback, **solve_options) + result = cg_solver.solve(x0, args, p=p, **SOLVE_OPTIONS) assert int(result.status) == int(LMStatus.CONVERGED) # Both solves stop on the same gtol, and a ridge-scaled stopping rule # leaves x-slack ~ gtol / ridge (1e-2 here), so the agreement of two # independently converged solves is a measured property rather than a - # CG-tolerance bound -- platform BLAS ordering moves the last accepted - # step. Kept an order below that slack: tight enough to catch a wrong - # preconditioner (which breaks convergence outright) with real margin. + # CG-tolerance bound. Kept an order below that slack: tight enough to + # catch a wrong preconditioner (which breaks convergence outright). np.testing.assert_allclose(result.x, reference.x, rtol=2e-3, atol=2e-4) -def test_ad_role_zero_damping_matches_cholesky_tangent(): - # The EXPLICIT ad_solver config pins the AD CG's tol/maxiter (the - # ad_solver=None inheritance path is covered separately below). +def test_prepared_state_is_rebuilt_from_the_live_iterate(): + # blocks_fn sees the whitened iterate: a counter proves prepare runs + # inside the loop, and the carried state tracks it. metric, residual, G = build_problem() - p = {"scale": jnp.asarray(1.0)} - p_dot = {"scale": jnp.asarray(1.0)} - x0 = jnp.zeros(P_DIM) - args = {"data": jnp.asarray(1.0), "preconditioner": exact_state(G)} - solve_options = dict(max_steps=60, gtol=1e-5, xtol=1e-7) - - def solved_x(solver): - def run(p_value): - return solver.solve(x0, args, p=p_value, **solve_options).x + seen = [] - return jax.jvp(run, (p,), (p_dot,))[1] + def blocks_fn(theta, ctx): + seen.append(theta) + return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] - reference = solved_x( - RidgeLevenbergMarquardt( - residual, metric=metric, ridge=RIDGE, linear_solver=Cholesky() - ) + solver = RidgeLevenbergMarquardt( + residual, + metric=metric, + ridge=RIDGE, + linear_solver=CG( + BlockEigenPreconditioner(blocks_fn, jnp.arange(P_DIM)), + tol=1e-7, + maxiter=200, + ), ) - cg_tangent = solved_x( - RidgeLevenbergMarquardt( - residual, - metric=metric, - ridge=RIDGE, - linear_solver=CG(BlockEigenPreconditioner(), tol=1e-7, maxiter=200), - ad_solver=CG(BlockEigenPreconditioner(), tol=1e-7, maxiter=200), - ) + x0 = jnp.zeros(P_DIM) + state = solver.init(x0, {"data": jnp.asarray(1.0)}, p={"scale": jnp.asarray(1.0)}) + # init builds the state at x0 and marks it valid there. + assert state.precond is not None + assert bool(state.precond_valid) + assert len(seen) == 1 + x1, state1, info = solver.update( + x0, state, {"data": jnp.asarray(1.0)}, {"scale": jnp.asarray(1.0)} ) - np.testing.assert_allclose(cg_tangent, reference, rtol=1e-3, atol=1e-4) + # An accepted step moved x, so the carried state is marked for rebuild. + assert bool(info.accepted) + assert not bool(state1.precond_valid) -def test_ad_solver_none_inherits_forward_cg_preconditioner(): - # ad_solver=None under a CG forward hands the forward preconditioner to - # the undamped implicit solve (the typed apply is damping-analytic at - # zero damping), keeping the AD-default tolerance and budget. +@pytest.mark.parametrize("explicit_ad_solver", [True, False]) +def test_ad_tangent_matches_cholesky(explicit_ad_solver): + # The zero-damping AD role applies the same typed preconditioner. With + # ad_solver=None the forward config's preconditioner is inherited, at the + # AD-default tolerance and budget. metric, residual, G = build_problem() p = {"scale": jnp.asarray(1.0)} p_dot = {"scale": jnp.asarray(1.0)} x0 = jnp.zeros(P_DIM) - args = {"data": jnp.asarray(1.0), "preconditioner": exact_state(G)} - solve_options = dict(max_steps=60, gtol=1e-5, xtol=1e-7) - - inheriting = RidgeLevenbergMarquardt( - residual, - metric=metric, - ridge=RIDGE, - linear_solver=CG(BlockEigenPreconditioner(), tol=1e-7, maxiter=200), - ) - assert inheriting.ad_solver_preconditioner == BlockEigenPreconditioner() - assert inheriting.ad_solver_tol is None - assert inheriting.ad_solver_maxiter is None + args = {"data": jnp.asarray(1.0)} def solved_x(solver): def run(p_value): - return solver.solve(x0, args, p=p_value, **solve_options).x + return solver.solve(x0, args, p=p_value, **SOLVE_OPTIONS).x return jax.jvp(run, (p,), (p_dot,))[1] - reference = solved_x( - RidgeLevenbergMarquardt( - residual, metric=metric, ridge=RIDGE, linear_solver=Cholesky() - ) + forward = CG(exact_preconditioner(G), tol=1e-7, maxiter=200) + ad_solver = ( + CG(exact_preconditioner(G), tol=1e-7, maxiter=200) + if explicit_ad_solver + else None ) - np.testing.assert_allclose(solved_x(inheriting), reference, rtol=1e-3, atol=1e-4) - - -def test_state_dataclass_survives_jit_boundary(): - # The instance is a static config field: equal instances must not - # retrace when only the args-carried state values change. - state, _, _, _ = packed_state(jax.random.key(5)) - preconditioner = BlockEigenPreconditioner() - traces = [] - - @jax.jit - def apply(v, damping, ridge, state): - traces.append(None) - ctx = MetricContext( - lm_state=LMState(damping=damping, ridge=ridge), - args={"preconditioner": state}, - ) - return preconditioner.apply(v, damping, ctx) - - v = jax.random.normal(jax.random.key(6), (12,)) - first = apply(v, jnp.asarray(0.1), jnp.asarray(0.01), state) - doubled = { - **state, - "families": tuple( - {**family, "eigenvalues": 2.0 * family["eigenvalues"]} - for family in state["families"] - ), - } - second = apply(v, jnp.asarray(0.1), jnp.asarray(0.01), doubled) - assert len(traces) == 1 - assert not jnp.allclose(first, second) - + cg_solver = RidgeLevenbergMarquardt( + residual, metric=metric, ridge=RIDGE, linear_solver=forward, ad_solver=ad_solver + ) + if not explicit_ad_solver: + assert cg_solver.ad_solver_preconditioner is forward.preconditioner + assert cg_solver.ad_solver_tol is None -def test_dataclass_replace_keeps_identity(): - config = CG(BlockEigenPreconditioner(), maxiter=32) - replaced = dataclasses.replace(config, maxiter=64) - assert replaced.preconditioner == config.preconditioner + reference = solved_x(cholesky_reference(metric, residual)) + np.testing.assert_allclose(solved_x(cg_solver), reference, rtol=1e-3, atol=1e-4) From 3fefd37b39ddf12bf4265abf712d1da447f1f484 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 01:30:17 -0700 Subject: [PATCH 04/22] refactor!: one Metric, one solver menu, one implicit-AD contract The metric solver moves onto everything the ridge solver already had. GramMetric is gone. With M = F'F its four optional callables are the ridge Metric's factor ops at identical cost -- inv_sqrt IS factor_solve, "whiten" and "unwhiten" ARE the factor solves -- so both solvers now take one Metric, and _validate_metric_requirements (the which-callbacks-does-this-solver-need matrix) has nothing left to check. metric_from_cholesky/metric_from_diagonal become CholeskyMetric/DiagonalMetric, and repeated_shifted_dense_metric becomes RepeatedFactorMetric.from_gram, with the old zero-pad tail now the solver's free block weighted by Metric.free_scale. gram_lm.py becomes metric_lm.py and subclasses LevenbergMarquardtBase. The eight-value string menu becomes the same typed configs the ridge solver takes: Cholesky(form=auto|gram|normal), QR(), CG(precond), GramCG(precond). QR is now the damping-row form, which is rank-safe and so subsumes both the old qr and augmented_qr. The five preconditioner keywords (dual_, normal_, whitened_, ad_solver_, and the factory) collapse into one typed Preconditioner whose space the config names, which deletes the mutual-exclusion matrix and the three missing_*_preconditioner branches along with it. Seven AD tangent implementations become four. The undamped AD operator is singular on whichever side the problem is deficient in, so each Krylov rule is now offered only where its operator is invertible and says so loudly otherwise -- previously CG returned a silently wrong tangent for n > m. regularized_normal_cg becomes CG(precond, penalty=...), so ad_solver_penalty stops being a free-floating kwarg that errors with five of seven methods. Reverse mode through the unpenalized normal rule uses the push-through identity N^+ = B'(BB')^{+2}B, since a cotangent does not lie in range(B'). Deleted: lsmr.py, recycled_cg.py, WhitenedPreconditioner, and the metric-LM constructor's other 17 keywords (30 -> 13). quasiseparable and the state-space metric move to experimental/ as StateSpaceMetric. The dual-space preconditioner helpers become classes (Nystrom/Woodbury/ShermanMorrison/Padded). Tests: 4697-line test_gram_lm.py plus test_normal_solvers, test_lsmr, test_recycled_cg, test_augmented_qr, test_implicit_geometry, test_metric_factory, test_preconditioner_factory, test_ad_solver_methods and test_jacobian_mode (9700 lines) replaced by a 400-line test_metric_lm.py where every check is against a closed form or an independent reference, plus a trimmed float64 suite. 149 passed, 13 skipped in 48s (was 596/195s). Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- benchmarks/test_augmented_qr_benchmark.py | 84 - src/nlls_gram/__init__.py | 156 +- src/nlls_gram/experimental/__init__.py | 12 + .../{ => experimental}/quasiseparable.py | 0 .../experimental/state_space_metric.py | 110 + src/nlls_gram/gram_lm.py | 2855 ---------- src/nlls_gram/linear_solvers.py | 366 +- src/nlls_gram/lm_core.py | 137 + src/nlls_gram/lsmr.py | 215 - src/nlls_gram/metric_lm.py | 700 +++ src/nlls_gram/metrics.py | 579 +- src/nlls_gram/preconditioners.py | 369 +- src/nlls_gram/recycled_cg.py | 601 --- src/nlls_gram/ridge_lm.py | 126 +- tests/test_ad_solver_methods.py | 150 - tests/test_augmented_qr.py | 184 - tests/test_failed_implicit_ad.py | 55 +- tests/test_float64_subprocess.py | 1199 +---- tests/test_gpu.py | 72 +- tests/test_gram_lm.py | 4697 ----------------- tests/test_implicit_geometry.py | 440 -- tests/test_jacobian_mode.py | 225 - tests/test_lsmr.py | 716 --- tests/test_metric_factory.py | 546 -- tests/test_metric_lm.py | 398 ++ tests/test_multi_start.py | 2 - tests/test_normal_solvers.py | 1343 ----- tests/test_preconditioner_factory.py | 556 -- tests/test_recycled_cg.py | 1194 ----- tests/test_ridge_metrics.py | 6 - 30 files changed, 2033 insertions(+), 16060 deletions(-) delete mode 100644 benchmarks/test_augmented_qr_benchmark.py create mode 100644 src/nlls_gram/experimental/__init__.py rename src/nlls_gram/{ => experimental}/quasiseparable.py (100%) create mode 100644 src/nlls_gram/experimental/state_space_metric.py delete mode 100644 src/nlls_gram/gram_lm.py delete mode 100644 src/nlls_gram/lsmr.py create mode 100644 src/nlls_gram/metric_lm.py delete mode 100644 src/nlls_gram/recycled_cg.py delete mode 100644 tests/test_ad_solver_methods.py delete mode 100644 tests/test_augmented_qr.py delete mode 100644 tests/test_gram_lm.py delete mode 100644 tests/test_implicit_geometry.py delete mode 100644 tests/test_jacobian_mode.py delete mode 100644 tests/test_lsmr.py delete mode 100644 tests/test_metric_factory.py create mode 100644 tests/test_metric_lm.py delete mode 100644 tests/test_normal_solvers.py delete mode 100644 tests/test_preconditioner_factory.py delete mode 100644 tests/test_recycled_cg.py diff --git a/benchmarks/test_augmented_qr_benchmark.py b/benchmarks/test_augmented_qr_benchmark.py deleted file mode 100644 index 71032dc..0000000 --- a/benchmarks/test_augmented_qr_benchmark.py +++ /dev/null @@ -1,84 +0,0 @@ -import jax -import jax.numpy as jnp -import pytest - -from nlls_gram import LevenbergMarquardt - -# The DAE stage pattern: 32 repeated warm-started algebraic solves over slowly -# drifting targets. A fixed-iteration direct-Newton loop is the lower-overhead -# baseline for the small systems where augmented QR is intended to be used. - -N_SOLVES = 32 -NEWTON_STEPS = 4 - - -def _devices(platform): - try: - return jax.devices(platform) - except RuntimeError: - return [] - - -def _make_problem(n, device): - W = jax.device_put(0.1 * jax.random.normal(jax.random.key(66), (n, n)), device) - b0 = jax.device_put(jax.random.normal(jax.random.key(67), (n,)), device) - drift = jax.device_put( - 0.02 * jax.random.normal(jax.random.key(68), (N_SOLVES, n)), device - ) - targets = b0 + jnp.cumsum(drift, axis=0) - - def residual(z, args, p): - return z + jnp.tanh(W @ z) - p - - return residual, targets - - -@pytest.mark.parametrize("platform", ["cpu", "gpu"]) -@pytest.mark.parametrize("n", [1, 4, 8]) -@pytest.mark.parametrize("method", ["augmented_qr", "direct_newton"]) -def test_warm_started_stage_solves(benchmark, platform, n, method): - if not _devices(platform): - pytest.skip(f"JAX {platform!r} backend is not available") - device = _devices(platform)[0] - residual, targets = _make_problem(n, device) - z0 = jax.device_put(jnp.zeros(n), device) - - if method == "augmented_qr": - solver = LevenbergMarquardt( - residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ) - - def stage(z, target): - result = solver.solve(z, p=target, max_steps=8, atol=1e-5) - return result.x, result.status - - else: - - def stage(z, target): - def newton(_, z): - J = jax.jacfwd(residual, argnums=0)(z, None, target) - return z - jnp.linalg.solve(J, residual(z, None, target)) - - z = jax.lax.fori_loop(0, NEWTON_STEPS, newton, z) - return z, jnp.asarray(0, dtype=jnp.int32) - - @jax.jit - def sweep(z): - def body(z, target): - z_next, status = stage(z, target) - return z_next, status - - z_final, statuses = jax.lax.scan(body, z, targets) - return z_final, statuses - - jax.block_until_ready(sweep(z0)) - - def run(): - out = sweep(z0) - jax.block_until_ready(out) - return out - - benchmark(run) diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index d441155..3600647 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -1,55 +1,40 @@ """Levenberg-Marquardt nonlinear least-squares for JAX, built for -underdetermined interpolation with an explicit selection of which -interpolant is returned. +underdetermined interpolation with an explicit selection of which interpolant +is returned. -Two solvers share one init/update/solve protocol (x is any JAX pytree; the -residual takes (x), (x, args), or (x, args, p); solve(...) runs a jitted -loop with callback control, save_steps histories, and multi-start retries or -parallel races; solve(...).x carries a custom implicit AD rule with respect -to p): +Two solvers share one ``init``/``update``/``solve`` protocol -- ``x`` is any +JAX pytree, the residual takes ``(x)``, ``(x, args)``, or ``(x, args, p)``, +``solve`` runs a jitted loop with callback control, ``save_steps`` histories, +and multi-start retries or parallel races, and ``solve(...).x`` carries a +custom implicit AD rule with respect to ``p``. They differ in where the +selection of the returned root lives: -- RidgeLevenbergMarquardt minimizes the ridge objective - ||r(x)||^2 + ridge * ||x_m||_W^2 for a positive-definite Metric W on the - metric block x_m of x = [x_m; x_f] (the free block x_f stays - unpenalized), with the ridge weight carried as traced state that a - callback can anneal toward a positive floor (ridge_continuation) — the - minimum-seminorm (min-RKHS-norm) selection lives in the OBJECTIVE, per - classical nonlinear Tikhonov regularization. The metric is supplied - through factor callbacks for W = F'F (IdentityMetric is plain ridge, - RepeatedFactorMetric the kernel workhorse) and the solver runs entirely - in the whitened variable y = F_bar x with constant penalty rows [I 0] — - a clean spectral floor at the ridge, so the default Cholesky() path - stays accurate at deep ridge. Stopping is conjunctive gtol + atol with - the whitened geometry (steps in the W-norm, gradients in the dual - W^{-1}-norm); calibrate gtol ~ 1e-3 * ridge * sqrt(q(x*)) since - info.penalty_grad_norm = sqrt(penalty_value). Linear solvers are typed - configs — Cholesky() (the default: dense normal equations with a - reject-step cache), QR() (damping-row QR for tiny ridge), - CG(preconditioner, ...) (matrix-free preconditioned CG on the damped - whitened normal operator) — and the AD side takes Cholesky() or CG(...), - defaulting to the forward family. -- LevenbergMarquardt minimizes ||r(x)||^2 with an optional positive-definite - parameter-space GramMetric (or iterate-aware MetricFactory) defining the - damping geometry, so the small-damping Gauss-Newton limit selects - minimum-metric-norm corrections. The default linear_solver="auto" - resolves to the smaller dense factorization (gram_cholesky / - normal_cholesky); QR, augmented QR, gram/normal CG, and LSMR variants - cover direct and matrix-free regimes, with a swappable ad_solver menu - (direct, svd, qr, augmented_qr, gram_cg, normal_cg, - regularized_normal_cg). +- ``RidgeLevenbergMarquardt`` puts it in the OBJECTIVE, minimizing + ``||r(x)||^2 + ridge * ||x_m||_W^2`` for a positive-definite ``Metric`` W on + the metric block, with the ridge weight carried as traced state a callback + can anneal (``ridge_continuation``). Classical nonlinear Tikhonov + regularization; the minimum-seminorm interpolant is what it converges to. +- ``LevenbergMarquardt`` puts it in the DAMPING GEOMETRY, minimizing + ``||r(x)||^2`` with the same ``Metric`` weighting the trust region, so the + small-damping Gauss-Newton limit selects minimum-metric-norm corrections. -The package depends only on JAX. Tuning heuristics (solver selection, -damping, inner-solve scheduling): +Both take the same typed linear-solver configs -- ``Cholesky()``, ``QR()``, +``CG(preconditioner)``, ``GramCG(preconditioner)`` -- and the same +``ad_solver`` menu, defaulting to the forward family. + +The package depends only on JAX. Tuning heuristics: https://highdimensionaleconlab.github.io/nlls_gram/tuning_guide/ """ -from nlls_gram.gram_lm import ( - LevenbergMarquardt, - MetricFactory, - PreconditionerFactory, - WhitenedPreconditioner, +from nlls_gram.linear_solvers import ( + CG, + QR, + SVD, + Cholesky, + CholeskyCache, + GramCG, + QRCache, ) -from nlls_gram.linear_solvers import CG, QR, Cholesky, CholeskyCache, QRCache from nlls_gram.lm_types import ( LMHyperparams, LMInfo, @@ -60,89 +45,60 @@ LMStatus, SolverContext, ) -from nlls_gram.lsmr import LSMRState, lsmr +from nlls_gram.metric_lm import LevenbergMarquardt from nlls_gram.metrics import ( - GramMetric, + CholeskyMetric, + DiagonalMetric, IdentityMetric, Metric, RepeatedFactorMetric, - metric_from_cholesky, - metric_from_diagonal, - repeated_shifted_dense_metric, - repeated_shifted_state_space_metric, ) from nlls_gram.multi_start import DrawNNXModule, MultiStart, MultiStartInfo from nlls_gram.preconditioners import ( BlockEigenPreconditioner, IdentityPreconditioner, + NystromPreconditioner, + PaddedPreconditioner, Preconditioner, + ShermanMorrisonPreconditioner, + WoodburyPreconditioner, block_eigen_state, - identity_preconditioner, - identity_right_preconditioner, - nystrom_preconditioner, - pad_dual_preconditioner, - sherman_morrison_preconditioner, - woodbury_preconditioner, -) -from nlls_gram.quasiseparable import matern_state_space -from nlls_gram.recycled_cg import ( - HarvestState, - RecycleConfig, - RecycleState, - build_coarse_operator, - deflated_pcg, - recycled_cg, ) from nlls_gram.ridge_lm import RidgeLevenbergMarquardt, ridge_continuation __all__ = [ + "CG", + "QR", + "SVD", "BlockEigenPreconditioner", "Cholesky", "CholeskyCache", - "LevenbergMarquardt", - "LMState", - "CG", - "QR", - "QRCache", + "CholeskyMetric", + "DiagonalMetric", + "DrawNNXModule", + "GramCG", + "IdentityMetric", + "IdentityPreconditioner", "LMHyperparams", "LMInfo", - "LMStatus", "LMSolveAction", "LMSolveContext", "LMSolveResult", - "GramMetric", - "IdentityMetric", + "LMState", + "LMStatus", + "LevenbergMarquardt", "Metric", - "SolverContext", - "MetricFactory", "MultiStart", - "IdentityPreconditioner", + "MultiStartInfo", + "NystromPreconditioner", + "PaddedPreconditioner", "Preconditioner", + "QRCache", "RepeatedFactorMetric", - "MultiStartInfo", - "DrawNNXModule", - "PreconditionerFactory", - "WhitenedPreconditioner", - "RecycleConfig", - "RecycleState", - "HarvestState", + "RidgeLevenbergMarquardt", + "ShermanMorrisonPreconditioner", + "SolverContext", + "WoodburyPreconditioner", "block_eigen_state", - "build_coarse_operator", - "deflated_pcg", - "identity_preconditioner", - "identity_right_preconditioner", - "lsmr", - "LSMRState", "ridge_continuation", - "RidgeLevenbergMarquardt", - "matern_state_space", - "metric_from_cholesky", - "metric_from_diagonal", - "nystrom_preconditioner", - "pad_dual_preconditioner", - "recycled_cg", - "repeated_shifted_dense_metric", - "repeated_shifted_state_space_metric", - "sherman_morrison_preconditioner", - "woodbury_preconditioner", ] diff --git a/src/nlls_gram/experimental/__init__.py b/src/nlls_gram/experimental/__init__.py new file mode 100644 index 0000000..e6de95a --- /dev/null +++ b/src/nlls_gram/experimental/__init__.py @@ -0,0 +1,12 @@ +"""Experimental extras: not part of the supported API, not documented, and +free to change or disappear. Import explicitly:: + + from nlls_gram.experimental import StateSpaceMetric, matern_state_space +""" + +from nlls_gram.experimental.state_space_metric import ( + StateSpaceMetric, + matern_state_space, +) + +__all__ = ["StateSpaceMetric", "matern_state_space"] diff --git a/src/nlls_gram/quasiseparable.py b/src/nlls_gram/experimental/quasiseparable.py similarity index 100% rename from src/nlls_gram/quasiseparable.py rename to src/nlls_gram/experimental/quasiseparable.py diff --git a/src/nlls_gram/experimental/state_space_metric.py b/src/nlls_gram/experimental/state_space_metric.py new file mode 100644 index 0000000..a88d675 --- /dev/null +++ b/src/nlls_gram/experimental/state_space_metric.py @@ -0,0 +1,110 @@ +"""Repeated state-space kernel metric in linear storage (experimental). + +``StateSpaceMetric`` is a :class:`~nlls_gram.Metric` whose factor is the +quasiseparable Cholesky of a stationary state-space kernel Gram matrix, never +formed densely: ``O(n)`` storage and ``O(n)`` work per apply for ``n`` +coordinates, against ``O(n^2)``/``O(n^3)`` for the dense route. One structured +factor is shared by every repeated block, which are processed as batched +right-hand sides. +""" + +from dataclasses import dataclass, field + +import jax +import jax.numpy as jnp + +from nlls_gram.experimental import quasiseparable +from nlls_gram.experimental.quasiseparable import matern_state_space +from nlls_gram.metrics import Metric, _check_leading_size + +__all__ = ["StateSpaceMetric", "matern_state_space"] + + +@dataclass(frozen=True, eq=False) +class StateSpaceMetric(Metric): + """``repeats`` copies of a shifted state-space kernel Gram matrix. + + ``t`` is a strictly increasing 1-D coordinate; ``h``, ``Pinf``, and + ``transition`` define the stationary state-space kernel, as + :func:`matern_state_space` supplies for Matern-1/2, -3/2, and -5/2. + ``transition(dt)`` returns the transpose of the textbook state transition + for each gap. Non-increasing coordinates propagate NaN rather than quietly + defining a nonstationary factor. + + The metric is ``blockdiag(K + epsilon I, ...)`` over ``repeats`` blocks; + ``epsilon`` is added before the quasiseparable factorization. Anything + beyond ``size = repeats * len(t)`` is the solver's free block, weighted by + ``free_scale``. + + ``parallel`` selects sequential or associative scans; the default picks + associative scans only for float64 off CPU. Pass it explicitly when arrays + use nondefault device placement. + """ + + t: jax.Array + h: jax.Array + Pinf: jax.Array + transition: object + repeats: int = field(default=1, kw_only=True) + epsilon: float = field(default=1e-8, kw_only=True) + free_scale: float = field(default=1.0, kw_only=True) + parallel: bool | None = field(default=None, kw_only=True) + size: int = field(init=False) + _factor: tuple = field(init=False) + + def __post_init__(self): + t = jnp.asarray(self.t) + if t.ndim != 1 or t.shape[0] == 0: + raise ValueError("t must be a nonempty 1-D array") + if self.repeats < 1: + raise ValueError("repeats must be a positive integer") + d, p, q, A = quasiseparable._state_space_generators( + t, self.h, self.Pinf, self.transition + ) + dtype = jnp.result_type(d, p, q, A, 1.0) + epsilon = jnp.asarray(self.epsilon, dtype=dtype) + # A non-increasing coordinate or a non-positive shift poisons the + # factor rather than silently producing a wrong one. + epsilon = jnp.where( + (epsilon > 0.0) & jnp.all(jnp.diff(t) > 0.0), epsilon, jnp.nan + ) + d = d.astype(dtype) + epsilon + p, q, A = (v.astype(dtype) for v in (p, q, A)) + parallel = self.parallel + if parallel is None: + parallel = jax.default_backend() != "cpu" and dtype == jnp.float64 + c, w = quasiseparable._cholesky(d, p, q, A) + object.__setattr__(self, "_factor", (c, p, w, A, parallel)) + object.__setattr__(self, "size", self.repeats * t.shape[0]) + + def _map_blocks(self, block_op, v): + _check_leading_size(v, self.size) + block = self.size // self.repeats + trailing = v.shape[1:] + packed = jnp.moveaxis( + v.reshape((self.repeats, block) + trailing), 0, 1 + ).reshape(block, -1) + return jnp.moveaxis( + block_op(packed).reshape((block, self.repeats) + trailing), 0, 1 + ).reshape((self.size,) + trailing) + + def factor_apply(self, v, ctx): + c, p, w, A, parallel = self._factor + return self._map_blocks( + lambda m: quasiseparable._cholesky_transpose_matvec( + c, p, w, A, m, parallel + ), + v, + ) + + def factor_solve(self, v, ctx): + c, p, w, A, parallel = self._factor + return self._map_blocks( + lambda m: quasiseparable._backward_substitution(c, p, w, A, m, parallel), v + ) + + def factor_solve_transpose(self, v, ctx): + c, p, w, A, parallel = self._factor + return self._map_blocks( + lambda m: quasiseparable._forward_substitution(c, p, w, A, m, parallel), v + ) diff --git a/src/nlls_gram/gram_lm.py b/src/nlls_gram/gram_lm.py deleted file mode 100644 index 4f810c0..0000000 --- a/src/nlls_gram/gram_lm.py +++ /dev/null @@ -1,2855 +0,0 @@ -import dataclasses - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import jax.scipy.sparse.linalg as jsp_sparse_linalg -import numpy as np -from jax.flatten_util import ravel_pytree - -from nlls_gram.lm_types import ( - LMHyperparams, - LMInfo, - LMSolveAction, - LMSolveContext, - LMSolveResult, - LMState, - LMStatus, - _cast_hyper, - _damping_floor, -) -from nlls_gram.lsmr import lsmr_solve -from nlls_gram.metrics import GramMetric, _metric_with_compute_dtype -from nlls_gram.multi_start import ( - DrawNNXModule, - MultiStart, - MultiStartInfo, - _accept_converged, - _accept_converged_or_max_steps, - _check_drawn_types, - _multi_start_parallel_jit, - _multi_start_python_impl, - _multi_start_sequential_jit, -) -from nlls_gram.preconditioners import WhitenedPreconditioner -from nlls_gram.recycled_cg import ( - RecycleConfig, - RecycleState, - build_coarse_operator, - deflated_pcg, -) -from nlls_gram.solve_loop import _solve_loop_jit, _solve_python_impl -from nlls_gram.utilities import ( - _hashable_hook, - _mask_tangent_tree, - _static_key_component, - _tree_changed, - _where_tree, - _zero_tangent_leaf, - canonicalize_ad_preconditioner, - canonicalize_residual, -) - -__all__ = [ - "DrawNNXModule", - "LevenbergMarquardt", - "LMHyperparams", - "LMInfo", - "LMSolveAction", - "LMSolveContext", - "LMSolveResult", - "LMState", - "LMStatus", - "MetricFactory", - "MultiStart", - "MultiStartInfo", - "PreconditionerFactory", - "WhitenedPreconditioner", - "canonicalize_ad_preconditioner", - "canonicalize_residual", -] - -# init() -> lm_state, update(x, lm_state, args, p) -> (new_x, lm_state, info), -# plus a solve() convenience loop. x is ANY pytree; the solver only ravels and -# unravels it with ravel_pytree and knows nothing about flax/nnx/optax. -# update() does not jit internally; solve(jit=True) wraps the loop in jax.jit. -# Hyperparameters are static Python scalars; data-dependent control flow is -# traced (jnp.where), so a rejected step returns the unchanged x rather than -# branching. Dtypes flow from the residual; damping scalars are cast to match. - - -class PreconditionerFactory: - """θ-adaptive dual preconditioner: a value-hashable ``(prepare, apply)`` pair. - - For ``linear_solver="gram_cg"``, supplies a dual preconditioner REBUILT - from the current iterate every step, replacing the frozen - ``dual_preconditioner``. - Pass exactly one of ``dual_preconditioner`` or ``preconditioner_factory``. - Use it when the dual operator ``J M^{-1} J' + damping I`` rotates enough as - LM drifts ``x`` that a preconditioner frozen at ``x0`` decays into an - ineffective (breakdown-inducing) approximation downstream, while one rebuilt - from the live iterate keeps the inner CG converging:: - - def prepare(x, args, p, aux): - # model-structured build from the CURRENT iterate x - return diag # any fixed-shape pytree of arrays - - def apply(state, v, damping): - return v / (state + damping) # SPD, linear in v - - solver = LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=..., - ) - - - ``prepare(x, args, p, aux) -> state`` builds a fixed-shape pytree of arrays - from the CURRENT solver iterate ``x`` (the user pytree, NOT the raveled flat - ``theta`` — model-structured access is the point), the residual ``args``, - ``p``, and the residual aux evaluated at the same linearization point - (``None`` when ``has_aux=False``) — the same signature as - ``MetricFactory.prepare``. Runs inside the jitted loop as traced ops (no - recompile), once per accepted step: after a rejected step ``x`` did not - move, so the carried state is reused and only the live ``damping`` changes. - - ``apply(state, v, damping) -> vector`` is the per-iteration apply: an SPD, - linear-in-``v`` approximation of ``(J M^{-1} J' + damping I)^{-1} v``. It - must stay well-defined at ``damping = 0``, since the cg-resolved AD - derivative reuses it (undamped) at the converged solution unless an - explicit ``ad_solver_preconditioner`` is given. - - Value-hashable on ``(prepare, apply)`` with jit's static-key semantics: equal - pairs share one compiled solve loop (like ``DrawNNXModule`` and the frozen - preconditioner identities). Define ``prepare``/``apply`` once at setup scope - so their identities are stable; a fresh closure per call keys a new compile. - ``prepare`` and ``apply`` must be hashable for that sharing; an unhashable - pair still works but keys the solver by identity (recompiling per instance). - """ - - def __init__(self, prepare, apply): - if not callable(prepare): - raise TypeError("PreconditionerFactory.prepare must be callable") - if not callable(apply): - raise TypeError("PreconditionerFactory.apply must be callable") - self.prepare = prepare - self.apply = apply - - def __hash__(self): - return hash((self.prepare, self.apply)) - - def __eq__(self, other): - return ( - isinstance(other, PreconditionerFactory) - and self.prepare == other.prepare - and self.apply == other.apply - ) - - -class MetricFactory: - """Iterate-aware metric: a value-hashable ``(prepare, build)`` pair. - - Supplies a :class:`~nlls_gram.GramMetric` REBUILT from the current iterate every - accepted step, replacing the fixed ``metric``. Pass at most one of ``metric`` - or ``metric_factory``. Use it when the metric depends on the current iterate - or on residual byproducts -- e.g. a kernel Gram factor over state points that - live in ``x``, or a factor the residual passes back through its aux output - (``has_aux=True``):: - - def residual(x, args, p): - value = economic_residual(x, args, p) - gram = kernel_gram(x["points"], p["kernel"]) - L = jnp.linalg.cholesky(gram + p["eps"] * jnp.eye(gram.shape[0])) - return value, {"L": L} - - solver = LevenbergMarquardt( - residual, - has_aux=True, - metric_factory=MetricFactory( - prepare=lambda x, args, p, aux: aux["L"], - build=metric_from_cholesky, - ), - ) - - - ``prepare(x, args, p, aux) -> state`` builds a fixed-shape pytree of - arrays from the CURRENT solver iterate ``x`` (the user pytree, NOT the - raveled flat ``theta``), the residual ``args``, ``p``, and the residual - aux evaluated at the same linearization point (``None`` when - ``has_aux=False``). Runs inside the jitted loop as traced ops (no - recompile), once per accepted step: after a rejected step ``x`` did not - move, so the carried state is reused. Expensive setup (Gram assembly, a - dense Cholesky) belongs here, where it is cached. - - ``build(state) -> GramMetric`` assembles the metric from the prepared state: - any ``GramMetric``-returning builder (for example - ``metric_from_cholesky``) or hand-rolled unary callbacks closing over - ``state``. - Called once per ``update`` BEFORE the iterative loops, so builder-internal - setup (e.g. a tridiagonal Cholesky scan) is loop-invariant -- computed - once per step, not per inner cg/lsmr iteration. - - The built metric obeys the same rules as a fixed custom ``metric``: which - callbacks the linear solver requires, the shape contract, and exactness - (unlike a preconditioner, the metric defines the subproblem). Validation of - the required callbacks runs when ``build`` first executes (at trace time) - rather than at construction. Within one ``update`` the velocity, - geodesic-acceleration, and norm applications all use the same pre-step - state. A ``solve`` callback that replaces ``x`` or ``args`` invalidates the - carried state, and multi-start draws never inherit another start's state. - - Under implicit differentiation of ``solve`` with respect to ``p``, the - metric is FROZEN at the returned solution: ``prepare``/``build`` run once at - ``(result.x, result.args, result.p, result.aux)`` and the state-dependence - is not differentiated -- the same contract as a fixed metric closing over - constants. The built metric must stay self-adjoint and positive definite - for that fixed state. - - Value-hashable on ``(prepare, build)`` with jit's static-key semantics: - equal pairs share one compiled solve loop, so define the callables once at - setup scope; a fresh closure per call keys a new compile. - """ - - def __init__(self, prepare, build): - if not callable(prepare): - raise TypeError("MetricFactory.prepare must be callable") - if not callable(build): - raise TypeError("MetricFactory.build must be callable") - self.prepare = prepare - self.build = build - - def __hash__(self): - return hash((self.prepare, self.build)) - - def __eq__(self, other): - return ( - isinstance(other, MetricFactory) - and self.prepare == other.prepare - and self.build == other.build - ) - - -def _validate_metric_requirements( - metric, solver, geodesic, source, *, keyword="linear_solver" -): - # The shared requirement matrix for a custom metric: the gram forms factor - # through metric.solve (P = M^{-1}); the normal/whitened forms -- and the - # whitened AD rules -- are built from the whitening pair - # S = inv_sqrt, S' = inv_sqrt_transpose; the geodesic correction measures - # its acceptance ratio in metric.norm (form-independent). "auto" (and - # solver=None, for the gram_cg AD rule with its S S' fallback) skips the - # solver-specific checks. - has_custom = any( - cb is not None - for cb in ( - metric.solve, - metric.norm, - metric.inv_sqrt, - metric.inv_sqrt_transpose, - ) - ) - if not has_custom: - return - if solver in ("gram_cholesky", "gram_cg") and metric.solve is None: - raise ValueError( - f'{keyword}="{solver}" with a custom metric requires metric.solve{source}' - ) - if solver in ( - "svd", - "normal_cholesky", - "normal_cg", - "regularized_normal_cg", - "qr", - "augmented_qr", - "lsmr", - ) and (metric.inv_sqrt is None or metric.inv_sqrt_transpose is None): - raise ValueError( - f'{keyword}="{solver}" with a custom metric requires ' - f"metric.inv_sqrt and metric.inv_sqrt_transpose{source}" - ) - if geodesic and metric.norm is None: - raise ValueError( - "geodesic_acceleration (on by default) with a custom metric " - f"requires metric.norm{source}; provide it or pass " - "geodesic_acceleration=False" - ) - - -class LevenbergMarquardt: - """Metric-damped Levenberg-Marquardt for ``min ||r(x, args, p)||^2`` over a - JAX pytree ``x``, built for interpolation problems: zero-residual roots - that stay rank-deficient along some directions at every shape, so the - minimum-metric-norm selection of the converged root (and of its implicit - derivative) is part of the contract, not a tie-break. Exposes per-step - ``update``, a jitted ``solve`` loop with callbacks, and implicit - differentiation of ``solve`` with respect to ``p``. - - Every solver damps the same whitened subproblem. With metric ``M``, - ``P = M^{-1}``, ``S = metric.inv_sqrt`` (``S S' = P``), and ``B = J S``, - the LM step solves ``min_u ||r + B u||^2 + damping ||u||^2`` with - ``step = S u``; the ``damping -> 0`` limit is the minimum-``M``-norm - Gauss-Newton step at any rank. ``linear_solver`` picks the algebra: - - - ``"auto"`` (default): trace-time shape rule -- strictly more parameters - than residuals factors the smaller ``m x m`` gram dual - (``"gram_cholesky"``), otherwise the ``n x n`` whitened normal system - (``"normal_cholesky"``). A cost choice, never a semantic one: by the - push-through identity - ``S (B'B + damping I)^{-1} B' = P J' (J P J' + damping I)^{-1}`` the two - steps are identical for every ``damping > 0``. Shapes are concrete while - tracing, so this is a plain Python branch resolved per compilation, and - a shape heuristic only -- it never inspects numerical rank. - - ``"gram_cholesky"`` / ``"gram_cg"``: the residual-space dual - ``(J P J' + damping I_m) w = rhs``, ``step = -P J' w`` -- dense - factorization or matrix-free preconditioned CG (``m``-dimensional - Krylov space). - - ``"normal_cholesky"`` / ``"normal_cg"``: the parameter-space whitened - normal system ``(B'B + damping I_n) u = -B' rhs``, ``step = S u`` -- - dense factorization or matrix-free CG (``n``-dimensional Krylov space). - The normal matrix has full rank whenever ``B`` has full column rank, so - ``m >= n`` no longer factors a structurally rank-deficient operator. - - ``"qr"`` / ``"augmented_qr"`` / ``"lsmr"``: direct or bidiagonalization - solvers on the whitened operator itself, at condition ``sqrt(cond)`` of - either squared system. - - ``linear_solver="augmented_qr"`` solves the whitened LM subproblem by a - direct reduced QR factorization of ``[J S; sqrt(damping) I]``. Unlike the - residual-dimension-reduced ``"qr"`` path, it remains well-defined for a - rank-deficient Jacobian whenever damping is positive, but its factorization - width is the flattened parameter count. It is therefore intended for small - systems, including square algebraic roots, rather than the package's usual - massively underdetermined regime. - - ``linear_solver="lsmr"`` is the matrix-free sibling of ``augmented_qr``: it - solves the same whitened damped subproblem - ``min_u ||r + B u||^2 + damping ||u||^2`` (``B = J S``, ``S = metric.inv_sqrt``, - step ``s = S u``) by LSMR bidiagonalization from ``J``/``J'`` matvecs alone. - Because it works on ``B`` -- whose condition number is the square root of the - ``gram_cg`` dual ``J P J' + damping I`` -- it keeps the step accurate at small - damping where the squared dual solve hits its ``eps * cond`` floor. It needs - the metric's ``inv_sqrt``/``inv_sqrt_transpose`` (the identity metric supplies - them) and maps the same ``iterative_tol``/``iterative_atol``/ - ``iterative_maxiter`` hooks onto its normal-equations stopping test. - ``dual_preconditioner``, ``preconditioner_factory``, and ``recycle`` are - ``gram_cg``-only. Its own preconditioner is ``whitened_preconditioner`` (a - ``WhitenedPreconditioner``): a parameter-space right-preconditioner ``R^{-1}`` - running LSMR on ``B R^{-1}`` to cluster the spectrum, which cuts the endgame - iteration count by orders of magnitude when ``B`` itself is ill-conditioned - (a Schur-complement factor is canonical). The augmented damping row keeps - every ``damping > 0`` subproblem exactly ``I``-damped in ``u = R^{-1} z``, - so the step is ``u = -(B'B + damping I)^{-1} B' r`` and the - ``damping -> 0`` selection limit is the minimum-metric-norm step for ANY - ``R``. For a nonsquare problem, differentiating a forward ``lsmr`` solve - uses the SVD AD rule under ``ad_solver="auto"``; a square problem uses - the direct solve described below. - - ``jacobian_mode`` controls how the dense paths -- the cholesky forms - (directly or via ``linear_solver="auto"``), ``qr``, ``augmented_qr``, and - the direct/SVD/QR AD rules -- materialize ``J'``: ``"auto"`` (the - default) takes ``n`` forward-mode JVP columns when the system is tall or - square (``n <= m``) and ``m`` reverse-mode VJP rows only when strictly - fat (``n > m``), so the identity basis that is vmapped over is always - the small side (an ``m x m`` residual basis over a tall system is a - compile-time memory blowup), with the square tie going to the cheaper - JVP passes; ``"fwd"``/``"rev"`` force one mode. The matrix-free solvers - (``gram_cg``, ``normal_cg``, ``lsmr``) never materialize ``J``, so a - forced mode that no dense forward path or dense AD method could - consume is rejected at construction rather than silently ignored. - - ``linear_solver="gram_cg"`` requires ``dual_preconditioner(v, damping)``: a - jit-traceable, linear, SPD approximation of - ``(J P J' + damping I_m)^{-1} v`` used as the CG preconditioner (for the - geodesic-acceleration solve as well); pass ``identity_preconditioner()`` - to run unpreconditioned CG. It never changes the subproblem: at - inner convergence the step is identical, and a budget-truncated step still - lies in ``range(P J')``, so the minimum-metric-norm selection for - underdetermined residuals is unchanged — the preconditioner may be - approximate even though ``metric.solve`` must stay exact. - - ``linear_solver="normal_cg"`` requires ``normal_preconditioner(v, - damping)``, its parameter-space sibling: a jit-traceable, linear, SPD - approximation of ``(B'B + damping I_n)^{-1} v`` (again - ``identity_preconditioner()`` opts out). Unlike the dual hook it CAN - change what is selected: on a column-rank-deficient ``B`` the - unpreconditioned Krylov space stays inside ``range(B')`` and a truncated - step keeps the minimum-``M``-norm selection, but a preconditioner ``C`` - with ``C(range(B')) !⊆ range(B')`` leaks the iterates into ``ker(B)`` - and the selection is lost. Safe constructions preserve the range by - construction: the identity, polynomials in ``B'B``, exact shifted - inverses ``(B'B + c I)^{-1}``, and any ``C`` commuting with the - orthogonal projector onto ``range(B')``. ``dual_preconditioner``, - ``preconditioner_factory``, and ``recycle`` are ``gram_cg``-only hooks. - - ``preconditioner_factory`` (a ``PreconditionerFactory``) is the θ-adaptive - alternative to the frozen ``dual_preconditioner``: exactly one of the two is - required for ``linear_solver="gram_cg"``. Its ``prepare(x, args, p, aux)`` - rebuilds the - preconditioner state from the CURRENT iterate inside the jitted loop (once - per accepted step; a rejected step reuses the carried state since ``x`` did - not move), and ``apply(state, v, damping)`` is the per-iteration apply. Reach - for it when a preconditioner frozen at ``x0`` decays as LM drifts ``x`` (the - dual operator rotates) where one rebuilt from the live iterate keeps CG - converging. It composes with ``recycle`` (unchanged deflation on top of the - rebuilt first level) and, when the AD solve resolves to ``gram_cg``, seeds - the AD preconditioner from the state at the converged solution unless an - explicit ``ad_solver_preconditioner`` overrides it. - - ``metric_factory`` (a ``MetricFactory``) is the iterate-aware alternative to - the fixed ``metric`` (pass at most one): ``prepare(x, args, p, aux)`` - rebuilds the metric state from the current iterate and the residual aux once - per accepted step (a rejected step reuses the carried state), and - ``build(state)`` assembles a plain ``GramMetric`` from it once per ``update``. - The built metric follows the same per-solver callback requirements as a - fixed custom metric, validated at trace time; under implicit - differentiation it is frozen at the returned solution WITHIN each - first-order AD solve -- the tangent treats the metric as constant, - while higher-order AD differentiates the resulting pointwise - metric-dependent tangent field. One shared limitation of the metric-aware - AD methods (all methods except ``direct``): they apply the frozen metric - (``S`` in the whitening and normal-CG methods, ``P`` under gram-CG) through - identity-matvec ``custom_linear_solve`` - wrappers whose declared solves are opaque to AD, so an identity matvec - exposes no parameters to differentiate. This makes first-order reverse - mode correct for any legal metric -- including a non-reverse- - differentiable ``inv_sqrt`` that supplies ``inv_sqrt_transpose`` (jit/vmap - exercised) -- but higher-order derivatives THROUGH a factory-built - metric's state dependence inside those applications are not propagated. - Take higher-order derivatives of ``solve`` with a fixed metric. See - :class:`MetricFactory`. - - ``min_damping`` is the absolute lower bound applied before every linear - solve and after every damping update. ``None`` (the default) resolves to - ``jnp.finfo(residual.dtype).tiny``, the smallest positive normal value, so - damping cannot enter a backend's flush-to-zero range. This is only an - underflow floor. A standard conditioning-oriented minimum is instead on - the order of machine epsilon times a representative scale of ``B'B`` (or - ``B B'``); pass that larger absolute value explicitly when the damping must - remain numerically effective in the linear system. - - ``solve(...).x`` has a custom implicit AD rule with respect to ``p``, - relinearized at the returned solution. ``ad_solver`` explicitly selects - one method from ``{"direct", "svd", "qr", "augmented_qr", "gram_cg", - "normal_cg", "regularized_normal_cg"}``, independently of the forward - solver. ``"direct"`` solves the general square equation - ``J theta_dot = -J_p p_dot`` with ``jnp.linalg.solve``. The root is unique, - so this method intentionally does not apply the parameter metric; it - rejects nonsquare systems. ``"svd"``, ``"qr"``, and ``"augmented_qr"`` - factor the whitened Jacobian from its small side (see ``jacobian_mode``) - and need the metric's ``inv_sqrt``/``inv_sqrt_transpose`` pair. A - solve-only metric must pair with ``ad_solver="direct"`` on a square - system or ``"gram_cg"``. - - ``"auto"`` resolves from traced shapes before inspecting the forward - solver: every square system uses ``"direct"``. For a nonsquare system a - ``gram_cg`` or ``normal_cg`` forward keeps its corresponding Krylov space; - every other forward uses ``"svd"``. Thus an ``lsmr`` forward with an - explicit ``normal_cg`` AD solve stays fully matrix-free, while a square - algebraic root gets the inexpensive direct solve even when its forward - solver is CG. - - Implicit AD is defined for ``LMStatus.CONVERGED`` and, by the forgiving - default, ``LMStatus.MAX_STEPS``. Pass ``max_steps_is_success=False`` to - treat exhaustion as failure instead. A failed result keeps its primal data - and diagnostics but returns exact zero tangents for ``result.x`` and - ``result.aux``; ``result.p`` remains an identity pass-through. The failed - lane's linear tangent program uses stop-gradient copies of the caller's - original ``(x0, args, p)``. Those values must be JVP-safe for the residual - and aux map, plus any ``MetricFactory`` or ``PreconditionerFactory`` - consumed by the resolved AD method. A selected multi-start winner that - fails this AD policy uses the caller's original initial point, not a drawn - retry, regardless of the custom acceptance result. - - A ``gram_cg`` AD solve requires ``ad_solver_preconditioner``, an - approximation of the UNDAMPED ``(J P J')^{-1} v``, taking either ``(v)`` - or ``(v, damping)``. A callable requiring the damping argument is called - with an explicit zero. Every shipped dual helper serves both hooks directly - except ``pad_dual_preconditioner``, which divides by live damping and is - rejected here. Under ``normal_cg`` or ``regularized_normal_cg`` the same - hook acts in parameter space -- an approximation of ``(B'B)^{-1} v``, - never served by the dual-space ``preconditioner_factory`` -- and is - optional. Its action must preserve ``range(B')`` exactly like - ``normal_preconditioner``. ``ad_solver_tol``/``ad_solver_atol``/ - ``ad_solver_maxiter`` are the CG stopping controls. - - The dense methods have deliberately separate numerical contracts: - - - ``ad_solver="svd"`` computes the spectral-filter pseudoinverse of - ``B'B``, taking singular values from an SVD of ``B`` itself at the - standard ``max(m, n) * eps * sigma_max`` cutoff. It gives the exact - full-rank sensitivity and minimum-``M``-norm tangent for a consistent - rank-deficient system, without ridge bias and at ``eps * cond(B)`` - accuracy. The cutoff is numerical: promote with ``linear_solve_dtype`` - when genuinely meaningful singular values fall below it. On a - rank-deficient problem whose active subspace rotates with ``p``, higher - derivatives carry only a first-order guarantee because the range - projector is frozen. - - ``ad_solver="qr"`` computes the exact unregularized tangent through a - reduced QR factorization. It applies the same numerical-rank cutoff to - the small ``R`` factor and returns a NaN tangent when the Jacobian is - numerically rank deficient instead of silently selecting a solution. - - ``ad_solver="augmented_qr"`` applies the trace-scaled Tikhonov ridge - ``B'B + ad_solver_penalty * trace(B'B) I`` through a QR factorization - of ``[B; sqrt(ridge) I]`` from the small side. It has - O(``ad_solver_penalty * dim``) relative bias on consistent systems and - stays smooth on nearly degenerate problems. - - ``ad_solver="regularized_normal_cg"`` applies a matrix-free ridge scaled - by a Rayleigh quotient of ``B'B`` over a fixed deterministic probe, - keeping the tangent linear in ``p_dot`` and the ridge alive at zero - tangent. - - ``ad_solver_penalty`` is required and positive only for - ``"augmented_qr"`` and ``"regularized_normal_cg"``. Passing it with any - other method is an error; the penalty never changes which algorithm runs. - ``gram_cg`` and ``normal_cg`` are unregularized and run to tolerance. A - zero Jacobian also zeroes the trace-scaled ``augmented_qr`` ridge and still - fails loudly. - - ``linear_solve_dtype=jnp.float64`` promotes the dense linear-solve - pipelines -- the forward ``gram_cholesky``/``normal_cholesky`` (and - ``auto``) branches and the direct/SVD/QR AD methods -- to float64: ``J'`` is - cast wide before the metric application, the assembly, factorization, and - triangular solves run wide, and only the returned step/tangent is cast - back, so the model, residual, and every output stay at the residual - dtype. Forming - ``J P J'`` squares the condition number of the whitened Jacobian - ``J S`` (``S S' = P``), which is what makes the dense paths - float32-fragile; the promotion buys full-x64 robustness for the dual - solve at the cost of up to two wide n x m intermediates and roughly - 1.4x per cholesky update measured at m=100, n=2000 with a trivial - residual (real residual/Jacobian costs dominate and stay float32). - ``metric.solve`` receives the promoted dtype and must return it - (JAX-composed callbacks promote automatically). - Requires x64 support to be enabled -- which by itself leaves explicitly - float32 data in float32. - - ``metric_solve_dtype=jnp.float64`` instead promotes only the resolved - metric callbacks themselves (``solve``/``norm``/``inv_sqrt``/ - ``inv_sqrt_transpose``, fixed or factory-built): inputs are cast to - float64 on the way in, the callback computes wide, and the result is - cast back to the caller's dtype, so every solver -- including the - matrix-free cg/lsmr paths that ``linear_solve_dtype`` cannot touch -- - keeps its own dtype while a stiff metric's internal - triangular/recurrence solves stop being the float32 accuracy - bottleneck. It requires a custom metric or ``metric_factory`` and x64 - support; often the single float64 knob an otherwise-float32 program needs. - """ - - def __init__( - self, - residual_fn, - *, - init_damping=1e-3, - damping_decrease=0.5, - damping_increase=4.0, - min_damping=None, - max_damping=None, - linear_solver="auto", - jacobian_mode="auto", - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=8, - dual_preconditioner=None, - preconditioner_factory=None, - normal_preconditioner=None, - whitened_preconditioner=None, - ad_solver="auto", - ad_solver_tol=None, - ad_solver_atol=0.0, - ad_solver_maxiter=None, - ad_solver_preconditioner=None, - ad_solver_penalty=None, - linear_solve_dtype=None, - metric_solve_dtype=None, - metric=None, - metric_factory=None, - has_aux=False, - cache_jacobian=True, - geodesic_acceleration=True, - geodesic_acceptance_ratio=0.75, - recycle=None, - ): - canonical_residual, residual_arity = canonicalize_residual(residual_fn) - if linear_solver not in ( - "auto", - "gram_cholesky", - "normal_cholesky", - "gram_cg", - "normal_cg", - "qr", - "augmented_qr", - "lsmr", - ): - raise ValueError(f"unknown linear_solver: {linear_solver}") - if jacobian_mode not in ("auto", "fwd", "rev"): - raise ValueError(f"unknown jacobian_mode: {jacobian_mode}") - if init_damping <= 0: - raise ValueError("init_damping must be positive") - if damping_decrease <= 0: - raise ValueError("damping_decrease must be positive") - if damping_increase <= 0: - raise ValueError("damping_increase must be positive") - if min_damping is not None and min_damping <= 0: - raise ValueError("min_damping must be positive or None") - if min_damping is not None and min_damping > init_damping: - raise ValueError("min_damping must not exceed init_damping") - if max_damping is not None and max_damping < init_damping: - raise ValueError("max_damping must be at least init_damping") - if iterative_tol < 0: - raise ValueError("iterative_tol must be nonnegative") - if iterative_atol < 0: - raise ValueError("iterative_atol must be nonnegative") - if iterative_maxiter is not None and iterative_maxiter <= 0: - raise ValueError("iterative_maxiter must be positive or None") - if iterative_tol == 0 and iterative_atol == 0 and iterative_maxiter is None: - raise ValueError( - "iterative_maxiter must be set when both iterative tolerances are zero" - ) - if dual_preconditioner is not None and linear_solver != "gram_cg": - raise ValueError('dual_preconditioner requires linear_solver="gram_cg"') - if preconditioner_factory is not None: - if linear_solver != "gram_cg": - raise ValueError( - 'preconditioner_factory requires linear_solver="gram_cg"' - ) - if dual_preconditioner is not None: - raise ValueError( - "pass exactly one of dual_preconditioner or " - "preconditioner_factory for a gram_cg linear_solver, not both" - ) - if normal_preconditioner is not None and linear_solver != "normal_cg": - raise ValueError('normal_preconditioner requires linear_solver="normal_cg"') - if linear_solver == "normal_cg" and normal_preconditioner is None: - raise ValueError( - 'linear_solver="normal_cg" requires normal_preconditioner, a ' - "jit-traceable, linear, SPD approximation of " - "(B'B + damping I)^{-1} v in parameter space; pass " - "identity_preconditioner() to run unpreconditioned CG" - ) - if whitened_preconditioner is not None and linear_solver != "lsmr": - raise ValueError('whitened_preconditioner requires linear_solver="lsmr"') - if recycle is not None: - if linear_solver != "gram_cg": - raise ValueError('recycle requires linear_solver="gram_cg"') - if not isinstance(recycle, RecycleConfig): - raise TypeError("recycle must be a RecycleConfig or None") - dense_ad_solvers = ("direct", "svd", "qr", "augmented_qr") - cg_ad_solvers = ("gram_cg", "normal_cg", "regularized_normal_cg") - if ad_solver not in ("auto", *dense_ad_solvers, *cg_ad_solvers): - raise ValueError(f"unknown ad_solver: {ad_solver}") - if ad_solver_tol is not None and ad_solver_tol < 0: - raise ValueError("ad_solver_tol must be nonnegative or None") - if ad_solver_atol < 0: - raise ValueError("ad_solver_atol must be nonnegative") - if ad_solver_maxiter is not None and ad_solver_maxiter <= 0: - raise ValueError("ad_solver_maxiter must be positive or None") - if ad_solver in ("augmented_qr", "regularized_normal_cg"): - if ad_solver_penalty is None or ad_solver_penalty <= 0: - raise ValueError( - f'ad_solver="{ad_solver}" requires a positive ad_solver_penalty' - ) - elif ad_solver_penalty is not None: - raise ValueError( - "ad_solver_penalty is accepted only with " - 'ad_solver="augmented_qr" or "regularized_normal_cg"' - ) - # Explicit methods resolve at construction. Auto stays unresolved until - # tracing, where static residual/parameter shapes select direct for a - # square system before considering the forward solver family. - resolved_ad_solver = ad_solver - if ( - resolved_ad_solver in cg_ad_solvers - and ad_solver_tol == 0 - and ad_solver_atol == 0 - and ad_solver_maxiter is None - ): - raise ValueError( - "ad_solver_maxiter must be set when both ad_solver tolerances are zero" - ) - # jacobian_mode is consumed by the dense forward paths (the cholesky - # forms directly or via "auto", qr, augmented_qr) and by the assembled - # AD methods. The matrix-free solvers never materialize J, so a forced mode - # that nothing could ever read is a construction error, not a silent - # no-op. - if ( - jacobian_mode != "auto" - and linear_solver in ("gram_cg", "normal_cg", "lsmr") - and resolved_ad_solver not in ("auto", *dense_ad_solvers) - ): - raise ValueError( - "jacobian_mode controls dense Jacobian assembly, but neither " - f'linear_solver="{linear_solver}" nor the ' - f'"{resolved_ad_solver}"-resolved ad_solver ever consumes it' - ) - auto_may_use_cg = ad_solver == "auto" and linear_solver in ( - "gram_cg", - "normal_cg", - ) - if ( - ad_solver_preconditioner is not None - and resolved_ad_solver not in cg_ad_solvers - and not auto_may_use_cg - ): - raise ValueError( - "ad_solver_preconditioner requires a cg-resolved ad_solver: " - 'ad_solver="gram_cg", "normal_cg", or ' - '"regularized_normal_cg", or "auto" alongside a cg forward ' - "solver" - ) - missing_dual_preconditioner = ( - linear_solver == "gram_cg" - and dual_preconditioner is None - and preconditioner_factory is None - ) - # A factory serves the gram_cg AD hook too (undamped apply at the - # solution), so it satisfies the gram_cg AD requirement like an - # explicit one. A normal_cg-resolved AD solve needs no preconditioner: - # its rhs lies in range(B'), so unpreconditioned CG from zero already - # converges to the minimum-norm tangent; an explicit - # ad_solver_preconditioner (the n-space hook there, never served by - # the dual-space preconditioner_factory) only accelerates it. - missing_ad_preconditioner = ( - resolved_ad_solver == "gram_cg" - and ad_solver_preconditioner is None - and preconditioner_factory is None - ) - if missing_dual_preconditioner and missing_ad_preconditioner: - raise ValueError( - 'linear_solver="gram_cg" requires dual_preconditioner (or ' - "preconditioner_factory), and the gram_cg-resolved ad_solver " - "requires ad_solver_preconditioner; pass " - "identity_preconditioner() for either to run unpreconditioned " - "CG, or use a dense AD solver" - ) - if missing_dual_preconditioner: - raise ValueError( - 'linear_solver="gram_cg" requires dual_preconditioner or ' - "preconditioner_factory; pass identity_preconditioner() to run " - "unpreconditioned CG" - ) - if missing_ad_preconditioner: - raise ValueError( - 'ad_solver="gram_cg" requires ad_solver_preconditioner ' - "pass identity_preconditioner() to run unpreconditioned CG, " - "or use a dense AD solver" - ) - if linear_solve_dtype is not None: - if jnp.dtype(linear_solve_dtype) != jnp.dtype(jnp.float64): - raise ValueError("linear_solve_dtype must be None or jnp.float64") - if linear_solver not in ( - "auto", - "gram_cholesky", - "normal_cholesky", - ) and resolved_ad_solver not in ("auto", *dense_ad_solvers): - raise ValueError( - "linear_solve_dtype promotes only the dense linear-solve " - "pipelines; it requires a gram_cholesky, normal_cholesky, " - "or auto forward solver, or a dense AD solver" - ) - if not jax.config.jax_enable_x64: - raise ValueError( - "linear_solve_dtype=jnp.float64 requires x64 support; call " - 'jax.config.update("jax_enable_x64", True) at startup ' - "(explicitly float32 problem data stays float32)" - ) - if metric_factory is not None: - if not isinstance(metric_factory, MetricFactory): - raise TypeError("metric_factory must be a MetricFactory or None") - if metric is not None: - raise ValueError("pass at most one of metric or metric_factory") - if metric is None: - metric = GramMetric() - has_custom_metric = any( - cb is not None - for cb in ( - metric.solve, - metric.norm, - metric.inv_sqrt, - metric.inv_sqrt_transpose, - ) - ) - # Concrete solver names validate eagerly; "auto" defers the - # solver-specific check to trace time, where the resolved form is known - # (the geodesic norm requirement is form-independent and stays eager). - if has_custom_metric: - _validate_metric_requirements( - metric, linear_solver, geodesic_acceleration, "" - ) - if resolved_ad_solver in ( - "svd", - "qr", - "augmented_qr", - "normal_cg", - "regularized_normal_cg", - ): - _validate_metric_requirements( - metric, - resolved_ad_solver, - False, - "", - keyword="ad_solver", - ) - if metric_solve_dtype is not None: - if jnp.dtype(metric_solve_dtype) != jnp.dtype(jnp.float64): - raise ValueError("metric_solve_dtype must be None or jnp.float64") - if not has_custom_metric and metric_factory is None: - raise ValueError( - "metric_solve_dtype wraps the resolved metric callbacks; " - "it requires a custom metric or a metric_factory" - ) - if not jax.config.jax_enable_x64: - raise ValueError( - "metric_solve_dtype=jnp.float64 requires x64 support; call " - 'jax.config.update("jax_enable_x64", True) at startup ' - "(explicitly float32 problem data stays float32)" - ) - self.residual_fn = canonical_residual - self.residual_arity = residual_arity - self.init_damping = init_damping - self.damping_decrease = damping_decrease - self.damping_increase = damping_increase - self.min_damping = min_damping - self.max_damping = max_damping - self.linear_solver = linear_solver - self.jacobian_mode = jacobian_mode - self.iterative_tol = iterative_tol - self.iterative_atol = iterative_atol - self.iterative_maxiter = iterative_maxiter - self.dual_preconditioner = dual_preconditioner - self.preconditioner_factory = preconditioner_factory - self.normal_preconditioner = normal_preconditioner - self.whitened_preconditioner = whitened_preconditioner - self.ad_solver = ad_solver - self.ad_solver_tol = ad_solver_tol - self.ad_solver_atol = ad_solver_atol - self.ad_solver_maxiter = ad_solver_maxiter - self.ad_solver_preconditioner = ( - None - if ad_solver_preconditioner is None - else canonicalize_ad_preconditioner(ad_solver_preconditioner) - ) - self.ad_solver_penalty = ad_solver_penalty - self.linear_solve_dtype = ( - None if linear_solve_dtype is None else jnp.dtype(linear_solve_dtype) - ) - self.metric_solve_dtype = ( - None if metric_solve_dtype is None else jnp.dtype(metric_solve_dtype) - ) - self._resolved_ad_solver = resolved_ad_solver - self.metric = metric - self.metric_factory = metric_factory - # Only the dense gram/normal cholesky paths materialize J' (the (n, m) - # cache serves both forms), so the flag is inert for the other solvers. - self.cache_jacobian = cache_jacobian and linear_solver in ( - "auto", - "gram_cholesky", - "normal_cholesky", - ) - self.has_aux = has_aux - self._has_custom_metric = has_custom_metric - self._has_metric_solve = metric.solve is not None - # The operative callbacks come from the (optionally dtype-wrapped) - # metric; the static key stays on the original metric plus the dtype, - # since the wrapper's fresh closures would degrade it to identity. - operative_metric = metric - if self.metric_solve_dtype is not None and metric_factory is None: - operative_metric = _metric_with_compute_dtype( - metric, self.metric_solve_dtype - ) - self.metric_solve = ( - (lambda x: x) if operative_metric.solve is None else operative_metric.solve - ) - self.metric_norm = ( - (lambda x: jnp.linalg.norm(x)) - if operative_metric.norm is None - else operative_metric.norm - ) - self.metric_inv_sqrt = ( - (lambda x: x) - if operative_metric.inv_sqrt is None - else operative_metric.inv_sqrt - ) - self.metric_inv_sqrt_transpose = ( - (lambda x: x) - if operative_metric.inv_sqrt_transpose is None - else operative_metric.inv_sqrt_transpose - ) - self.geodesic_acceleration = geodesic_acceleration - self.geodesic_acceptance_ratio = geodesic_acceptance_ratio - self.recycle = recycle - # Value-based identity: the jitted solve loop marks the solver itself - # static, so equal-config solvers built around the same residual (and - # metric/preconditioner objects) share the compiled loop across - # instances instead of retracing once per construction. Keyed on the - # constructor arguments -- every derived attribute is a function of them. - self._static_key = tuple( - _static_key_component(value) - for value in ( - residual_fn, - init_damping, - damping_decrease, - damping_increase, - min_damping, - max_damping, - linear_solver, - jacobian_mode, - iterative_tol, - iterative_atol, - iterative_maxiter, - dual_preconditioner, - preconditioner_factory, - normal_preconditioner, - whitened_preconditioner, - ad_solver, - ad_solver_tol, - ad_solver_atol, - ad_solver_maxiter, - ad_solver_preconditioner, - ad_solver_penalty, - self.linear_solve_dtype, - self.metric_solve_dtype, - metric, - metric_factory, - has_aux, - self.cache_jacobian, - geodesic_acceleration, - geodesic_acceptance_ratio, - recycle, - ) - ) - self._static_hash = hash(self._static_key) - - def __eq__(self, other): - if self is other: - return True - if type(other) is not type(self): - return NotImplemented - return self._static_key == other._static_key - - def __hash__(self): - return self._static_hash - - def hyperparams(self, dtype=None): - """``LMHyperparams`` built from the constructor values.""" - return LMHyperparams( - jnp.asarray(self.damping_decrease, dtype=dtype), - jnp.asarray(self.damping_increase, dtype=dtype), - _damping_floor(self.min_damping, dtype), - None - if self.max_damping is None - else jnp.asarray(self.max_damping, dtype=dtype), - jnp.asarray(self.geodesic_acceptance_ratio, dtype=dtype), - jnp.asarray(self.iterative_tol, dtype=dtype), - jnp.asarray(self.iterative_atol, dtype=dtype), - None - if self.iterative_maxiter is None - else jnp.asarray(self.iterative_maxiter, dtype=jnp.int32), - ) - - def init(self, x0, args=None, *, p=None): - # One residual evaluation types the damping to match what update() - # returns (keeping the jit signature and solve-loop carry stable) and - # sizes the Jacobian cache buffers when cache_jacobian=True. hyper - # stays None so manual update() loops carry no extra buffers; solve() - # populates it for its callbacks. - self._check_residual_args(args, p) - residual, aux = self._residual_and_aux(x0, args, p) - min_damping = _damping_floor(self.min_damping, residual.dtype) - damping = jnp.maximum( - jnp.asarray(self.init_damping, dtype=residual.dtype), min_damping - ) - recycle = self._init_recycle_state(residual) - precond, precond_valid = self._init_precond(x0, args, p, aux) - metric_state, metric_valid = self._init_metric_state(x0, args, p, aux) - if not self.cache_jacobian: - return LMState( - damping, - recycle=recycle, - precond=precond, - precond_valid=precond_valid, - metric_state=metric_state, - metric_valid=metric_valid, - ) - theta, _ = ravel_pytree(x0) - return LMState( - damping, - resid=jnp.zeros(residual.shape, dtype=residual.dtype), - Jt=jnp.zeros((theta.size, residual.size), dtype=residual.dtype), - jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), - aux=jax.tree.map(jnp.zeros_like, aux), - recycle=recycle, - precond=precond, - precond_valid=precond_valid, - metric_state=metric_state, - metric_valid=metric_valid, - ) - - def _init_precond(self, x0, args, p, aux): - # State built at x0 and valid there: the first update reuses it (x has - # not moved yet), so init pays the one build and the first step does not - # rebuild. None for the default path. - if self.preconditioner_factory is None: - return None, None - state = jax.lax.stop_gradient( - self.preconditioner_factory.prepare(x0, args, p, aux) - ) - return state, jnp.asarray(True, dtype=jnp.bool_) - - def _init_metric_state(self, x0, args, p, aux): - # Same lifecycle as _init_precond, but NOT stop-gradient'd: unlike a - # preconditioner, the metric defines the subproblem, so differentiating - # an update through init keeps the prepared state's dependence on - # (x0, args, p, aux). - if self.metric_factory is None: - return None, None - state = self.metric_factory.prepare(x0, args, p, aux) - return state, jnp.asarray(True, dtype=jnp.bool_) - - def _metric_callbacks_from(self, metric, solver, *, keyword="linear_solver"): - # Trace-time validation and identity defaulting for a factory-built - # metric, matching the constructor rules for the fixed ``metric=`` path; - # ``solver`` is the trace-time-resolved form consuming the callbacks. - if not isinstance(metric, GramMetric): - raise TypeError( - "metric_factory.build must return a GramMetric; got " - f"{type(metric).__name__}" - ) - _validate_metric_requirements( - metric, - solver, - self.geodesic_acceleration, - " on the GramMetric returned by metric_factory.build", - keyword=keyword, - ) - return ( - (lambda v: v) if metric.solve is None else metric.solve, - (lambda v: jnp.linalg.norm(v)) if metric.norm is None else metric.norm, - (lambda v: v) if metric.inv_sqrt is None else metric.inv_sqrt, - (lambda v: v) - if metric.inv_sqrt_transpose is None - else metric.inv_sqrt_transpose, - metric.solve is not None, - ) - - def _init_recycle_state(self, residual): - # Cold recycle state sized from the dual dimension m = residual.size: - # zero basis and zero warm starts, valid=False. The zero-U invariant - # makes the first deflated solve a pure P-only PCG (no branch). - if self.recycle is None: - return None - m = residual.size - k = self.recycle.rank - w = self.recycle.resolved_window - if k > m or w > m: - raise ValueError( - f"recycle rank ({k}) and window ({w}) must be <= the dual " - f"dimension m ({m})" - ) - dtype = residual.dtype - return RecycleState( - U=jnp.zeros((m, k), dtype=dtype), - dual_velocity=jnp.zeros(m, dtype=dtype), - dual_accel=jnp.zeros(m, dtype=dtype), - valid=jnp.asarray(False, dtype=jnp.bool_), - iterations=jnp.zeros((), dtype=jnp.int32), - residual_norm=jnp.zeros((), dtype=dtype), - ) - - def _resolve_jacobian_mode(self, m, n): - # Static (shape-driven) choice of dense Jacobian assembly: "auto" - # takes n forward-mode columns when the system is tall or square - # (n <= m) and m reverse-mode rows only when strictly fat (n > m), - # so the identity basis being vmapped is always the small side (an - # m x m residual basis over a tall system is a compile-time memory - # blowup). The square tie goes to forward mode: at equal pass counts - # a JVP is cheaper than a VJP. - if self.jacobian_mode != "auto": - return self.jacobian_mode - return "fwd" if n <= m else "rev" - - def _assemble_jt(self, jvp_fn, theta, resid): - # J' with shape (n, m) from a linearized JVP closure, assembled per - # _resolve_jacobian_mode. - if self._resolve_jacobian_mode(resid.shape[0], theta.shape[0]) == "fwd": - parameter_basis = jnp.eye(theta.shape[0], dtype=theta.dtype) - return jax.vmap(jvp_fn)(parameter_basis) - transpose_fn = jax.linear_transpose(jvp_fn, theta) - residual_basis = jnp.eye(resid.shape[0], dtype=resid.dtype) - return jax.vmap(lambda cotangent: transpose_fn(cotangent)[0])(residual_basis).T - - def _dense_resid_jt_aux(self, residual_flat, theta): - # Materialize the residual and J' for the dense paths. - if self.has_aux: - resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) - else: - resid, jvp_fn = jax.linearize(residual_flat, theta) - aux = None - return resid, self._assemble_jt(jvp_fn, theta, resid), aux - - def _residual_and_aux(self, x, args, p): - if self.has_aux: - value, aux = self.residual_fn(x, args, p) - # aux rides through the jitted loop carry and the implicit-AD - # zero-tangent map, so non-numeric leaves can never work; fail - # here with a clear message instead of a dtype error deep in - # the trace. - for leaf in jax.tree.leaves(aux): - if not isinstance( - leaf, (jax.Array, np.ndarray, np.generic, bool, int, float, complex) - ): - raise TypeError( - "has_aux=True: aux leaves must be JAX numeric types " - f"(arrays or scalars); got {type(leaf).__name__}" - ) - return jnp.ravel(value), aux - return jnp.ravel(self.residual_fn(x, args, p)), None - - def _initial_info(self, x, lm_state, args, p): - # grad_norm is a +inf sentinel (computing it would cost a Jacobian - # before the first step) and step_norm is zero; neither can satisfy - # gtol/xtol before any update has run. - residual, aux = self._residual_and_aux(x, args, p) - loss = jnp.sum(residual**2) - zero = jnp.zeros((), dtype=residual.dtype) - one = jnp.ones((), dtype=residual.dtype) - return LMInfo( - loss=loss, - loss_old=loss, - loss_candidate=loss, - accepted=jnp.asarray(False, dtype=jnp.bool_), - damping=jnp.asarray(lm_state.damping, dtype=residual.dtype), - damping_factor=one, - used_geodesic=jnp.asarray(False, dtype=jnp.bool_), - acceleration_ratio=zero, - grad_norm=jnp.asarray(jnp.inf, dtype=residual.dtype), - step_norm=zero, - aux=aux, - ) - - def update(self, x, lm_state, args=None, p=None): - self._check_residual_args(args, p) - # Linearize at x: flatten the pytree and view the residual over theta. - theta, unravel = ravel_pytree(x) - - if self.has_aux: - - def residual_flat(th): - value, aux = self.residual_fn(unravel(th), args, p) - return jnp.ravel(value), aux - - def residual_value(th): - return residual_flat(th)[0] - - else: - - def residual_flat(th): - return jnp.ravel(self.residual_fn(unravel(th), args, p)) - - residual_value = residual_flat - - # Build J': matrix-free JVP/VJP closures for the cg forms and lsmr; the - # dense paths materialize J' from the small side per jacobian_mode, - # reused from the cache after a rejected step. - if self.linear_solver in ("gram_cg", "normal_cg", "lsmr"): - if self.has_aux: - resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) - else: - resid, jvp_fn = jax.linearize(residual_flat, theta) - aux = None - elif self.cache_jacobian: - if lm_state.jacobian_valid is None: - raise ValueError( - "cache_jacobian=True but the lm_state has no Jacobian cache; " - "create the lm_state with init(x, args, p=p)" - ) - - def compute_resid_and_jt(_): - return self._dense_resid_jt_aux(residual_flat, theta) - - def reuse_resid_and_jt(_): - return lm_state.resid, lm_state.Jt, lm_state.aux - - resid, Jt, aux = jax.lax.cond( - lm_state.jacobian_valid, - reuse_resid_and_jt, - compute_resid_and_jt, - operand=None, - ) - else: - resid, Jt, aux = self._dense_resid_jt_aux(residual_flat, theta) - # Traced hyperparameters from the lm_state when present (resettable by - # solve callbacks); the None fallback compiles to the same constants - # as reading the constructor values directly. - hyper = ( - lm_state.hyper - if lm_state.hyper is not None - else self.hyperparams(resid.dtype) - ) - damping_decrease = jnp.asarray(hyper.damping_decrease, dtype=resid.dtype) - damping_increase = jnp.asarray(hyper.damping_increase, dtype=resid.dtype) - min_damping = _damping_floor(hyper.min_damping, resid.dtype) - damping = jnp.maximum( - jnp.asarray(lm_state.damping, dtype=resid.dtype), min_damping - ) - - # Trace-time shape resolution of the default solver: shapes are concrete - # while tracing, so this is a plain Python branch (never a lax.cond). - # Strictly more parameters than residuals keeps the smaller m x m gram - # dual; otherwise the n x n normal system is the smaller factor and the - # only full-rank one for m >= n. - resolved_solver = self.linear_solver - if resolved_solver == "auto": - resolved_solver = ( - "gram_cholesky" if theta.size > resid.size else "normal_cholesky" - ) - - # Iterate-aware metric: rebuild the prepared state from the pre-step x - # and this linearization's aux, or reuse the carried state when the - # previous step was rejected (x did not move) -- the precond_valid - # lax.cond pattern. build() runs once per update, before the iterative - # loops, so builder-internal setup (e.g. a tridiagonal Cholesky scan) - # is loop-invariant across the inner cg/lsmr iterations. The velocity, - # geodesic-acceleration, and norm applications below all share this - # one pre-step metric. - if self.metric_factory is not None: - if lm_state.metric_state is None: - raise ValueError( - "metric_factory is set but the lm_state has no metric " - "state; create the lm_state with init(x, args, p=p)" - ) - metric_state = jax.lax.cond( - lm_state.metric_valid, - lambda _: lm_state.metric_state, - lambda _: self.metric_factory.prepare(x, args, p, aux), - operand=None, - ) - built_metric = self.metric_factory.build(metric_state) - if self.metric_solve_dtype is not None: - built_metric = _metric_with_compute_dtype( - built_metric, self.metric_solve_dtype - ) - ( - metric_solve, - metric_norm, - metric_inv_sqrt, - metric_inv_sqrt_transpose, - _, - ) = self._metric_callbacks_from(built_metric, resolved_solver) - else: - # The auto forward deferred the fixed metric's solver-specific - # requirement to here, where the resolved form is known. - if self.linear_solver == "auto" and self._has_custom_metric: - _validate_metric_requirements(self.metric, resolved_solver, False, "") - metric_solve = self.metric_solve - metric_norm = self.metric_norm - metric_inv_sqrt = self.metric_inv_sqrt - metric_inv_sqrt_transpose = self.metric_inv_sqrt_transpose - - # Recycled dual solutions + harvest, captured in call order by the - # gram_cg branch's solve_step when recycling is active; consumed below - # to build the next RecycleState. Stays None for every non-recycled path. - recycle_solves = None - if self.linear_solver == "gram_cg": - transpose_fn = jax.linear_transpose(jvp_fn, theta) - - def JT(cotangent): - return transpose_fn(cotangent)[0] - - grad = JT(resid) - # Typed tolerances keep CG's scalars in the residual dtype under x64. - cg_tol = jnp.asarray(hyper.iterative_tol, dtype=resid.dtype) - cg_atol = jnp.asarray(hyper.iterative_atol, dtype=resid.dtype) - - def gram_matvec(cotangent): - return jvp_fn(metric_solve(JT(cotangent))) + damping * cotangent - - # θ-adaptive preconditioner: rebuild the state from the pre-step x - # (this step's dual linearization point), or reuse the carried state - # when the previous step was rejected (x did not move) -- the - # jacobian_valid lax.cond pattern, so the rebuild cost is skipped - # exactly when nothing changed. apply reads the live damping, so a - # reused state is still correct at the new damping. - if self.preconditioner_factory is not None: - if lm_state.precond is None: - raise ValueError( - "preconditioner_factory is set but the lm_state has no " - "preconditioner state; create the lm_state with " - "init(x, args, p=p)" - ) - precond_state = jax.lax.cond( - lm_state.precond_valid, - lambda _: lm_state.precond, - lambda _: jax.lax.stop_gradient( - self.preconditioner_factory.prepare(x, args, p, aux) - ), - operand=None, - ) - - def cg_preconditioner(cotangent): - return self.preconditioner_factory.apply( - precond_state, cotangent, damping - ) - - else: - - def cg_preconditioner(cotangent): - return self.dual_preconditioner(cotangent, damping) - - if self.recycle is not None and lm_state.recycle is not None: - # Recycled/deflated dual solve: build the coarse operator once on - # the current damped gram_matvec (reused across velocity and the - # geodesic-acceleration RHS), harvest the next basis from the - # velocity solve only, and capture the dual solutions (in call - # order: velocity first, acceleration second) so the new - # RecycleState can thread out through the returned lm_state. - recycle = lm_state.recycle - rank = self.recycle.rank - window = self.recycle.resolved_window - warm_start = self.recycle.warm_start - reorthogonalize = self.recycle.reorthogonalize - _, e_factor = build_coarse_operator( - gram_matvec, recycle.U, ridge=self.recycle.ridge - ) - recycle_solves = [] - - def solve_step(rhs): - is_velocity = len(recycle_solves) == 0 - x0 = None - if warm_start: - x0 = ( - recycle.dual_velocity if is_velocity else recycle.dual_accel - ) - dual_solution, harvest = deflated_pcg( - gram_matvec, - rhs, - U=recycle.U, - E_factor=e_factor, - M=cg_preconditioner, - x0=x0, - tol=cg_tol, - atol=cg_atol, - maxiter=hyper.iterative_maxiter, - window=window, - rank=rank, - reorthogonalize=reorthogonalize, - harvest=is_velocity, - ) - recycle_solves.append((dual_solution, harvest)) - return -metric_solve(JT(dual_solution)) - - else: - - def solve_step(rhs): - dual_solution, _ = jsp_sparse_linalg.cg( - gram_matvec, - rhs, - tol=cg_tol, - atol=cg_atol, - maxiter=hyper.iterative_maxiter, - M=cg_preconditioner, - ) - return -metric_solve(JT(dual_solution)) - - elif self.linear_solver == "normal_cg": - # Matrix-free whitened normal equations in parameter space: - # (B'B + damping I) u = -B' r with B = J S (S = metric.inv_sqrt), - # step s = S u. The Krylov space is n-dimensional (iterative_maxiter - # budgets n-space iterations) and the rhs lies in range(B'), so CG - # from zero keeps the minimum-M-norm selection for rank-deficient B; - # normal_preconditioner must preserve range(B') to keep that (see - # the docs' range-preservation warning). - transpose_fn = jax.linear_transpose(jvp_fn, theta) - - def JT(cotangent): - return transpose_fn(cotangent)[0] - - grad = JT(resid) - cg_tol = jnp.asarray(hyper.iterative_tol, dtype=resid.dtype) - cg_atol = jnp.asarray(hyper.iterative_atol, dtype=resid.dtype) - - def B_matvec(u): - return jvp_fn(metric_inv_sqrt(u)) - - def Bt_matvec(w): - return metric_inv_sqrt_transpose(JT(w)) - - def normal_matvec(u): - return Bt_matvec(B_matvec(u)) + damping * u - - def cg_preconditioner(u): - return self.normal_preconditioner(u, damping) - - def solve_step(rhs): - u, _ = jsp_sparse_linalg.cg( - normal_matvec, - Bt_matvec(-rhs), - tol=cg_tol, - atol=cg_atol, - maxiter=hyper.iterative_maxiter, - M=cg_preconditioner, - ) - return metric_inv_sqrt(u) - - elif self.linear_solver == "lsmr": - # Matrix-free whitened damped LS: min_u ||r + B u||^2 + damping ||u||^2 - # with B = J S (S = metric.inv_sqrt). Working on B (condition sqrt of - # the cg dual's J M^{-1} J' + damping I) restores endgame accuracy in - # the selection-critical slow directions where the squared dual solve - # bottoms out at eps * cond. Step s = S u. - transpose_fn = jax.linear_transpose(jvp_fn, theta) - - def JT(cotangent): - return transpose_fn(cotangent)[0] - - grad = JT(resid) - # Hook -> Fong-Saunders/scipy LSMR name mapping (kept standard in - # lsmr.py): iterative_tol becomes LSMR's atol (relative, scaled by - # normar0 = ||A'b||, i.e. operator-scaled) and iterative_atol becomes - # btol (absolute). Passed as lsmr_solve's atol/btol positionals below. - lsmr_tol = jnp.asarray(hyper.iterative_tol, dtype=resid.dtype) - lsmr_atol = jnp.asarray(hyper.iterative_atol, dtype=resid.dtype) - sqrt_damping = jnp.sqrt(damping) - m = resid.shape[0] - n = theta.shape[0] - # None (uncapped) has no meaning for a fixed-shape loop; a - # tolerance-only stop still needs a hard cap. min(m, n) is the - # bidiagonalization's exact-arithmetic termination bound. - lsmr_maxiter = ( - hyper.iterative_maxiter - if hyper.iterative_maxiter is not None - else 4 * min(m, n) - ) - - # Parameter-space right-preconditioner R^{-1} (whitened_preconditioner): - # LSMR runs in z = R u on the augmented operator below, whose damping - # row is sqrt(damping) R^{-1} z = sqrt(damping) u -- so every - # damping > 0 subproblem is EXACTLY the I-damped - # min_u ||r + B u||^2 + damping ||u||^2 for ANY R. R changes the - # iteration path (a good one clusters the spectrum of B R^{-1}), - # never the subproblem, and the damping -> 0 selection limit stays - # the minimum-M-norm step. None -> plain LSMR. - if self.whitened_preconditioner is not None: - - def apply_Rinv(v): - return self.whitened_preconditioner.solve(v, damping) - - def apply_RinvT(w): - return self.whitened_preconditioner.solve_transpose(w, damping) - - else: - - def apply_Rinv(v): - return v - - def apply_RinvT(w): - return w - - def B_matvec(u): - return jvp_fn(metric_inv_sqrt(u)) - - def Bt_matvec(w): - return metric_inv_sqrt_transpose(JT(w)) - - # N = B'B + damping I: the R-free SPD normal operator that - # custom_linear_solve differentiates through, posed on u (not z) so - # a generic cotangent rhs needs only R^{-1}/R^{-T} inside the solve. - def N_matvec(u): - return Bt_matvec(B_matvec(u)) + damping * u - - def solve_N(_, c): - # Solve (B'B + damping I) u = c for arbitrary c by LSMR on the - # R-preconditioned augmented operator - # [B R^{-1}; sqrt(damping) R^{-1}] in z = R u: its normal - # equations in u read (B'B + damping I) u = B' b1 + sqrt(damping) b2, - # so b_aug = [0; c / sqrt(damping)] targets c exactly, at - # condition sqrt(cond(N)). Stopping is measured on the - # preconditioned operator (the well-conditioned z coordinates). - # The forward c and every cotangent RHS route through here. - def A_aug(zz): - u_zz = apply_Rinv(zz) - return jnp.concatenate([B_matvec(u_zz), sqrt_damping * u_zz]) - - def At_aug(ww): - return apply_RinvT(Bt_matvec(ww[:m]) + sqrt_damping * ww[m:]) - - b_aug = jnp.concatenate([jnp.zeros(m, resid.dtype), c / sqrt_damping]) - z, _ = lsmr_solve( - A_aug, - At_aug, - b_aug, - jnp.zeros((), resid.dtype), - lsmr_tol, - lsmr_atol, - lsmr_maxiter, - n, - ) - return apply_Rinv(z) - - def solve_step(rhs): - # u solves min ||B u + rhs||^2 + damping ||u||^2; step s = S u. - c = Bt_matvec(-rhs) - u = jax.lax.custom_linear_solve( - N_matvec, c, solve=solve_N, transpose_solve=solve_N, symmetric=True - ) - return metric_inv_sqrt(u) - - else: - grad = Jt @ resid - - if self.linear_solver == "augmented_qr": - transformed_Jt = metric_inv_sqrt_transpose(Jt) - n = transformed_Jt.shape[0] - augmented_matrix = jnp.concatenate( - ( - transformed_Jt.T, - jnp.sqrt(damping) * jnp.eye(n, dtype=resid.dtype), - ), - axis=0, - ) - Q, R = jnp.linalg.qr(augmented_matrix, mode="reduced") - - def solve_step(rhs): - augmented_rhs = jnp.concatenate( - (-rhs, jnp.zeros(n, dtype=rhs.dtype)) - ) - transformed_step = jsp_linalg.solve_triangular( - R, - Q.T @ augmented_rhs, - ) - return metric_inv_sqrt(transformed_step) - - elif self.linear_solver == "qr": - # Whitened residual-dimension reduction followed by augmented QR. - transformed_Jt = metric_inv_sqrt_transpose(Jt) - if transformed_Jt.shape[0] >= transformed_Jt.shape[1]: - R = jnp.linalg.qr(transformed_Jt, mode="r") - basis_eye = jnp.eye(R.shape[0], dtype=resid.dtype) - augmented_matrix = jnp.concatenate( - (R.T, jnp.sqrt(damping) * basis_eye), - axis=0, - ) - Qa, Ra = jnp.linalg.qr(augmented_matrix, mode="reduced") - - def solve_step(rhs): - augmented_rhs = jnp.concatenate( - (-rhs, jnp.zeros(R.shape[0], dtype=rhs.dtype)) - ) - z = jsp_linalg.solve_triangular( - Ra, - Qa.T @ augmented_rhs, - ) - y = jsp_linalg.solve_triangular(R, z) - return metric_inv_sqrt(transformed_Jt @ y) - - else: - Q, R = jnp.linalg.qr(transformed_Jt, mode="reduced") - basis_eye = jnp.eye(R.shape[0], dtype=resid.dtype) - augmented_matrix = jnp.concatenate( - (R.T, jnp.sqrt(damping) * basis_eye), - axis=0, - ) - Qa, Ra = jnp.linalg.qr(augmented_matrix, mode="reduced") - - def solve_step(rhs): - augmented_rhs = jnp.concatenate( - (-rhs, jnp.zeros(R.shape[0], dtype=rhs.dtype)) - ) - z = jsp_linalg.solve_triangular( - Ra, - Qa.T @ augmented_rhs, - ) - return metric_inv_sqrt(Q @ z) - - elif resolved_solver == "normal_cholesky": - # Damped whitened normal factorization: cholesky of - # N = B'B + damping I_n with B' = S' J' (S = metric.inv_sqrt), - # step s = -S N^{-1} B' rhs. By the push-through identity - # S (B'B + damping I)^{-1} B' = P J' (J P J' + damping I)^{-1}, - # the step equals the gram form's for every damping > 0, and the - # damping -> 0 limit is the minimum-M-norm step -- but N has - # full rank whenever B does, so m >= n no longer factors a - # structurally rank-deficient dual. Same wide-pipeline recipe as - # the gram branch: J' promoted BEFORE the whitening application, - # wide assembly/factor/solves, only the step cast back. - dense_dtype = ( - resid.dtype - if self.linear_solve_dtype is None - else self.linear_solve_dtype - ) - whitened_jacobian_t = metric_inv_sqrt_transpose(Jt.astype(dense_dtype)) - normal_matrix = whitened_jacobian_t @ whitened_jacobian_t.T - normal_matrix = normal_matrix + jnp.asarray( - damping, dtype=dense_dtype - ) * jnp.eye(theta.shape[0], dtype=dense_dtype) - - normal_factor = jsp_linalg.cho_factor(normal_matrix) - - def solve_step(rhs): - whitened_step = jsp_linalg.cho_solve( - normal_factor, - -(whitened_jacobian_t @ rhs.astype(dense_dtype)), - ) - return metric_inv_sqrt(whitened_step).astype(resid.dtype) - - else: - # Damped Gram factorization: cholesky of J P J' + damping I. - # With linear_solve_dtype the whole dual pipeline runs wide: - # J' is promoted BEFORE the metric solve (a stiff metric's - # 1/eps rows amplify float32 rounding of P J' into O(1) Gram - # errors -- promoting only the assembly was measured ~4 - # digits worse), and the dual solution stays wide through the - # final product. Only the returned step is cast back, so it - # keeps the residual dtype. metric.solve therefore receives - # the promoted dtype; jnp-composed callbacks promote - # automatically. - dense_dtype = ( - resid.dtype - if self.linear_solve_dtype is None - else self.linear_solve_dtype - ) - transposed_jacobian = Jt.astype(dense_dtype) - gram_step_left = metric_solve(transposed_jacobian) - linear_matrix = transposed_jacobian.T @ gram_step_left - linear_matrix = linear_matrix + jnp.asarray( - damping, dtype=dense_dtype - ) * jnp.eye(resid.shape[0], dtype=dense_dtype) - - linear_factor = jsp_linalg.cho_factor(linear_matrix) - - def solve_step(rhs): - dual_solution = jsp_linalg.cho_solve( - linear_factor, rhs.astype(dense_dtype) - ) - step = -gram_step_left @ dual_solution - return step.astype(resid.dtype) - - # Dual solve for the first-order step (velocity). - velocity = solve_step(resid) - resid_velocity = residual_value(theta + velocity) - loss_old = jnp.sum(resid**2) - loss_velocity = jnp.sum(resid_velocity**2) - zero = jnp.zeros((), dtype=resid.dtype) - - # Geodesic second-order correction, solved with the same factorization. - if self.geodesic_acceleration: - geodesic_acceptance_ratio = jnp.asarray( - hyper.geodesic_acceptance_ratio, dtype=resid.dtype - ) - - def first_jvp(th): - # [1] is the tangent with and without has_aux. - return jax.jvp(residual_flat, (th,), (velocity,), has_aux=self.has_aux)[ - 1 - ] - - f_vv = jax.jvp(first_jvp, (theta,), (velocity,))[1] - acceleration = solve_step(f_vv) - accelerated_step = velocity + 0.5 * acceleration - acceleration_ratio = ( - 2.0 - * metric_norm(acceleration) - / (metric_norm(velocity) + jnp.finfo(resid.dtype).eps) - ) - ratio_accepted = ( - (geodesic_acceptance_ratio > zero) - & (acceleration_ratio > zero) - & (acceleration_ratio <= geodesic_acceptance_ratio) - ) - - def accelerated_loss(_): - resid_accelerated = residual_value(theta + accelerated_step) - return jnp.sum(resid_accelerated**2) - - loss_accelerated = jax.lax.cond( - ratio_accepted, - accelerated_loss, - lambda _: jnp.asarray(jnp.inf, dtype=resid.dtype), - operand=None, - ) - used_geodesic = ratio_accepted & (loss_accelerated <= loss_velocity) - step = jnp.where(used_geodesic, accelerated_step, velocity) - loss_candidate = jnp.where(used_geodesic, loss_accelerated, loss_velocity) - else: - step = velocity - loss_candidate = loss_velocity - used_geodesic = jnp.asarray(False) - acceleration_ratio = zero - - # Accept iff the sum of squared residuals decreases and is finite. - improved = jnp.isfinite(loss_candidate) & (loss_candidate < loss_old) - theta_new = jnp.where(improved, theta + step, theta) - # Damping update: decrease on acceptance, increase on rejection. - damping_factor = jnp.where(improved, damping_decrease, damping_increase) - new_damping = damping * damping_factor - if hyper.max_damping is not None: - new_damping = jnp.minimum( - new_damping, - jnp.maximum( - jnp.asarray(hyper.max_damping, dtype=resid.dtype), min_damping - ), - ) - new_damping = jnp.maximum(new_damping, min_damping) - loss = jnp.where(improved, loss_candidate, loss_old) - # New recycle state: the velocity solve's harvested basis and the (stop- - # gradient'd) dual solutions become warm starts for the next step. Threads - # through unchanged (None) for every non-recycled path. dual_accel is the - # acceleration dual when geodesic acceleration ran, else zeros -- a single - # stable carry shape independent of the geodesic flag. - new_recycle = lm_state.recycle - if recycle_solves is not None: - velocity_dual, velocity_harvest = recycle_solves[0] - if len(recycle_solves) > 1: - accel_dual = recycle_solves[1][0] - else: - accel_dual = jnp.zeros_like(velocity_dual) - new_recycle = RecycleState( - U=jax.lax.stop_gradient(velocity_harvest.basis), - dual_velocity=jax.lax.stop_gradient(velocity_dual), - dual_accel=jax.lax.stop_gradient(accel_dual), - valid=jnp.asarray(True, dtype=jnp.bool_), - iterations=jax.lax.stop_gradient(velocity_harvest.iterations), - residual_norm=jax.lax.stop_gradient(velocity_harvest.residual_norm), - ) - # Carry the state built at this step's pre-step x; precond_valid = ~improved - # marks it reusable next step exactly when the step was rejected (x did - # not move). On acceptance the carried state is stale but shape-stable -- - # the flag forces a rebuild at the new x before it is applied. - new_precond = lm_state.precond - new_precond_valid = lm_state.precond_valid - if self.preconditioner_factory is not None: - new_precond = precond_state - new_precond_valid = ~improved - new_metric_state = lm_state.metric_state - new_metric_valid = lm_state.metric_valid - if self.metric_factory is not None: - new_metric_state = metric_state - new_metric_valid = ~improved - # The input hyper (not the fallback) passes through so the loop carry - # structure and dtypes are stable. - if self.cache_jacobian: - new_lm_state = LMState( - new_damping, - resid=resid, - Jt=Jt, - jacobian_valid=~improved, - aux=aux, - hyper=lm_state.hyper, - recycle=new_recycle, - precond=new_precond, - precond_valid=new_precond_valid, - metric_state=new_metric_state, - metric_valid=new_metric_valid, - ) - else: - new_lm_state = LMState( - new_damping, - hyper=lm_state.hyper, - recycle=new_recycle, - precond=new_precond, - precond_valid=new_precond_valid, - metric_state=new_metric_state, - metric_valid=new_metric_valid, - ) - return ( - unravel(theta_new), - new_lm_state, - LMInfo( - loss=loss, - loss_old=loss_old, - loss_candidate=loss_candidate, - accepted=improved, - damping=new_damping, - damping_factor=damping_factor, - used_geodesic=used_geodesic, - acceleration_ratio=acceleration_ratio, - grad_norm=jnp.linalg.norm(grad), - step_norm=jnp.linalg.norm(step), - aux=aux, - ), - ) - - def solve( - self, - x0, - args=None, - *, - p=None, - lm_state=None, - max_steps=256, - max_steps_is_success=True, - atol=0.0, - gtol=0.0, - xtol=0.0, - callback=None, - user_state=None, - save_steps=False, - multi_start=None, - jit=True, - ): - """Run repeated LM updates until a stopping rule fires. - - Parameters are the same as ``update`` plus loop controls. ``max_steps`` - is always enforced. ``max_steps_is_success=True`` (the default) treats - ``LMStatus.MAX_STEPS`` as a usable result for implicit AD and the - default multi-start acceptance policy while preserving the - ``MAX_STEPS`` status for diagnostics. Set it to ``False`` for strict - failure semantics. ``atol`` stops when the residual norm is below the - threshold, ``gtol`` when the gradient norm ``||J' r||`` is below the - threshold, and ``xtol`` when an accepted step has norm below the - threshold; each tolerance set to ``0`` disables that check, and all - three report ``LMStatus.CONVERGED``. ``callback`` receives an - ``LMSolveContext`` after each step and may return an ``LMSolveAction`` - to stop or to override x/lm_state/args/user_state. ``p`` is passed to - the residual and callback but cannot be replaced by the action. A - callback that installs an invalid ``x`` or ``args`` must also stop with - a failed status such as ``LMStatus.NONFINITE``; otherwise a final-step - replacement is legitimately reported as ``MAX_STEPS`` and follows the - configured success policy. - ``save_steps=True`` records the full iterate history onto the result: - ``x_history`` stacks x0 and every kept post-step iterate along a - ``(max_steps + 1)`` leading axis (rows beyond ``steps`` are zero - padding — slice with ``result.steps``), plus the row-aligned - ``args_history`` (the kept post-action args, recorded even when no - callback ever replaces them; ``None`` when ``args`` is ``None``) and, - with ``has_aux``, the row-aligned ``aux_history``. The history buffers - cost ``(max_steps + 1) x (size(x) + size(args) [+ size(aux)])`` - memory, are differentiation-inert, and (unlike the default) make the - jitted loop retrace when ``max_steps`` changes, since the buffer shape - depends on it. - - ``multi_start`` (a ``MultiStart``, default ``None``) retries or - parallelizes the solve over fresh initial conditions drawn by - ``multi_start.draw`` and returns the single best result, with - diagnostics on ``result.multi_start`` (a ``MultiStartInfo``). - Sequential mode retries only on failure and stops at the first - success; ``parallel=True`` solves every start under ``vmap`` and - selects the accepted lane with the lowest loss. Gradients with - respect to ``p`` flow through the selected solution only, via the - same implicit rule as a plain solve. With ``multi_start=None`` - nothing changes. - - Implicit AD uses ``LMStatus.CONVERGED`` and also ``LMStatus.MAX_STEPS`` - when ``max_steps_is_success=True``. Every failed status receives zero - tangents for ``result.x`` and ``result.aux``. To keep automatic VJP - transposition finite under ``vmap``, the failed lane's linear tangent - program is evaluated at differentiation-inert copies of the original - ``(x0, args, p)``. Those initial values must be valid for JVP evaluation - of the residual, aux map, and any metric or preconditioner factory that - the resolved AD method consumes. The primal failed result is never - replaced. - """ - self._check_residual_args(args, p) - if not isinstance(max_steps_is_success, bool): - raise TypeError("max_steps_is_success must be a bool") - if max_steps <= 0: - raise ValueError("max_steps must be positive") - # Tolerances are traced data inside the loop, so vmapped/traced values - # skip the concrete-only sign validation. - if not isinstance(atol, jax.core.Tracer) and atol < 0: - raise ValueError("atol must be nonnegative") - if not isinstance(gtol, jax.core.Tracer) and gtol < 0: - raise ValueError("gtol must be nonnegative") - if not isinstance(xtol, jax.core.Tracer) and xtol < 0: - raise ValueError("xtol must be nonnegative") - if lm_state is None: - # The loop recasts the damping and hyperparameter dtypes itself; the - # Jacobian cache (cache_jacobian), the recycle state (sized from the - # residual), and the preconditioner/metric states (built by prepare) - # need an eager init() for their shapes. - if ( - self.cache_jacobian - or self.recycle is not None - or self.preconditioner_factory is not None - or self.metric_factory is not None - ): - lm_state = self.init(x0, args, p=p) - else: - lm_state = LMState(jnp.asarray(self.init_damping)) - if lm_state.hyper is None: - # Populate here (not in init) so manual update() loops stay lean; - # inside the loop the extra scalars are loop-carried, not - # re-dispatched per step. - lm_state = dataclasses.replace(lm_state, hyper=self.hyperparams()) - # The history buffers need a concrete length, so it is fixed here (like - # callback and jit, via closure) and the buffers are allocated inside - # the loop implementations; with save_steps=False nothing changes, and - # with save_steps=True the buffer shape retraces per max_steps anyway. - history_len = max_steps + 1 if save_steps else None - - if multi_start is not None: - if not isinstance(multi_start, MultiStart): - raise TypeError("multi_start must be a MultiStart or None") - num_starts = multi_start.num_starts - # A single start never draws: normalizing to None keeps the jit - # cache key independent of the (unused) draw identity. The hooks - # are jit statics, so unhashable callables get an - # identity-hashing wrapper (hash/eq by the wrapped function, so - # repeat calls still share the compilation). - draw = _hashable_hook(multi_start.draw if num_starts > 1 else None) - default_accept = ( - _accept_converged_or_max_steps - if max_steps_is_success - else _accept_converged - ) - accept = _hashable_hook( - default_accept if multi_start.accept is None else multi_start.accept - ) - parallel = multi_start.parallel and num_starts > 1 - if draw is not None and jit: - # Abstract trace only (no RNG, no FLOPs): fail loudly here - # instead of deep inside the while_loop/vmap carry checks. - # jit=False validates the first concrete draw instead, so a - # successful first attempt never invokes draw. - drawn = jax.eval_shape(draw, multi_start.key, x0, args) - _check_drawn_types(x0, args, drawn) - - @jax.custom_jvp - def solve_multi_start_with_ad_p( - x, - lm_state, - args, - p, - user_state, - key, - max_steps, - atol, - gtol, - xtol, - ): - return self._multi_start_impl( - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - num_starts, - draw, - accept, - parallel, - ) - - @solve_multi_start_with_ad_p.defjvp - def solve_multi_start_with_ad_p_jvp(primals, tangents): - p_dot = tangents[3] - result = solve_multi_start_with_ad_p(*primals) - initial_ad_point = (primals[0], primals[2], primals[3]) - return result, self._ad_result_tangent( - result, p_dot, initial_ad_point, max_steps_is_success - ) - - return solve_multi_start_with_ad_p( - x0, - lm_state, - args, - p, - user_state, - multi_start.key, - max_steps, - atol, - gtol, - xtol, - ) - - @jax.custom_jvp - def solve_with_ad_p( - x, - lm_state, - args, - p, - user_state, - max_steps, - atol, - gtol, - xtol, - ): - return self._solve_impl( - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - ) - - @solve_with_ad_p.defjvp - def solve_with_ad_p_jvp(primals, tangents): - p_dot = tangents[3] - result = solve_with_ad_p(*primals) - initial_ad_point = (primals[0], primals[2], primals[3]) - return result, self._ad_result_tangent( - result, p_dot, initial_ad_point, max_steps_is_success - ) - - return solve_with_ad_p( - x0, - lm_state, - args, - p, - user_state, - max_steps, - atol, - gtol, - xtol, - ) - - def _solve_impl( - self, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - ): - if jit: - return _solve_loop_jit( - self, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - ) - return _solve_python_impl( - self, - x, - lm_state, - args, - p, - user_state, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - ) - - def _multi_start_impl( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - jit, - num_starts, - draw, - accept, - parallel, - ): - if not jit: - return _multi_start_python_impl( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - num_starts, - draw, - accept, - parallel, - ) - if parallel: - return _multi_start_parallel_jit( - self, - x, - lm_state, - args, - p, - user_state, - key, - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, - num_starts, - ) - return _multi_start_sequential_jit( - self, - x, - lm_state, - args, - p, - user_state, - key, - jnp.asarray(num_starts, dtype=jnp.int32), - history_len, - max_steps, - atol, - gtol, - xtol, - callback, - draw, - accept, - ) - - def _cast_state(self, lm_state, dtype): - # Shared-loop protocol hook: recast the carried scalars so the - # while_loop carry matches what update() returns. - return dataclasses.replace( - lm_state, - damping=jnp.asarray(lm_state.damping, dtype=dtype), - hyper=_cast_hyper(lm_state.hyper, dtype), - ) - - def _cold_state(self, lm_state): - # Shared-loop protocol hook for multi-start lane resets. - return _cold_lm_state(lm_state) - - def _ranking_objective(self, result, p, callback): - # Shared-loop protocol hook for multi-start selection. - return _ranking_loss(self, result, p, callback) - - def _ad_result_tangent(self, result, p_dot, initial_ad_point, max_steps_is_success): - # A successful tangent relinearizes at the returned solution. A failed - # tangent uses the differentiation-inert original initial point so an - # invalid returned iterate cannot poison a vmapped transpose. Nothing - # reuses the forward iterations. Everything except x, p, and aux -- - # histories, counters, multi-start diagnostics -- is bookkeeping with - # zero tangents. - initial_x, initial_args, initial_p = jax.tree.map( - jax.lax.stop_gradient, initial_ad_point - ) - ad_success = result.status == LMStatus.CONVERGED - if max_steps_is_success: - ad_success = ad_success | (result.status == LMStatus.MAX_STEPS) - ad_x = _where_tree(ad_success, result.x, initial_x) - ad_args = _where_tree(ad_success, result.args, initial_args) - ad_p = _where_tree(ad_success, result.p, initial_p) - ad_p_dot = _mask_tangent_tree(ad_success, p_dot) - resolved = None if ad_p is None else self._ad_solver_at(ad_x, ad_args, ad_p) - - factory_needs_aux = ( - ad_p is not None - and self.has_aux - and resolved != "direct" - and ( - self.metric_factory is not None - or ( - resolved == "gram_cg" - and self.ad_solver_preconditioner is None - and self.preconditioner_factory is not None - ) - ) - ) - ad_aux = result.aux - if factory_needs_aux: - ad_aux = jax.lax.cond( - ad_success, - lambda: result.aux, - lambda: self._residual_and_aux(ad_x, ad_args, ad_p)[1], - ) - - x_dot = self._ad_x_tangent_from_p( - ad_x, ad_args, ad_p, ad_p_dot, ad_aux, resolved - ) - zero_result = jax.tree.map(_zero_tangent_leaf, result) - x_dot = _where_tree(ad_success, x_dot, zero_result.x) - aux_dot = zero_result.aux - if self.has_aux and ad_p is not None: - # aux depends on p directly and through the solution x*(p); - # linearize the aux map at the returned solution with args - # fixed (the same point where the primal result.aux is - # evaluated) to account for both paths. - def aux_at_solution(x_value, p_value): - return self.residual_fn(x_value, ad_args, p_value)[1] - - aux_dot = jax.jvp(aux_at_solution, (ad_x, ad_p), (x_dot, ad_p_dot))[1] - aux_dot = _where_tree(ad_success, aux_dot, zero_result.aux) - return dataclasses.replace(zero_result, x=x_dot, p=p_dot, aux=aux_dot) - - def _ad_solver_at(self, x, args, p): - if self.ad_solver != "auto": - return self.ad_solver - theta, _ = ravel_pytree(x) - residual_shape = jax.eval_shape( - lambda x_value, args_value, p_value: self._residual_and_aux( - x_value, args_value, p_value - )[0], - x, - args, - p, - ).shape - if residual_shape[0] == theta.size: - return "direct" - if self.linear_solver == "gram_cg": - return "gram_cg" - if self.linear_solver == "normal_cg": - return "normal_cg" - return "svd" - - def _ad_x_tangent_from_p(self, x, args, p, p_dot, aux, resolved): - if p is None: - return jax.tree.map(_zero_tangent_leaf, x) - if resolved == "direct": - return self._ad_tangent_direct(x, args, p, p_dot) - if ( - resolved in ("gram_cg", "normal_cg", "regularized_normal_cg") - and self.ad_solver_tol == 0 - and self.ad_solver_atol == 0 - and self.ad_solver_maxiter is None - ): - raise ValueError( - "ad_solver_maxiter must be set when both ad_solver tolerances are zero" - ) - if ( - resolved == "gram_cg" - and self.ad_solver_preconditioner is None - and self.preconditioner_factory is None - ): - raise ValueError( - 'auto-resolved ad_solver="gram_cg" requires ' - "ad_solver_preconditioner; pass identity_preconditioner() " - "to run unpreconditioned CG or select another ad_solver" - ) - if self.metric_factory is not None: - # The metric is FROZEN at the returned solution: prepare/build once - # from (x, args, p, aux) -- x/args/p are the traced solution, so the - # state is traced data (never a closure constant) and repeated - # solves at different p do not recompile. Its state-dependence is - # not differentiated within this first-order solve, the same - # contract as a fixed metric closing over constants (higher-order - # AD differentiates the resulting pointwise tangent field). - built_metric = self.metric_factory.build( - self.metric_factory.prepare(x, args, p, aux) - ) - if self.metric_solve_dtype is not None: - built_metric = _metric_with_compute_dtype( - built_metric, self.metric_solve_dtype - ) - # Gram CG accepts either metric.solve or the whitening pair; the - # remaining non-direct methods require the whitening pair. - solve_cb, _, inv_sqrt_cb, inv_sqrt_transpose_cb, has_solve = ( - self._metric_callbacks_from( - built_metric, - resolved if resolved != "gram_cg" else None, - keyword="ad_solver", - ) - ) - else: - if self._has_custom_metric and resolved != "gram_cg": - _validate_metric_requirements( - self.metric, - resolved, - False, - "", - keyword="ad_solver", - ) - solve_cb = self.metric_solve - inv_sqrt_cb = self.metric_inv_sqrt - inv_sqrt_transpose_cb = self.metric_inv_sqrt_transpose - has_solve = self._has_metric_solve - if resolved == "normal_cg": - return self._ad_tangent_normal_cg( - x, args, p, p_dot, inv_sqrt_cb, inv_sqrt_transpose_cb - ) - if resolved == "regularized_normal_cg": - return self._ad_tangent_regularized_normal_cg( - x, args, p, p_dot, inv_sqrt_cb, inv_sqrt_transpose_cb - ) - if resolved == "svd": - return self._ad_tangent_svd( - x, args, p, p_dot, inv_sqrt_cb, inv_sqrt_transpose_cb - ) - if resolved == "qr": - return self._ad_tangent_qr( - x, args, p, p_dot, inv_sqrt_cb, inv_sqrt_transpose_cb - ) - if resolved == "augmented_qr": - return self._ad_tangent_augmented_qr( - x, args, p, p_dot, inv_sqrt_cb, inv_sqrt_transpose_cb - ) - if has_solve: - metric_inverse = solve_cb - else: - - def metric_inverse(v): - return inv_sqrt_cb(inv_sqrt_transpose_cb(v)) - - return self._ad_tangent_gram_cg(x, args, p, p_dot, metric_inverse, aux) - - def _ad_dense_linearization(self, x, args, p, p_dot): - theta, unravel = ravel_pytree(x) - - def residual_from_theta(theta_value): - return self._residual_and_aux(unravel(theta_value), args, p)[0] - - residual, theta_jvp = jax.linearize(residual_from_theta, theta) - Jt = self._assemble_jt(theta_jvp, theta, residual) - - def residual_from_p(p_value): - return self._residual_and_aux(x, args, p_value)[0] - - residual_p_dot = jax.jvp(residual_from_p, (p,), (p_dot,))[1] - ad_dtype = ( - residual.dtype - if self.linear_solve_dtype is None - else self.linear_solve_dtype - ) - return theta, unravel, residual, Jt, residual_p_dot, ad_dtype - - def _ad_tangent_direct(self, x, args, p, p_dot): - theta, unravel, residual, Jt, residual_p_dot, ad_dtype = ( - self._ad_dense_linearization(x, args, p, p_dot) - ) - if Jt.shape[0] != Jt.shape[1]: - raise ValueError( - 'ad_solver="direct" requires a square residual Jacobian; ' - f"got {residual.shape[0]} residuals and {theta.shape[0]} parameters" - ) - theta_dot = jnp.linalg.solve( - Jt.T.astype(ad_dtype), -residual_p_dot.astype(ad_dtype) - ) - return unravel(theta_dot.astype(residual.dtype)) - - def _ad_whitened_linearization(self, x, args, p, p_dot, inv_sqrt_transpose): - theta, unravel, residual, Jt, residual_p_dot, ad_dtype = ( - self._ad_dense_linearization(x, args, p, p_dot) - ) - whitened_jacobian_t = inv_sqrt_transpose(Jt.astype(ad_dtype)) - return ( - theta, - unravel, - residual, - residual_p_dot, - ad_dtype, - whitened_jacobian_t, - ) - - def _unwhiten_ad_tangent( - self, whitened_tangent, inv_sqrt, inv_sqrt_transpose, unravel, dtype - ): - theta_dot = -jax.lax.custom_linear_solve( - lambda v: v, - whitened_tangent, - lambda _, b: inv_sqrt(b), - transpose_solve=lambda _, b: inv_sqrt_transpose(b), - ) - return unravel(theta_dot.astype(dtype)) - - def _ad_tangent_svd(self, x, args, p, p_dot, inv_sqrt, inv_sqrt_transpose): - _, unravel, residual, residual_p_dot, ad_dtype, whitened_jacobian_t = ( - self._ad_whitened_linearization(x, args, p, p_dot, inv_sqrt_transpose) - ) - n, m = whitened_jacobian_t.shape - eps = jnp.asarray(np.finfo(jnp.dtype(ad_dtype)).eps, dtype=ad_dtype) - rank_dim = max(n, m) - rhs = whitened_jacobian_t @ residual_p_dot.astype(ad_dtype) - left, sigma, _ = jnp.linalg.svd(whitened_jacobian_t, full_matrices=False) - cutoff = rank_dim * eps * sigma[0] - inverse_sigma_sq = jnp.where(sigma > cutoff, 1.0 / sigma**2, 0.0) - - def pinv_solve(_, rhs_value): - return left @ (inverse_sigma_sq * (left.T @ rhs_value)) - - whitened_tangent = jax.lax.custom_linear_solve( - lambda v: whitened_jacobian_t @ (whitened_jacobian_t.T @ v), - rhs, - pinv_solve, - symmetric=True, - ) - return self._unwhiten_ad_tangent( - whitened_tangent, - inv_sqrt, - inv_sqrt_transpose, - unravel, - residual.dtype, - ) - - def _ad_tangent_qr(self, x, args, p, p_dot, inv_sqrt, inv_sqrt_transpose): - _, unravel, residual, residual_p_dot, ad_dtype, whitened_jacobian_t = ( - self._ad_whitened_linearization(x, args, p, p_dot, inv_sqrt_transpose) - ) - n, m = whitened_jacobian_t.shape - eps = jnp.asarray(np.finfo(jnp.dtype(ad_dtype)).eps, dtype=ad_dtype) - rank_dim = max(n, m) - rhs = whitened_jacobian_t @ residual_p_dot.astype(ad_dtype) - small_side = whitened_jacobian_t.T if m >= n else whitened_jacobian_t - _, r_factor = jnp.linalg.qr(small_side) - r_sigma = jnp.linalg.svd(r_factor, compute_uv=False) - singular = r_sigma[-1] <= rank_dim * eps * r_sigma[0] - if m >= n: - half = jsp_linalg.solve_triangular(r_factor.T, rhs, lower=True) - whitened_tangent = jsp_linalg.solve_triangular(r_factor, half, lower=False) - else: - dual_rhs = residual_p_dot.astype(ad_dtype) - half = jsp_linalg.solve_triangular(r_factor.T, dual_rhs, lower=True) - dual_solution = jsp_linalg.solve_triangular(r_factor, half, lower=False) - whitened_tangent = whitened_jacobian_t @ dual_solution - whitened_tangent = jnp.where(singular, jnp.nan, whitened_tangent) - return self._unwhiten_ad_tangent( - whitened_tangent, - inv_sqrt, - inv_sqrt_transpose, - unravel, - residual.dtype, - ) - - def _ad_tangent_augmented_qr(self, x, args, p, p_dot, inv_sqrt, inv_sqrt_transpose): - _, unravel, residual, residual_p_dot, ad_dtype, whitened_jacobian_t = ( - self._ad_whitened_linearization(x, args, p, p_dot, inv_sqrt_transpose) - ) - n, m = whitened_jacobian_t.shape - rhs = whitened_jacobian_t @ residual_p_dot.astype(ad_dtype) - ridge = jnp.sqrt(self.ad_solver_penalty * jnp.sum(whitened_jacobian_t**2)) - if m >= n: - stack = jnp.concatenate( - [whitened_jacobian_t.T, ridge * jnp.eye(n, dtype=ad_dtype)] - ) - _, r_factor = jnp.linalg.qr(stack) - half = jsp_linalg.solve_triangular(r_factor.T, rhs, lower=True) - whitened_tangent = jsp_linalg.solve_triangular(r_factor, half, lower=False) - else: - stack = jnp.concatenate( - [whitened_jacobian_t, ridge * jnp.eye(m, dtype=ad_dtype)] - ) - _, r_factor = jnp.linalg.qr(stack) - dual_rhs = residual_p_dot.astype(ad_dtype) - half = jsp_linalg.solve_triangular(r_factor.T, dual_rhs, lower=True) - dual_solution = jsp_linalg.solve_triangular(r_factor, half, lower=False) - whitened_tangent = whitened_jacobian_t @ dual_solution - return self._unwhiten_ad_tangent( - whitened_tangent, - inv_sqrt, - inv_sqrt_transpose, - unravel, - residual.dtype, - ) - - def _ad_tangent_gram_cg(self, x, args, p, p_dot, metric_inverse, aux): - theta, unravel = ravel_pytree(x) - - def residual_from_theta(theta_value): - return self._residual_and_aux(unravel(theta_value), args, p)[0] - - residual, theta_jvp = jax.linearize(residual_from_theta, theta) - theta_transpose = jax.linear_transpose(theta_jvp, theta) - - def JT(cotangent): - return theta_transpose(cotangent)[0] - - def gram_matvec(cotangent): - return theta_jvp(metric_inverse(JT(cotangent))) - - def residual_from_p(p_value): - return self._residual_and_aux(x, args, p_value)[0] - - cg_tol = self._ad_cg_tol(residual.dtype) - cg_atol = jnp.asarray(self.ad_solver_atol, dtype=residual.dtype) - - # An explicit ad_solver_preconditioner wins; otherwise a factory seeds - # the AD preconditioner from the state at the converged solution - # (undamped, since the AD dual has no damping floor). x/args/p are - # the traced returned solution, so prepare() yields a traced state (never - # a closure constant) and repeated solves at different p do not recompile; - # stop_gradient because the preconditioner never moves the root. - if self.ad_solver_preconditioner is not None: - cg_preconditioner = self.ad_solver_preconditioner - elif self.preconditioner_factory is not None: - precond_state = jax.lax.stop_gradient( - self.preconditioner_factory.prepare(x, args, p, aux) - ) - zero_damping = jnp.zeros((), dtype=residual.dtype) - - def cg_preconditioner(v): - return self.preconditioner_factory.apply(precond_state, v, zero_damping) - - else: - cg_preconditioner = None - - def solve(matvec, rhs): - solution, _ = jsp_sparse_linalg.cg( - matvec, - rhs, - tol=cg_tol, - atol=cg_atol, - maxiter=self.ad_solver_maxiter, - M=cg_preconditioner, - ) - return solution - - residual_p_dot = jax.jvp(residual_from_p, (p,), (p_dot,))[1] - dual_solution = jax.lax.custom_linear_solve( - gram_matvec, - residual_p_dot, - solve, - symmetric=True, - ) - - # The final metric inverse acts on tangent data, so VJP transposes - # it. A custom iterative metric solve need not be transposable by JAX, - # but P is self-adjoint by contract - # (for a metric_factory metric: self-adjoint at the fixed prepared - # state), so declare the application as its own transpose: every - # rule of this custom_linear_solve routes through `solve` (the - # identity matvec contributes nothing), and with symmetric=True the - # cotangent pass just EVALUATES metric.solve. custom_linear_solve - # is used rather than jax.custom_derivatives.linear_call because - # linear_call has no batching rule, which would break jax.vmap - # (and vmap-based second derivatives) over differentiated solves. - theta_dot = -jax.lax.custom_linear_solve( - lambda v: v, - JT(dual_solution), - lambda _, rhs: metric_inverse(rhs), - symmetric=True, - ) - return unravel(theta_dot) - - def _ad_tangent_normal_cg(self, x, args, p, p_dot, inv_sqrt, inv_sqrt_transpose): - return self._ad_tangent_normal_cg_impl( - x, - args, - p, - p_dot, - inv_sqrt, - inv_sqrt_transpose, - ridge_penalty=None, - ) - - def _ad_tangent_regularized_normal_cg( - self, x, args, p, p_dot, inv_sqrt, inv_sqrt_transpose - ): - return self._ad_tangent_normal_cg_impl( - x, - args, - p, - p_dot, - inv_sqrt, - inv_sqrt_transpose, - ridge_penalty=self.ad_solver_penalty, - ) - - def _ad_tangent_normal_cg_impl( - self, - x, - args, - p, - p_dot, - inv_sqrt, - inv_sqrt_transpose, - *, - ridge_penalty, - ): - theta, unravel = ravel_pytree(x) - - def residual_from_theta(theta_value): - return self._residual_and_aux(unravel(theta_value), args, p)[0] - - residual, theta_jvp = jax.linearize(residual_from_theta, theta) - theta_transpose = jax.linear_transpose(theta_jvp, theta) - - def JT(cotangent): - return theta_transpose(cotangent)[0] - - def B_matvec(u): - return theta_jvp(inv_sqrt(u)) - - def Bt_matvec(w): - return inv_sqrt_transpose(JT(w)) - - def residual_from_p(p_value): - return self._residual_and_aux(x, args, p_value)[0] - - residual_p_dot = jax.jvp(residual_from_p, (p,), (p_dot,))[1] - # rhs = B'(r_p p_dot) lies in range(B') = range(B'B), so the undamped - # normal system is consistent even for rank-deficient B and CG from - # zero converges to the minimum-norm whitened tangent in exact - # arithmetic -- no ridge by default (loud-failure philosophy: a - # divergent CG shows up as a non-finite or huge tangent, never a - # silently biased one). - rhs = Bt_matvec(residual_p_dot) - # regularized_normal_cg supplies a positive ridge_penalty explicitly. - # trace(N) is unavailable matrix-free, so its scale is a Rayleigh quotient of - # N (one extra matvec) over a FIXED normalized probe vector -- never - # the rhs, whose direction would make this tangent map nonlinear in - # p_dot and zero the ridge on a zero tangent. A deterministic - # jax.random draw is almost surely outside ker(B), where a - # constant-vector probe can sit for centered models; - # stop_gradient'ed as pure conditioning data. - ridge = None - if ridge_penalty is not None: - probe = jax.random.normal( - jax.random.key(0), (theta.shape[0],), dtype=residual.dtype - ) - probe = probe / jnp.linalg.norm(probe) - rayleigh = jax.lax.stop_gradient( - jnp.vdot(probe, Bt_matvec(B_matvec(probe))) - ) - ridge = ridge_penalty * rayleigh - - def normal_matvec(u): - product = Bt_matvec(B_matvec(u)) - if ridge is not None: - product = product + ridge * u - return product - - cg_tol = self._ad_cg_tol(residual.dtype) - cg_atol = jnp.asarray(self.ad_solver_atol, dtype=residual.dtype) - - def solve(matvec, rhs_value): - solution, _ = jsp_sparse_linalg.cg( - matvec, - rhs_value, - tol=cg_tol, - atol=cg_atol, - maxiter=self.ad_solver_maxiter, - M=self.ad_solver_preconditioner, - ) - return solution - - if ridge is not None: - # Ridged N is nonsingular SPD: plain symmetric CG serves both - # directions (a transpose cotangent's ker(B) component comes out - # finite at 1/ridge scale and the downstream B annihilates it). - whitened_tangent = jax.lax.custom_linear_solve( - normal_matvec, - rhs, - solve, - symmetric=True, - ) - else: - # Unridged transpose pass: the cotangent rhs S' theta_bar has no - # reason to lie in range(B'), and CG on the singular N with an - # inconsistent rhs breaks down (the residual floor stalls rho - # while p'Np -> 0). Route it through the push-through identity - # N^+ = B' G^{+2} B with G = BB' (check in the SVD B = U S V': - # B' G^{+2} B = V S^{-2} V'): both dual solves are consistent for - # ANY cotangent (B maps into range(G), G^+ stays there), CG from - # zero returns their minimum-norm solutions in exact arithmetic, - # and the final B' annihilates dual-null rounding noise -- the - # same self-cleaning that makes the gram composition robust. The - # n-space ad_solver_preconditioner does not apply in the m-space - # dual solves, which run unpreconditioned. - def dual_matvec(w): - return B_matvec(Bt_matvec(w)) - - def dual_solve(rhs_value): - solution, _ = jsp_sparse_linalg.cg( - dual_matvec, - rhs_value, - tol=cg_tol, - atol=cg_atol, - maxiter=self.ad_solver_maxiter, - ) - return solution - - def transpose_solve(_, cotangent): - return Bt_matvec(dual_solve(dual_solve(B_matvec(cotangent)))) - - whitened_tangent = jax.lax.custom_linear_solve( - normal_matvec, - rhs, - solve, - transpose_solve=transpose_solve, - ) - # theta_dot = -S u with S = metric.inv_sqrt, applied through the - # identity-matvec custom_linear_solve (the same deliberate deviation - # from the documented solve-inverts-matvec invariant as the gram_cg - # rule: every AD rule routes through the declared solves, and the - # identity matvec contributes nothing). Unlike the self-adjoint P - # there, S is NOT self-adjoint, so its transpose must be declared - # explicitly -- reverse mode EVALUATES inv_sqrt_transpose; declaring - # symmetric would silently apply S twice. - theta_dot = -jax.lax.custom_linear_solve( - lambda v: v, - whitened_tangent, - lambda _, b: inv_sqrt(b), - transpose_solve=lambda _, b: inv_sqrt_transpose(b), - ) - return unravel(theta_dot) - - def _ad_cg_tol(self, dtype): - if self.ad_solver_tol is not None: - return jnp.asarray(self.ad_solver_tol, dtype=dtype) - default_tol = 1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6 - return jnp.asarray(default_tol, dtype=dtype) - - def _action_or_default(self, action): - if action is None: - return LMSolveAction() - return action - - def _apply_action(self, action, x, lm_state, args, user_state): - action = self._action_or_default(action) - # The step's diagnostics and the cached Jacobian describe the - # pre-action (x, args), so both are stale iff the action actually - # changed the values — a traced comparison, so a jit-style callback - # that returns the field every step with unchanged values (the - # jnp.where recipe pattern) changes nothing. - problem_changed = jnp.asarray(False) - if action.x is not None: - problem_changed = problem_changed | _tree_changed(action.x, x) - x = action.x - if action.lm_state is not None: - previous_hyper = lm_state.hyper - lm_state = action.lm_state - if self.cache_jacobian and lm_state.jacobian_valid is None: - raise ValueError( - "cache_jacobian=True but the callback action returned an " - "lm_state without the Jacobian cache; use " - "dataclasses.replace(ctx.lm_state, ...) to preserve the " - "cache fields" - ) - if self.recycle is not None and lm_state.recycle is None: - raise ValueError( - "recycle is set but the callback action returned an lm_state " - "without the RecycleState; use dataclasses.replace(" - "ctx.lm_state, ...) to preserve the recycle field (rank and " - "window are static and cannot change mid-solve)" - ) - if self.preconditioner_factory is not None and lm_state.precond is None: - raise ValueError( - "preconditioner_factory is set but the callback action " - "returned an lm_state without the preconditioner state; use " - "dataclasses.replace(ctx.lm_state, ...) to preserve the " - "precond and precond_valid fields" - ) - if self.metric_factory is not None and lm_state.metric_state is None: - raise ValueError( - "metric_factory is set but the callback action returned an " - "lm_state without the metric state; use " - "dataclasses.replace(ctx.lm_state, ...) to preserve the " - "metric_state and metric_valid fields" - ) - # Trace-time guard so the hyper contract fails identically with - # and without jit (jit would reject the carry mismatch anyway). - if previous_hyper is not None and ( - lm_state.hyper is None - or jax.tree_util.tree_structure(previous_hyper) - != jax.tree_util.tree_structure(lm_state.hyper) - or [leaf.dtype for leaf in jax.tree_util.tree_leaves(previous_hyper)] - != [leaf.dtype for leaf in jax.tree_util.tree_leaves(lm_state.hyper)] - ): - raise ValueError( - "the callback action changed the structure or dtypes of " - "lm_state.hyper; reset values with " - "dataclasses.replace(ctx.lm_state.hyper, ...) using arrays " - "of the same dtype — a knob constructed as None cannot be " - "enabled mid-solve" - ) - if action.args is not None: - problem_changed = problem_changed | _tree_changed(action.args, args) - args = action.args - if action.user_state is not None: - user_state = action.user_state - if self.cache_jacobian and (action.x is not None or action.args is not None): - lm_state = dataclasses.replace( - lm_state, jacobian_valid=lm_state.jacobian_valid & ~problem_changed - ) - # A metric state prepared at the pre-action (x, args) no longer describes - # the subproblem once either changes; force a rebuild at the new point. - if self.metric_factory is not None and ( - action.x is not None or action.args is not None - ): - lm_state = dataclasses.replace( - lm_state, metric_valid=lm_state.metric_valid & ~problem_changed - ) - return action, x, lm_state, args, user_state, problem_changed - - def _check_residual_args(self, args, p): - # Silently dropping args/p a residual never sees would, in particular, - # make the implicit derivative with respect to p a silent zero. - if args is not None and self.residual_arity < 2: - raise ValueError( - "args was passed but residual_fn takes only (x); " - "use residual_fn(x, args)" - ) - if p is not None and self.residual_arity < 3: - raise ValueError( - "p was passed but residual_fn takes no p argument; " - "use residual_fn(x, args, p)" - ) - - def _converged(self, info, atol, gtol, xtol): - atol_met = (atol > 0) & (jnp.sqrt(info.loss) < atol) - gtol_met = (gtol > 0) & (info.grad_norm < gtol) - xtol_met = (xtol > 0) & info.accepted & (info.step_norm < xtol) - return atol_met | gtol_met | xtol_met - - -def _cold_lm_state(lm_state): - # Drawn starts must not reuse a Jacobian cache, a deflation basis, or a - # preconditioner/metric state built at another (x, args); damping and - # hyperparameters stay inherited from the caller's initial state. Never - # materializes fields from None -- the carry structure must match the - # attempt-0 result. - updates = {} - if lm_state.jacobian_valid is not None: - updates["jacobian_valid"] = jnp.zeros_like(lm_state.jacobian_valid) - if lm_state.precond is not None: - # Zero the stale state and mark it invalid so the drawn start's first - # update rebuilds prepare() at its own x before applying it. - updates["precond"] = jax.tree.map(jnp.zeros_like, lm_state.precond) - updates["precond_valid"] = jnp.zeros_like(lm_state.precond_valid) - if lm_state.metric_state is not None: - updates["metric_state"] = jax.tree.map(jnp.zeros_like, lm_state.metric_state) - updates["metric_valid"] = jnp.zeros_like(lm_state.metric_valid) - if lm_state.recycle is not None: - recycle = lm_state.recycle - updates["recycle"] = RecycleState( - U=jnp.zeros_like(recycle.U), - dual_velocity=jnp.zeros_like(recycle.dual_velocity), - dual_accel=jnp.zeros_like(recycle.dual_accel), - valid=jnp.zeros_like(recycle.valid), - iterations=jnp.zeros_like(recycle.iterations), - residual_norm=jnp.zeros_like(recycle.residual_norm), - ) - if not updates: - return lm_state - return dataclasses.replace(lm_state, **updates) - - -def _ranking_loss(solver, result, p, callback): - # A callback can replace x/args after the last update, leaving info.loss - # stale relative to the returned solution, so any callback-bearing solve - # pays one extra residual evaluation per attempt. Nonfinite losses mask - # to +inf so selection prefers any finite attempt and comparisons never - # propagate NaN. - if callback is None: - loss = result.info.loss - else: - residual = solver._residual_and_aux(result.x, result.args, p)[0] - loss = jnp.sum(residual**2) - return jnp.where(jnp.isfinite(loss), loss, jnp.asarray(jnp.inf, dtype=loss.dtype)) diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index 9940f45..4ecc537 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -114,6 +114,10 @@ class Subproblem: cache_enabled: bool hyper: Any ctx: Any + # Static: the ridge solver carries penalty rows, the metric solver + # does not. ridge is zero when unpenalized, so only the structural + # choices (extra QR rows, the diagonal shift) key on this. + penalized: bool = True @property def dtype(self): @@ -156,17 +160,21 @@ def cached(self, assemble): class StepSolver(NamedTuple): """What a linear solver returns for one LM step. - ``grad`` is the whitened half-gradient; ``velocity()`` the first-order - step in the whitened variable; ``solve(rhs)`` the same damped system - against an arbitrary right-hand side (the geodesic correction); - ``accel_rhs(f_vv)`` the correction's right-hand side; and - ``make_cache(valid)`` the pytree to carry, or ``None``. + ``grad`` is the whitened half-gradient (reported as ``info.grad_norm``); + ``velocity()`` the first-order step in the whitened variable; + ``correction(f_vv)`` the geodesic second-order correction from the + directional second derivative, also whitened; and ``make_cache(valid)`` + the pytree to carry, or ``None``. + + The two solves are one method rather than a ``solve(rhs)`` the caller + feeds: the Gram forms pose their right-hand side in residual space and the + normal forms in parameter space, and nothing outside the config needs to + know which. """ grad: jax.Array velocity: Any - solve: Any - accel_rhs: Any + correction: Any make_cache: Any @@ -176,7 +184,7 @@ class LinearSolver: materializes_jacobian = True - def new_cache(self, m, n, n_m, dtype): + def new_cache(self, m, n, n_m, dtype, penalized): """The reject-step cache pytree at ``init``, or ``None``.""" return None @@ -186,43 +194,88 @@ def prepare(self, sub): @dataclass(frozen=True) class Cholesky(LinearSolver): - """Dense normal equations. - - Assembles ``G = J~'J~ + ridge E`` -- cached across rejected steps, where - only the damping changed, so a reject pays the ``n^3/3`` refactor without - the GEMM and without re-materializing ``J~'`` -- and factors - ``G + damping I`` per step. No knobs. + """Dense factorization of the damped subproblem. + + ``form="normal"`` factors the ``n x n`` whitened normal system + ``G = J~'J~ + ridge E`` (cached across rejected steps, where only the + damping changed, so a reject pays the ``n^3/3`` refactor without the GEMM + and without re-materializing ``J~'``) and solves + ``(G + damping I) u = -g``. + + ``form="gram"`` factors the ``m x m`` dual ``D = J~ J~'`` instead and + takes the step ``u = -J~'(D + damping I)^{-1} r``. For ``damping > 0`` the + two produce the SAME step, by the push-through identity + ``B'(BB' + lam I)^{-1} = (B'B + lam I)^{-1}B'``; they differ only in which + dimension they factor in. ``form="auto"`` (the default) picks the smaller + at trace time -- gram when ``n > m``, normal otherwise -- so it is a cost + choice, not a semantics choice, and it keys on shape alone, never on + numerical rank. """ - def new_cache(self, m, n, n_m, dtype): + form: str = "auto" + + def _resolved_form(self, m, n, penalized): + # The ridge solver's penalty rows have no dual analogue -- the dual + # operator J~J~' never sees them -- so a penalized subproblem is + # always the normal form. The ridge constructor rejects an explicit + # form="gram" rather than silently ignoring it. + if penalized: + return "normal" + if self.form != "auto": + return self.form + return "gram" if n > m else "normal" + + def new_cache(self, m, n, n_m, dtype, penalized): + size = m if self._resolved_form(m, n, penalized) == "gram" else n return CholeskyCache( - G=jnp.zeros((n, n), dtype=dtype), + G=jnp.zeros((size, size), dtype=dtype), valid=jnp.asarray(False, dtype=jnp.bool_), ridge=jnp.zeros((), dtype=dtype), ) def prepare(self, sub): n_m, ridge, dtype = sub.n_m, sub.ridge, sub.dtype - grad = sub.whitened_transpose(sub.Jt @ sub.resid) + ridge * sub.penalty_gradient + # B' = F_bar^{-T} J', shape (n, m). Every form below is built from it. + grad = sub.whitened_transpose(sub.Jt @ sub.resid) + if sub.penalized: + grad = grad + ridge * sub.penalty_gradient + gram = self._resolved_form(sub.m, sub.n, sub.penalized) == "gram" def assemble(): - Jt_sub = sub.whitened_transpose(sub.Jt) + Bt = sub.whitened_transpose(sub.Jt) + if gram: + return Bt.T @ Bt + normal = Bt @ Bt.T + if not sub.penalized: + return normal diagonal = jnp.arange(n_m) - return (Jt_sub @ Jt_sub.T).at[diagonal, diagonal].add(ridge) + return normal.at[diagonal, diagonal].add(ridge) + + matrix = sub.cached(assemble) + size = sub.m if gram else sub.n + factor = jsp_linalg.cho_factor( + matrix + sub.damping * jnp.eye(size, dtype=dtype) + ) + if gram: + # u = -B'(D + damping I)^{-1} c on residual-space right-hand sides. + def dual_step(c): + return -sub.whitened_transpose(sub.Jt @ jsp_linalg.cho_solve(factor, c)) - normal_matrix = sub.cached(assemble) - shifted = normal_matrix + sub.damping * jnp.eye(sub.n, dtype=dtype) - factor = jsp_linalg.cho_factor(shifted) + velocity, correction = (lambda: dual_step(sub.resid)), dual_step + else: - def solve(rhs): - return -jsp_linalg.cho_solve(factor, rhs) + def normal_step(c): + return -jsp_linalg.cho_solve(factor, c) + velocity = lambda: normal_step(grad) # noqa: E731 + correction = lambda f_vv: normal_step( # noqa: E731 + sub.whitened_transpose(sub.Jt @ f_vv) + ) return StepSolver( grad=grad, - velocity=lambda: solve(grad), - solve=solve, - accel_rhs=lambda f_vv: sub.whitened_transpose(sub.Jt @ f_vv), - make_cache=lambda valid: CholeskyCache(normal_matrix, valid, ridge), + velocity=velocity, + correction=correction, + make_cache=lambda valid: CholeskyCache(matrix, valid, ridge), ) @@ -230,17 +283,21 @@ def solve(rhs): class QR(LinearSolver): """Damping-row QR of the augmented whitened stack. - One QR of ``[J~; sqrt(ridge) [I 0] | b~]`` with ``b~ = [r; sqrt(ridge) - y_m]`` is cached per ``(x, ridge)``: its leading columns are the stack's R - factor and its last column carries ``Q'b``, so the velocity is a - backward-stable least-squares solve with NO normal equations -- More - 1978's damping-row structure, accurate at ``cond(A)`` rather than - ``cond(A)^2``. Each step re-factors only the damping rows. No knobs. + One QR of ``[J~; sqrt(ridge) [I 0] | b~]`` (the penalty rows and the + ``b~`` tail only for the ridge solver) is cached per ``(x, ridge)``: its + leading columns are the stack's R factor and its last column carries + ``Q'b``, so the velocity is a backward-stable least-squares solve with NO + normal equations -- More 1978's damping-row structure, accurate at + ``cond(A)`` rather than ``cond(A)^2``. Each step re-factors only the + damping rows, and those rows keep the system full rank for any + ``damping > 0``, so a rank-deficient Jacobian is handled rather than + producing a non-finite step. No knobs. """ - def new_cache(self, m, n, n_m, dtype): + def new_cache(self, m, n, n_m, dtype, penalized): + rows = min(m + n_m, n + 1) if penalized else min(m, n + 1) return QRCache( - R=jnp.zeros((min(m + n_m, n + 1), n + 1), dtype=dtype), + R=jnp.zeros((rows, n + 1), dtype=dtype), valid=jnp.asarray(False, dtype=jnp.bool_), ridge=jnp.zeros((), dtype=dtype), ) @@ -248,14 +305,18 @@ def new_cache(self, m, n, n_m, dtype): def prepare(self, sub): n, n_m, ridge, dtype = sub.n, sub.n_m, sub.ridge, sub.dtype sqrt_ridge = jnp.sqrt(ridge) - grad = sub.whitened_transpose(sub.Jt @ sub.resid) + ridge * sub.penalty_gradient + grad = sub.whitened_transpose(sub.Jt @ sub.resid) + if sub.penalized: + grad = grad + ridge * sub.penalty_gradient def assemble(): - Jt_sub = sub.whitened_transpose(sub.Jt) - stacked = jnp.concatenate( - [Jt_sub.T, sqrt_ridge * jnp.eye(n_m, n, dtype=dtype)], axis=0 - ) - b_stacked = jnp.concatenate([sub.resid, sqrt_ridge * sub.y_m]) + Bt = sub.whitened_transpose(sub.Jt) + rows, rhs = [Bt.T], [sub.resid] + if sub.penalized: + rows.append(sqrt_ridge * jnp.eye(n_m, n, dtype=dtype)) + rhs.append(sqrt_ridge * sub.y_m) + stacked = jnp.concatenate(rows, axis=0) + b_stacked = jnp.concatenate(rhs) return jnp.linalg.qr( jnp.concatenate([stacked, b_stacked[:, None]], axis=1), mode="r" ) @@ -263,9 +324,9 @@ def assemble(): qr_R = sub.cached(assemble) r_factor, transformed_rhs = qr_R[:, :-1], qr_R[:, -1] # Per-step damping-row refactor: [R; sqrt(damping) I] = Q2 R2 with - # R2'R2 = A'A + damping I. When m + n_m < n the cached R is upper - # trapezoidal and these rows are what make the system full rank. Q2 is - # retained to transform the velocity right-hand side stably. + # R2'R2 = A'A + damping I. When the cached R is upper trapezoidal these + # rows are what make the system full rank. Q2 is retained to transform + # the velocity right-hand side stably. damped_stack = jnp.concatenate( [r_factor, jnp.sqrt(sub.damping) * jnp.eye(n, dtype=dtype)], axis=0 ) @@ -273,16 +334,19 @@ def assemble(): def damped_normal_matvec(v): gauss_newton = sub.whitened_transpose(sub.Jt @ (sub.Jt.T @ sub.whitened(v))) - metric_shift = jnp.concatenate([v[:n_m], jnp.zeros(sub.n_f, dtype=dtype)]) - return gauss_newton + ridge * metric_shift + sub.damping * v - - def solve(rhs): - # Corrected semi-normal equations (Bjorck 1987) for the geodesic - # right-hand side: triangular solves against R_mu, then ONE fixed - # iterative-refinement pass through matvecs (Bjorck 1996 Sec. - # 6.6.5). The second-order correction tolerates the squared - # conditioning; accept/reject guards it. - b = -rhs + shift = sub.damping * v + if sub.penalized: + shift = shift + ridge * jnp.concatenate( + [v[:n_m], jnp.zeros(sub.n_f, dtype=dtype)] + ) + return gauss_newton + shift + + def correction(f_vv): + # Corrected semi-normal equations (Bjorck 1987): triangular solves + # against R_mu, then ONE fixed iterative-refinement pass through + # matvecs (Bjorck 1996 Sec. 6.6.5). The second-order correction + # tolerates the squared conditioning; accept/reject guards it. + b = -sub.whitened_transpose(sub.Jt @ f_vv) half = jsp_linalg.solve_triangular(R_mu.T, b, lower=True) delta = jsp_linalg.solve_triangular(R_mu, half, lower=False) correction_rhs = b - damped_normal_matvec(delta) @@ -298,28 +362,59 @@ def velocity(): return StepSolver( grad=grad, velocity=velocity, - solve=solve, - accel_rhs=lambda f_vv: sub.whitened_transpose(sub.Jt @ f_vv), + correction=correction, make_cache=lambda valid: QRCache(qr_R, valid, ridge), ) +class _KrylovConfig(LinearSolver): + """Shared field validation for the matrix-free configs.""" + + materializes_jacobian = False + + def __post_init__(self): + if self.tol is not None and self.tol < 0: + raise ValueError("tol must be nonnegative or None") + if self.atol < 0: + raise ValueError("atol must be nonnegative") + if self.maxiter is not None and self.maxiter <= 0: + raise ValueError("maxiter must be positive or None") + if self.tol == 0 and self.atol == 0 and self.maxiter is None: + raise ValueError("maxiter must be set when both tolerances are zero") + + def _cg(self, matvec, c, sub, apply_M): + solution, _ = jsp_sparse_linalg.cg( + matvec, + c, + tol=jnp.asarray(sub.hyper.iterative_tol, dtype=sub.dtype), + atol=jnp.asarray(sub.hyper.iterative_atol, dtype=sub.dtype), + maxiter=sub.hyper.iterative_maxiter, + M=apply_M, + ) + return solution + + @dataclass(frozen=True) -class CG(LinearSolver): - """Matrix-free preconditioned CG on the whitened normal operator. +class CG(_KrylovConfig): + """Matrix-free preconditioned CG on the whitened NORMAL operator, in + parameter space. As ``linear_solver`` it solves the damped forward subproblem ``(J~'J~ + ridge E + damping I) delta_y = -g`` -- the same SPD system - :class:`Cholesky` factors -- with the ``preconditioner`` in CG's ``M`` - slot at the live damping. As ``ad_solver`` it solves the undamped - implicit-AD system ``J~'J~ + ridge E``, with the preconditioner applied at - zero damping (subclasses marked ``requires_positive_damping`` are rejected - for that role). - - ``preconditioner`` is REQUIRED in both roles -- nobody should run Krylov - methods without a preconditioning decision, so - :class:`~nlls_gram.IdentityPreconditioner` is the explicit opt-out and a - custom one is a small subclass implementing ``apply(v, damping, ctx)``. + :class:`Cholesky` factors -- with the ``preconditioner`` in CG's ``M`` slot + at the live damping. As ``ad_solver`` it solves the undamped implicit-AD + system, with the preconditioner applied at zero damping (subclasses marked + ``requires_positive_damping`` are rejected for that role) and ``penalty`` + optionally adding a small ridge that stabilizes a rank-deficient tangent. + + ``preconditioner`` is REQUIRED -- nobody should run Krylov methods without + a preconditioning decision, so :class:`~nlls_gram.IdentityPreconditioner` + is the explicit opt-out and a custom one is a small subclass implementing + ``apply(v, damping, ctx)``. On rank-deficient problems it must map + ``range(B')`` into itself or the minimum-norm selection is silently lost; + the identity, polynomials in the operator, and exact shifted inverses are + safe, and on full-column-rank problems the condition is vacuous. + ``tol=None`` resolves to a dtype default (``1e-10`` in float64, ``1e-6`` in float32); ``maxiter`` must be set when both tolerances are explicitly zero, since an uncapped zero-tolerance CG loop has no stopping rule. @@ -329,22 +424,11 @@ class CG(LinearSolver): tol: float | None = None atol: float = 0.0 maxiter: int | None = None - - materializes_jacobian = False - - def __post_init__(self): - if self.tol is not None and self.tol < 0: - raise ValueError("CG.tol must be nonnegative or None") - if self.atol < 0: - raise ValueError("CG.atol must be nonnegative") - if self.maxiter is not None and self.maxiter <= 0: - raise ValueError("CG.maxiter must be positive or None") - if self.tol == 0 and self.atol == 0 and self.maxiter is None: - raise ValueError("CG.maxiter must be set when both tolerances are zero") + penalty: float | None = None def prepare(self, sub): n_m, n_f, ridge, dtype = sub.n_m, sub.n_f, sub.ridge, sub.dtype - m, damping, ctx = sub.m, sub.damping, sub.ctx + damping, ctx = sub.damping, sub.ctx sqrt_ridge = jnp.sqrt(ridge) # Whitened operator J~ = J F_bar^{-1}: products route through the @@ -355,47 +439,109 @@ def J_sub(u): def JT_sub(w): return sub.whitened_transpose(sub.JT(w)) - grad = JT_sub(sub.resid) + ridge * sub.penalty_gradient + grad = JT_sub(sub.resid) + if sub.penalized: + grad = grad + ridge * sub.penalty_gradient - # Augmented operator A = [J~; sqrt(ridge) [I 0]]: the penalty rows are - # the constant metric-block identity on y. - def A_matvec(u): - return jnp.concatenate([J_sub(u), sqrt_ridge * u[:n_m]]) - - def At_matvec(w): - pullback = sqrt_ridge * jnp.concatenate( - [w[m:], jnp.zeros(n_f, dtype=dtype)] - ) - return JT_sub(w[:m]) + pullback - - # N = A'A + damping I, the preconditioner-free SPD operator that - # custom_linear_solve differentiates through, posed on u. + # N = A'A + damping I for the augmented A = [J~; sqrt(ridge) [I 0]] -- + # the preconditioner-free SPD operator that custom_linear_solve + # differentiates through, posed on u. def N_matvec(u): - return At_matvec(A_matvec(u)) + damping * u + normal = JT_sub(J_sub(u)) + if sub.penalized: + pullback = sqrt_ridge * jnp.concatenate( + [sqrt_ridge * u[:n_m], jnp.zeros(n_f, dtype=dtype)] + ) + normal = normal + pullback + return normal + damping * u def apply_M(v): return self.preconditioner.apply(v, damping, ctx) def solve_N(_, c): - solution, _ = jsp_sparse_linalg.cg( - N_matvec, - c, - tol=jnp.asarray(sub.hyper.iterative_tol, dtype=dtype), - atol=jnp.asarray(sub.hyper.iterative_atol, dtype=dtype), - maxiter=sub.hyper.iterative_maxiter, - M=apply_M, - ) - return solution + return self._cg(N_matvec, c, sub, apply_M) - def solve(rhs): + def solve(c): return jax.lax.custom_linear_solve( - N_matvec, -rhs, solve=solve_N, transpose_solve=solve_N, symmetric=True + N_matvec, -c, solve=solve_N, transpose_solve=solve_N, symmetric=True ) return StepSolver( grad=grad, velocity=lambda: solve(grad), - solve=solve, - accel_rhs=JT_sub, + correction=lambda f_vv: solve(JT_sub(f_vv)), make_cache=lambda valid: None, ) + + +@dataclass(frozen=True) +class GramCG(_KrylovConfig): + """Matrix-free preconditioned CG on the DUAL operator, in residual space. + + Applies ``y -> J~ J~' y + damping y`` on ``m``-vectors and takes the step + ``u = -J~'y``, so the Krylov iteration lives in residual dimension -- the + matrix-free form for the ``m << n`` regime this package targets, where + :class:`CG`'s ``n``-dimensional iteration is the expensive one. At inner + convergence the step matches :class:`CG`'s, and a budget-truncated step + still lies in ``range(J~')``, so the minimum-metric-norm structure + survives truncation. + + ``preconditioner`` acts on residual-space vectors -- an SPD approximation + of ``(J~J~' + damping I)^{-1}`` -- which is the only difference from + :class:`CG`'s contract, and the reason the two are separate configs rather + than one with a flag. Only the ridge solver has penalty rows, and they + have no dual analogue, so this config serves + :class:`~nlls_gram.LevenbergMarquardt` alone. + """ + + preconditioner: Preconditioner + tol: float | None = None + atol: float = 0.0 + maxiter: int | None = None + + def prepare(self, sub): + damping, ctx = sub.damping, sub.ctx + + def dual_matvec(y): + return sub.jvp_fn(sub.whitened(sub.whitened_transpose(sub.JT(y)))) + ( + damping * y + ) + + def apply_M(v): + return self.preconditioner.apply(v, damping, ctx) + + def solve_dual(_, c): + return self._cg(dual_matvec, c, sub, apply_M) + + def step(c): + y = jax.lax.custom_linear_solve( + dual_matvec, + c, + solve=solve_dual, + transpose_solve=solve_dual, + symmetric=True, + ) + return -sub.whitened_transpose(sub.JT(y)) + + return StepSolver( + grad=sub.whitened_transpose(sub.JT(sub.resid)), + velocity=lambda: step(sub.resid), + correction=step, + make_cache=lambda valid: None, + ) + + +@dataclass(frozen=True) +class SVD(LinearSolver): + """Spectral-filter pseudoinverse, for the ``ad_solver`` role only. + + The implicit-AD system is UNDAMPED, so it is singular whenever the + whitened Jacobian is rank deficient -- padded zero residuals make it so by + construction. This rule truncates at ``max(m, n) * eps * sigma_max`` and + returns the minimum-metric-norm tangent, which is the right answer there + rather than a NaN or a silent pseudo-solve. It assembles, so it is the + dense fallback rather than the default. + """ + + def prepare(self, sub): + raise NotImplementedError("SVD is an ad_solver, not a forward solver") diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 5770732..02f1116 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -11,10 +11,14 @@ import jax import jax.numpy as jnp +from jax.flatten_util import ravel_pytree from nlls_gram.lm_types import ( + LMHyperparams, LMSolveAction, LMStatus, + SolverContext, + _damping_floor, ) from nlls_gram.multi_start import ( MultiStart, @@ -25,6 +29,7 @@ _multi_start_python_impl, _multi_start_sequential_jit, ) +from nlls_gram.preconditioners import Preconditioner from nlls_gram.solve_loop import _solve_loop_jit, _solve_python_impl from nlls_gram.utilities import ( _hashable_hook, @@ -94,6 +99,138 @@ def _check_residual_args(self, args, p): "use residual_fn(x, args, p)" ) + def hyperparams(self, dtype=None): + """``LMHyperparams`` built from the constructor values.""" + iterative_tol = self.iterative_tol + if iterative_tol is None: + # CG's tol=None: the _ad_cg_tol dtype-default convention. + resolved = jnp.result_type(float) if dtype is None else dtype + iterative_tol = 1e-10 if jnp.finfo(resolved).bits > 32 else 1e-6 + return LMHyperparams( + jnp.asarray(self.damping_decrease, dtype=dtype), + jnp.asarray(self.damping_increase, dtype=dtype), + _damping_floor(self.min_damping, dtype), + None + if self.max_damping is None + else jnp.asarray(self.max_damping, dtype=dtype), + jnp.asarray(self.geodesic_acceptance_ratio, dtype=dtype), + jnp.asarray(iterative_tol, dtype=dtype), + jnp.asarray(self.iterative_atol, dtype=dtype), + None + if self.iterative_maxiter is None + else jnp.asarray(self.iterative_maxiter, dtype=jnp.int32), + ) + + def _block_sizes(self, theta_size): + # The free-block size is inferred from the flattened iterate: the + # metric covers the leading metric.size coordinates, the rest is free. + n_f = theta_size - self.metric.size + if n_f < 0: + raise ValueError( + f"the metric covers {self.metric.size} leading coordinates " + f"but x flattens to only {theta_size}; the free block is " + "len(x) - metric.size and must be nonnegative" + ) + return self.metric.size, n_f + + # The solver-internal extension F_bar = blockdiag(F, sqrt(free_scale) I): + # the metric's factor op on the metric block, a scalar on the free block. + # Applied to vectors or leading-axis-batched matrices; F_bar itself is + # never materialized, and the free block drops out entirely when it is + # empty or unscaled. + def _free_scale(self, v): + scale = self.metric.free_scale + return v if scale == 1.0 else v / jnp.sqrt(jnp.asarray(scale, v.dtype)) + + def _extended_solve(self, v, ctx): + n_m = self.metric.size + if n_m == 0: + return self._free_scale(v) + if v.shape[0] == n_m: + return self.metric.factor_solve(v, ctx) + return jnp.concatenate( + [self.metric.factor_solve(v[:n_m], ctx), self._free_scale(v[n_m:])], axis=0 + ) + + def _extended_solve_transpose(self, v, ctx): + n_m = self.metric.size + if n_m == 0: + return self._free_scale(v) + if v.shape[0] == n_m: + return self.metric.factor_solve_transpose(v, ctx) + return jnp.concatenate( + [ + self.metric.factor_solve_transpose(v[:n_m], ctx), + self._free_scale(v[n_m:]), + ], + axis=0, + ) + + def _hook_state(self, theta, lm_state, args, p): + """The metric's and preconditioner's prepared state for this step: + reused while still valid (a rejected step left ``x`` in place, or the + hook declined to rebuild), rebuilt from the live iterate otherwise.""" + bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) + metric_state = precond_state = None + if self._metric_prepares: + metric_state = jax.lax.cond( + lm_state.metric_valid | ~jnp.asarray(self.metric.rebuild(bare)), + lambda _: lm_state.metric_state, + lambda _: self.metric.prepare(theta, bare), + operand=None, + ) + if self._precond_prepares: + precond_state = jax.lax.cond( + lm_state.precond_valid + | ~jnp.asarray(self.preconditioner.rebuild(bare)), + lambda _: lm_state.precond, + lambda _: self.preconditioner.prepare(theta, bare), + operand=None, + ) + return metric_state, precond_state + + def _carried_ctx(self, theta, lm_state, args, p): + return SolverContext( + x=theta, + lm_state=lm_state, + args=args, + p=p, + metric_state=lm_state.metric_state, + preconditioner_state=lm_state.precond, + ) + + def _frozen_ctx(self, theta, lm_state, args, p, preconditioner): + # Under implicit AD the hooks are FROZEN at the returned solution: + # prepare runs once there and the state-dependence is not + # differentiated, the same contract as a fixed metric closing over + # constants. + bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) + metric_state = ( + self.metric.prepare(theta, bare) if self._metric_prepares else None + ) + precond_state = None + if preconditioner is not None and ( + type(preconditioner).prepare is not Preconditioner.prepare + ): + precond_state = preconditioner.prepare(theta, bare) + return dataclasses.replace( + bare, metric_state=metric_state, preconditioner_state=precond_state + ) + + def _ad_linearization(self, x, args, p, p_dot): + theta, unravel = ravel_pytree(x) + + def residual_from_theta(theta_value): + return self._residual_and_aux(unravel(theta_value), args, p)[0] + + residual, theta_jvp = jax.linearize(residual_from_theta, theta) + + def residual_from_p(p_value): + return self._residual_and_aux(x, args, p_value)[0] + + residual_p_dot = jax.jvp(residual_from_p, (p,), (p_dot,))[1] + return theta, unravel, residual, theta_jvp, residual_p_dot + def _ad_cg_tol(self, dtype): if self.ad_solver_tol is not None: return jnp.asarray(self.ad_solver_tol, dtype=dtype) diff --git a/src/nlls_gram/lsmr.py b/src/nlls_gram/lsmr.py deleted file mode 100644 index 12624b2..0000000 --- a/src/nlls_gram/lsmr.py +++ /dev/null @@ -1,215 +0,0 @@ -"""Matrix-free LSMR for the whitened damped least-squares LM subproblem. - -LSMR (Fong & Saunders 2011) solves ``min_x ||A x - b||^2 + damp^2 ||x||^2`` given -only ``A`` and ``A'`` as matvecs, via Golub-Kahan bidiagonalization. It drives the -normal-equations residual ``||A'(b - A x) - damp^2 x||`` monotonically to zero. - -The LM use is the whitened subproblem ``min_u ||r + B u||^2 + lambda ||u||^2`` with -``B = J S`` (``S = metric.inv_sqrt``, ``S S' = M^{-1}``) and step ``s = S u``. That -operator has condition number ``sqrt`` of the ``cg`` dual's ``J M^{-1} J' + lambda -I`` -- LSMR reaches the accuracy floor of the whitened operator, not its square, so -the selection-critical slow directions stay resolved at small ``lambda`` where the -squared dual solve degrades. - -Stopping maps the package's iterative hooks: the normal-equations residual -``normar = |zetabar|`` (LSMR's exact monotone quantity) is driven below -``iterative_tol * normar_0 + iterative_atol`` where ``normar_0 = ||A'b||``, capped -by ``iterative_maxiter`` (all traced, so a solve callback can reschedule them). -""" - -from typing import NamedTuple - -import jax -import jax.numpy as jnp -from jax import lax - -_HIGHEST = lax.Precision.HIGHEST - - -class LSMRState(NamedTuple): - """Diagnostics emitted by :func:`lsmr` alongside the solution. - - A ``NamedTuple``: positional unpacking - (``iterations, normal_residual = state``) is part of the stable API. - - Attributes: - iterations: number of LSMR iterations run (``()`` int32). - normal_residual: final ``||A'(b - A x) - damp^2 x||`` (``()`` scalar), the - monotone normal-equations residual LSMR minimizes. - """ - - iterations: jax.Array - normal_residual: jax.Array - - -def _norm(x): - return jnp.sqrt(jnp.real(jnp.vdot(x, x, precision=_HIGHEST))) - - -def _safe_div(a, b): - # Divisions by a rotation scalar that is only zero at exact convergence (the - # loop has stopped); keep the carry finite so a post-stop step stays clean. - return jnp.where( - b == 0, jnp.zeros_like(a), a / jnp.where(b == 0, jnp.ones_like(b), b) - ) - - -def _sym_ortho(a, b): - # Givens rotation [c s; -s c] [a; b] = [r; 0] with r = hypot(a, b) >= 0. - r = jnp.hypot(a, b) - c = _safe_div(a, r) - s = _safe_div(b, r) - return c, s, r - - -def lsmr_solve(A, At, b, damp, atol, btol, maxiter, n): - """Core LSMR loop solving ``min ||A x - b||^2 + damp^2 ||x||^2``. - - ``A`` maps ``R^n -> R^m`` and ``At`` its transpose ``R^m -> R^n`` (matvecs); - ``b`` is ``R^m``. ``damp >= 0`` is the Tikhonov weight (``sqrt(lambda)`` for LM). - ``atol`` (relative) and ``btol`` (absolute) bound the normal-equations residual; - ``maxiter`` (traced int) caps iterations, ``n`` is the static solution size. - Returns ``(x, LSMRState)``. Not reverse-differentiable on its own (a raw - ``while_loop``) -- wrap the solution in ``lax.custom_linear_solve`` for AD. - """ - dtype = b.dtype - zero = jnp.zeros((), dtype) - one = jnp.ones((), dtype) - damp = jnp.asarray(damp, dtype) - atol = jnp.asarray(atol, dtype) - btol = jnp.asarray(btol, dtype) - - beta = _norm(b) - u = jnp.where(beta > 0, b / jnp.where(beta > 0, beta, one), b) - v0 = At(u) - alpha = _norm(v0) - v = jnp.where(alpha > 0, v0 / jnp.where(alpha > 0, alpha, one), v0) - - normar0 = alpha * beta # ||A' b|| - x0 = jnp.zeros((n,), dtype) - hbar0 = jnp.zeros((n,), dtype) - - # (itn, u, v, alpha, beta, zetabar, alphabar, rho, rhobar, cbar, sbar, h, hbar, - # x, normar, stop) - init = ( - jnp.zeros((), jnp.int32), - u, - v, - alpha, - beta, - alpha * beta, # zetabar - alpha, # alphabar - one, # rho - one, # rhobar - one, # cbar - zero, # sbar - v, # h - hbar0, - x0, - normar0, # normar (pre-loop estimate) - (normar0 <= btol) | (maxiter <= 0), # already converged / no iterations - ) - - def cond(carry): - itn = carry[0] - stop = carry[-1] - return (~stop) & (itn < maxiter) - - def body(carry): - ( - itn, - u, - v, - alpha, - beta, - zetabar, - alphabar, - rho, - rhobar, - cbar, - sbar, - h, - hbar, - x, - _, - _, - ) = carry - itn = itn + 1 - - # Continue the bidiagonalization: next beta, u and alpha, v. - u = A(v) - alpha * u - beta = _norm(u) - u = jnp.where(beta > 0, u / jnp.where(beta > 0, beta, one), u) - v_raw = At(u) - beta * v - alpha = _norm(v_raw) - v = jnp.where(alpha > 0, v_raw / jnp.where(alpha > 0, alpha, one), v_raw) - - # Damping rotation, then the two plane rotations of LSMR. - chat, shat, alphahat = _sym_ortho(alphabar, damp) - rhoold = rho - c, s, rho = _sym_ortho(alphahat, beta) - thetanew = s * alpha - alphabar = c * alpha - - rhobarold = rhobar - thetabar = sbar * rho - cbar, sbar, rhobar = _sym_ortho(cbar * rho, thetanew) - zeta = cbar * zetabar - zetabar = -sbar * zetabar - - # Update h, hbar, x. - hbar = h - _safe_div(thetabar * rho, rhoold * rhobarold) * hbar - x = x + _safe_div(zeta, rho * rhobar) * hbar - h = v - _safe_div(thetanew, rho) * h - - normar = jnp.abs(zetabar) # ||A' r_k|| exactly - stop = (normar <= atol * normar0 + btol) | (itn >= maxiter) - return ( - itn, - u, - v, - alpha, - beta, - zetabar, - alphabar, - rho, - rhobar, - cbar, - sbar, - h, - hbar, - x, - normar, - stop, - ) - - carry = lax.while_loop(cond, body, init) - itn = carry[0] - x = carry[13] - normar = carry[14] - return x, LSMRState(iterations=itn, normal_residual=normar) - - -def lsmr(A, At, b, *, damp=0.0, atol=1e-6, btol=0.0, maxiter, n=None): - """Solve ``min_x ||A x - b||^2 + damp^2 ||x||^2`` by LSMR (see :func:`lsmr_solve`). - - ``A``/``At`` are the operator and its transpose as matvec callables, ``b`` the - right-hand side. ``n`` (the solution size) defaults to ``At(b).shape[0]``. - ``atol`` (relative, scaled by ``normar0 = ||A'b||``) and ``btol`` (absolute) - bound the normal-equations residual; in the LM solver these carry the - package's ``iterative_tol`` -> ``atol`` and ``iterative_atol`` -> ``btol``. - Returns ``(x, LSMRState)``; not reverse-differentiable (raw loop). - """ - # Concrete (non-tracer) inputs are validated up front, mirroring the solver - # constructors; traced values (the LM hooks pass these) skip the check. - if not isinstance(damp, jax.core.Tracer) and float(damp) < 0.0: - raise ValueError("damp must be nonnegative") - if not isinstance(atol, jax.core.Tracer) and float(atol) < 0.0: - raise ValueError("atol must be nonnegative") - if not isinstance(btol, jax.core.Tracer) and float(btol) < 0.0: - raise ValueError("btol must be nonnegative") - if not isinstance(maxiter, jax.core.Tracer) and int(maxiter) <= 0: - raise ValueError("maxiter must be positive") - if n is None: - n = At(b).shape[0] - return lsmr_solve(A, At, b, damp, atol, btol, maxiter, n) diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py new file mode 100644 index 0000000..21f3d07 --- /dev/null +++ b/src/nlls_gram/metric_lm.py @@ -0,0 +1,700 @@ +"""Metric-damped Levenberg-Marquardt for ``min ||r(x, args, p)||^2``. + +Built for interpolation problems: zero-residual roots that stay rank-deficient +along some directions at every shape, so WHICH root the solver returns is part +of the contract rather than a tie-break. The optional +:class:`~nlls_gram.Metric` defines the damping geometry, and the small-damping +Gauss-Newton limit selects the minimum-metric-norm correction; the same +selection carries into the implicit derivative of ``solve(...).x`` with +respect to ``p``. + +The ridge sibling, :class:`~nlls_gram.RidgeLevenbergMarquardt`, puts that +selection in the OBJECTIVE instead. Prefer it when the interpolant itself is +the deliverable; prefer this one when the root is a means to an end and +Euclidean damping is fine. +""" + +import dataclasses + +import jax +import jax.numpy as jnp +import jax.scipy.linalg as jsp_linalg +import jax.scipy.sparse.linalg as jsp_sparse_linalg +from jax.flatten_util import ravel_pytree + +from nlls_gram.linear_solvers import ( + CG, + SVD, + Cholesky, + GramCG, + Subproblem, +) +from nlls_gram.lm_core import LevenbergMarquardtBase +from nlls_gram.lm_types import ( + LMInfo, + LMState, + SolverContext, + _cast_hyper, + _damping_floor, +) +from nlls_gram.metrics import Metric +from nlls_gram.preconditioners import Preconditioner +from nlls_gram.utilities import ( + _static_key_component, + _zero_tangent_leaf, + canonicalize_residual, +) + +__all__ = ["LevenbergMarquardt"] + + +class _EuclideanMetric(Metric): + """The default metric: ``F = I`` over however many coordinates ``x`` + flattens to, resolved at trace time rather than at construction.""" + + size = 0 # the free block absorbs everything, so F_bar is the identity + free_scale = 1.0 + + +class LevenbergMarquardt(LevenbergMarquardtBase): + """Levenberg-Marquardt least squares over a JAX pytree ``x``. + + ``residual_fn`` takes ``(x)``, ``(x, args)``, or ``(x, args, p)`` and + returns a residual pytree (or ``(residual, aux)`` with ``has_aux=True``). + ``args`` is solver-inert auxiliary data; ``p`` is what ``solve(...).x`` + carries an implicit derivative with respect to. + + ``metric`` (default ``None`` -- Euclidean) is a + :class:`~nlls_gram.Metric` covering the leading ``metric.size`` + coordinates of the flattened iterate, with the rest a free block. It + defines the damping geometry: the subproblem is + ``min ||r + J s||^2 + damping ||s||_W^2``, so the ``damping -> 0`` limit + is the minimum-``W``-norm correction. + + ``linear_solver`` is a typed config -- :class:`~nlls_gram.Cholesky` (the + default; ``form="auto"`` factors the smaller of the ``m x m`` dual and the + ``n x n`` normal system), :class:`~nlls_gram.QR` (damping-row QR, stable + at tiny damping and rank-safe), :class:`~nlls_gram.CG` (matrix-free in + parameter space), or :class:`~nlls_gram.GramCG` (matrix-free in residual + space, the ``m << n`` form). ``ad_solver`` takes ``None`` (match the + forward family), ``Cholesky()``, :class:`~nlls_gram.SVD` (the + pseudoinverse rule, for a rank-deficient undamped tangent), ``CG(...)``, + or ``GramCG(...)``. + + ``init``/``update``/``solve``, the callback protocol, ``save_steps``, + ``multi_start``, and implicit AD are shared with the ridge solver; + ``info.loss`` here is the plain sum of squared residuals. Stopping is + disjunctive: ``atol`` on the residual norm, ``gtol`` on the whitened + stationarity ``info.grad_norm``, ``xtol`` on an accepted step's whitened + norm; any one firing reports ``CONVERGED``. + """ + + def __init__( + self, + residual_fn, + *, + metric=None, + init_damping=1e-3, + damping_decrease=0.5, + damping_increase=4.0, + min_damping=None, + max_damping=None, + linear_solver=Cholesky(), # noqa: B008 -- frozen, immutable default + jacobian_mode="auto", + ad_solver=None, + has_aux=False, + cache_jacobian=True, + geodesic_acceleration=True, + geodesic_acceptance_ratio=0.75, + ): + canonical_residual, residual_arity = canonicalize_residual(residual_fn) + if init_damping <= 0 or damping_decrease <= 0 or damping_increase <= 0: + raise ValueError( + "init_damping, damping_decrease, and damping_increase must be positive" + ) + if min_damping is not None and not 0 < min_damping <= init_damping: + raise ValueError("min_damping must be positive and at most init_damping") + if max_damping is not None and max_damping < init_damping: + raise ValueError("max_damping must be at least init_damping") + self.residual_fn = canonical_residual + self.residual_arity = residual_arity + self.metric = _EuclideanMetric() if metric is None else metric + self.ridge = None + self.init_damping = init_damping + self.damping_decrease = damping_decrease + self.damping_increase = damping_increase + self.min_damping = min_damping + self.max_damping = max_damping + self.linear_solver = linear_solver + self.jacobian_mode = jacobian_mode + self.ad_solver = ad_solver + krylov = isinstance(linear_solver, (CG, GramCG)) + if krylov: + self.preconditioner = linear_solver.preconditioner + self.iterative_tol = linear_solver.tol + self.iterative_atol = linear_solver.atol + self.iterative_maxiter = linear_solver.maxiter + else: + self.preconditioner = None + self.iterative_tol = 0.0 + self.iterative_atol = 0.0 + self.iterative_maxiter = 8 + if isinstance(ad_solver, (CG, GramCG)): + if ad_solver.preconditioner.requires_positive_damping: + raise ValueError( + "this preconditioner divides by the live damping and cannot " + "serve in ad_solver (the AD system is undamped)" + ) + self.ad_solver_tol = ad_solver.tol + self.ad_solver_atol = ad_solver.atol + self.ad_solver_maxiter = ad_solver.maxiter + self.ad_solver_preconditioner = ad_solver.preconditioner + self.ad_solver_penalty = getattr(ad_solver, "penalty", None) + else: + self.ad_solver_tol = None + self.ad_solver_atol = 0.0 + self.ad_solver_maxiter = None + self.ad_solver_penalty = None + # ad_solver=None under a matrix-free forward hands that + # preconditioner to the undamped implicit solve: the AD operator IS + # the forward operator at zero damping. Damping-dividing hooks fall + # back to unpreconditioned. + inherit = ( + ad_solver is None + and krylov + and not linear_solver.preconditioner.requires_positive_damping + ) + self.ad_solver_preconditioner = ( + linear_solver.preconditioner if inherit else None + ) + self.has_aux = has_aux + # Only the dense paths materialize J', and the caches ride the same + # reject-reuse lifecycle, so the flag is inert for the matrix-free forms. + self.cache_jacobian = cache_jacobian and linear_solver.materializes_jacobian + self.geodesic_acceleration = geodesic_acceleration + self.geodesic_acceptance_ratio = geodesic_acceptance_ratio + self._metric_prepares = type(self.metric).prepare is not Metric.prepare + self._precond_prepares = self.preconditioner is not None and ( + type(self.preconditioner).prepare is not Preconditioner.prepare + ) + self._static_key = tuple( + _static_key_component(value) + for value in ( + residual_fn, + metric, + init_damping, + damping_decrease, + damping_increase, + min_damping, + max_damping, + linear_solver, + jacobian_mode, + ad_solver, + has_aux, + self.cache_jacobian, + geodesic_acceleration, + geodesic_acceptance_ratio, + ) + ) + self._static_hash = hash(self._static_key) + + def _block_sizes(self, theta_size): + # The Euclidean default has size 0, so the whole vector is free block. + n_m = self.metric.size + if n_m > theta_size: + raise ValueError( + f"the metric covers {n_m} leading coordinates but x flattens " + f"to only {theta_size}" + ) + return n_m, theta_size - n_m + + def init(self, x0, args=None, *, p=None): + """Build the initial :class:`~nlls_gram.LMState` at ``x0``. + + One residual evaluation types ``damping`` and sizes the Jacobian and + linear-solver cache buffers. ``hyper`` stays ``None`` so manual + ``update`` loops carry no extra buffers; ``solve`` populates it. + """ + self._check_residual_args(args, p) + residual, aux = self._residual_and_aux(x0, args, p) + theta, _ = ravel_pytree(x0) + n_m, _ = self._block_sizes(theta.size) + dtype = residual.dtype + min_damping = _damping_floor(self.min_damping, dtype) + damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) + hooks = {} + ctx = SolverContext(x=theta, args=args, p=p) + valid = jnp.asarray(True, dtype=jnp.bool_) + if self._metric_prepares: + hooks["metric_state"] = self.metric.prepare(theta, ctx) + hooks["metric_valid"] = valid + if self._precond_prepares: + hooks["precond"] = self.preconditioner.prepare(theta, ctx) + hooks["precond_valid"] = valid + if not self.cache_jacobian: + return LMState(damping, **hooks) + return LMState( + damping, + resid=jnp.zeros(residual.shape, dtype=dtype), + Jt=jnp.zeros((theta.size, residual.size), dtype=dtype), + jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), + aux=jax.tree.map(jnp.zeros_like, aux), + solver_cache=self.linear_solver.new_cache( + residual.size, theta.size, n_m, dtype, False + ), + **hooks, + ) + + def _solve_lm_state(self, x0, args, p, lm_state): + if lm_state is not None: + return lm_state + if self.cache_jacobian or self._metric_prepares or self._precond_prepares: + return self.init(x0, args, p=p) + # Nothing needs sizing from a residual evaluation, so skip it: the + # loop recasts the damping dtype itself. + return LMState(jnp.asarray(self.init_damping)) + + def _initial_info(self, x, lm_state, args, p): + # grad_norm is a +inf sentinel (computing it would cost a Jacobian + # before the first step) and step_norm is zero; neither can satisfy + # gtol/xtol before any update has run. + residual, aux = self._residual_and_aux(x, args, p) + loss = jnp.sum(residual**2) + zero = jnp.zeros((), dtype=residual.dtype) + return LMInfo( + loss=loss, + loss_old=loss, + loss_candidate=loss, + accepted=jnp.asarray(False, dtype=jnp.bool_), + damping=jnp.asarray(lm_state.damping, dtype=residual.dtype), + damping_factor=jnp.ones((), dtype=residual.dtype), + used_geodesic=jnp.asarray(False, dtype=jnp.bool_), + acceleration_ratio=zero, + grad_norm=jnp.asarray(jnp.inf, dtype=residual.dtype), + step_norm=zero, + aux=aux, + ) + + def update(self, x, lm_state, args=None, p=None): + """One LM step: returns ``(x_new, lm_state, info)``.""" + self._check_residual_args(args, p) + theta, unravel = ravel_pytree(x) + + if self.has_aux: + + def residual_flat(th): + value, aux = self.residual_fn(unravel(th), args, p) + return jnp.ravel(value), aux + + def residual_value(th): + return residual_flat(th)[0] + + else: + + def residual_flat(th): + return jnp.ravel(self.residual_fn(unravel(th), args, p)) + + residual_value = residual_flat + + jvp_fn = JT = Jt = None + if not self.linear_solver.materializes_jacobian: + if self.has_aux: + resid, jvp_fn, aux = jax.linearize(residual_flat, theta, has_aux=True) + else: + resid, jvp_fn = jax.linearize(residual_flat, theta) + aux = None + transpose_fn = jax.linear_transpose(jvp_fn, theta) + + def JT(cotangent): + return transpose_fn(cotangent)[0] + + elif self.cache_jacobian: + resid, Jt, aux = jax.lax.cond( + lm_state.jacobian_valid, + lambda _: (lm_state.resid, lm_state.Jt, lm_state.aux), + lambda _: self._dense_resid_jt_aux(residual_flat, theta), + operand=None, + ) + else: + resid, Jt, aux = self._dense_resid_jt_aux(residual_flat, theta) + + hyper = ( + lm_state.hyper + if lm_state.hyper is not None + else self.hyperparams(resid.dtype) + ) + damping_decrease = jnp.asarray(hyper.damping_decrease, dtype=resid.dtype) + damping_increase = jnp.asarray(hyper.damping_increase, dtype=resid.dtype) + min_damping = _damping_floor(hyper.min_damping, resid.dtype) + damping = jnp.maximum( + jnp.asarray(lm_state.damping, dtype=resid.dtype), min_damping + ) + + n_m, n_f = self._block_sizes(theta.shape[0]) + metric_state, precond_state = self._hook_state(theta, lm_state, args, p) + ctx = SolverContext( + x=theta, + lm_state=lm_state, + args=args, + p=p, + metric_state=metric_state, + preconditioner_state=precond_state, + ) + zero = jnp.zeros((), dtype=resid.dtype) + step_solver = self.linear_solver.prepare( + Subproblem( + resid=resid, + theta=theta, + Jt=Jt, + jvp_fn=jvp_fn, + JT=JT, + whiten=lambda v: self._extended_solve(v, ctx), + whiten_transpose=lambda v: self._extended_solve_transpose(v, ctx), + y_m=jnp.zeros(n_m, dtype=resid.dtype), + penalty_gradient=jnp.zeros(theta.shape[0], dtype=resid.dtype), + ridge=zero, + damping=damping, + n_m=n_m, + n_f=n_f, + cache=lm_state.solver_cache, + cache_enabled=self.cache_jacobian, + hyper=hyper, + ctx=ctx, + penalized=False, + ) + ) + + # The solves produce the whitened step; the x-space step maps back + # through the factor solve. + velocity_sub = step_solver.velocity() + velocity = jnp.asarray(self._extended_solve(velocity_sub, ctx), resid.dtype) + loss_old = jnp.sum(resid**2) + resid_velocity = residual_value(theta + velocity) + loss_velocity = jnp.sum(resid_velocity**2) + + # Geodesic second-order correction, sharing the factorization. + if self.geodesic_acceleration: + geodesic_acceptance_ratio = jnp.asarray( + hyper.geodesic_acceptance_ratio, dtype=resid.dtype + ) + + def first_jvp(th): + # [1] is the tangent with and without has_aux. + return jax.jvp(residual_flat, (th,), (velocity,), has_aux=self.has_aux)[ + 1 + ] + + f_vv = jax.jvp(first_jvp, (theta,), (velocity,))[1] + acceleration_sub = step_solver.correction(f_vv) + acceleration = jnp.asarray( + self._extended_solve(acceleration_sub, ctx), dtype=resid.dtype + ) + accelerated_step = velocity + 0.5 * acceleration + # The ratio criterion lives in the damping geometry's norm -- the + # whitened one. + acceleration_ratio = ( + 2.0 + * jnp.linalg.norm(acceleration_sub) + / (jnp.linalg.norm(velocity_sub) + jnp.finfo(resid.dtype).eps) + ) + ratio_accepted = ( + (geodesic_acceptance_ratio > zero) + & (acceleration_ratio > zero) + & (acceleration_ratio <= geodesic_acceptance_ratio) + ) + loss_accelerated = jax.lax.cond( + ratio_accepted, + lambda _: jnp.sum(residual_value(theta + accelerated_step) ** 2), + lambda _: jnp.asarray(jnp.inf, dtype=resid.dtype), + operand=None, + ) + used_geodesic = ratio_accepted & (loss_accelerated <= loss_velocity) + step = jnp.where(used_geodesic, accelerated_step, velocity) + step_sub = jnp.where( + used_geodesic, velocity_sub + 0.5 * acceleration_sub, velocity_sub + ) + loss_candidate = jnp.where(used_geodesic, loss_accelerated, loss_velocity) + else: + step, step_sub = velocity, velocity_sub + loss_candidate = loss_velocity + used_geodesic = jnp.asarray(False) + acceleration_ratio = zero + + improved = jnp.isfinite(loss_candidate) & (loss_candidate < loss_old) + theta_new = jnp.where(improved, theta + step, theta) + damping_factor = jnp.where(improved, damping_decrease, damping_increase) + new_damping = damping * damping_factor + if hyper.max_damping is not None: + new_damping = jnp.minimum( + new_damping, + jnp.maximum( + jnp.asarray(hyper.max_damping, dtype=resid.dtype), min_damping + ), + ) + new_damping = jnp.maximum(new_damping, min_damping) + loss = jnp.where(improved, loss_candidate, loss_old) + + hooks = {} + if self._metric_prepares: + hooks["metric_state"] = metric_state + hooks["metric_valid"] = ~improved + if self._precond_prepares: + hooks["precond"] = precond_state + hooks["precond_valid"] = ~improved + if self.cache_jacobian: + new_lm_state = LMState( + new_damping, + resid=resid, + Jt=Jt, + jacobian_valid=~improved, + aux=aux, + hyper=lm_state.hyper, + solver_cache=step_solver.make_cache(~improved), + **hooks, + ) + else: + new_lm_state = LMState(new_damping, hyper=lm_state.hyper, **hooks) + return ( + unravel(theta_new), + new_lm_state, + LMInfo( + loss=loss, + loss_old=loss_old, + loss_candidate=loss_candidate, + accepted=improved, + damping=new_damping, + damping_factor=damping_factor, + used_geodesic=used_geodesic, + acceleration_ratio=acceleration_ratio, + grad_norm=jnp.linalg.norm(step_solver.grad), + step_norm=jnp.linalg.norm(step_sub), + aux=aux, + ), + ) + + def _converged(self, info, atol, gtol, xtol): + atol_met = (atol > 0) & (jnp.sqrt(info.loss) < atol) + gtol_met = (gtol > 0) & (info.grad_norm < gtol) + xtol_met = (xtol > 0) & info.accepted & (info.step_norm < xtol) + return atol_met | gtol_met | xtol_met + + def _cast_state(self, lm_state, dtype): + return dataclasses.replace( + lm_state, + damping=jnp.asarray(lm_state.damping, dtype=dtype), + hyper=_cast_hyper(lm_state.hyper, dtype), + ) + + def _cold_state(self, lm_state): + # Drawn multi-start lanes must not reuse caches or hook state built at + # another (x, args); damping and hyper stay inherited. + updates = {} + for flag in ("jacobian_valid", "metric_valid", "precond_valid"): + if getattr(lm_state, flag) is not None: + updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) + if lm_state.solver_cache is not None: + updates["solver_cache"] = jax.tree.map( + jnp.zeros_like, lm_state.solver_cache + ) + return dataclasses.replace(lm_state, **updates) if updates else lm_state + + def _ranking_objective(self, result, p, callback): + # Without a callback info.loss already reports the objective at the + # retained iterate; a callback can replace x/args after the last + # update, so recompute. Nonfinite masks to +inf. + if callback is None: + loss = result.info.loss + else: + residual = self._residual_and_aux(result.x, result.args, p)[0] + loss = jnp.sum(residual**2) + return jnp.where( + jnp.isfinite(loss), loss, jnp.asarray(jnp.inf, dtype=loss.dtype) + ) + + def _resolved_ad_solver(self, m, n): + # The implicit-AD system is UNDAMPED, so the dual J~J~' is singular + # whenever m > n and the normal J~'J~ whenever n > m. Each rule below + # is only offered where its operator is invertible; SVD() covers the + # cases where neither is (rank deficiency within the small side, as + # padded zero residuals produce). + resolved = self.ad_solver + if resolved is None: + # Match the forward family where its operator is invertible; + # otherwise fall back to the assembled rule, which picks the + # nonsingular side itself. + if isinstance(self.linear_solver, GramCG) and m <= n: + return self.linear_solver + if isinstance(self.linear_solver, CG) and ( + n <= m or self.linear_solver.penalty is not None + ): + return self.linear_solver + return Cholesky() + if isinstance(resolved, GramCG) and m > n: + raise ValueError( + f"ad_solver=GramCG() needs m <= n, but the residual is {m} and " + f"x flattens to {n}: the undamped dual J~J~' is singular there, " + "so CG returns a wrong tangent rather than failing. Use SVD(), " + "or CG(precond, penalty=...) to regularize" + ) + if isinstance(resolved, CG) and n > m and resolved.penalty is None: + raise ValueError( + f"ad_solver=CG() needs n <= m, but the residual is {m} and x " + f"flattens to {n}: the undamped normal J~'J~ is singular there, " + "so CG returns a wrong tangent rather than failing. Use " + "GramCG(precond), SVD(), or CG(precond, penalty=...)" + ) + return resolved + + def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point): + if p is None: + return jax.tree.map(_zero_tangent_leaf, x) + lm_state = jax.lax.stop_gradient(result.lm_state) + theta, unravel, residual, theta_jvp, residual_p_dot = self._ad_linearization( + x, args, p, p_dot + ) + resolved = self._resolved_ad_solver(residual.shape[0], theta.shape[0]) + ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) + n_m, n_f = self._block_sizes(theta.shape[0]) + dtype = residual.dtype + + def whiten(v): + return jnp.asarray(self._extended_solve(v, ctx), dtype=dtype) + + def whiten_transpose(v): + return jnp.asarray(self._extended_solve_transpose(v, ctx), dtype=dtype) + + if isinstance(resolved, (CG, GramCG)): + u = self._ad_tangent_krylov( + resolved, + theta, + theta_jvp, + residual_p_dot, + whiten, + whiten_transpose, + ctx, + ) + else: + # B' = F_bar^{-T} J', shape (n, m). + Bt = whiten_transpose(self._assemble_jt(theta_jvp, theta, residual)) + u = ( + self._ad_tangent_svd(Bt, residual_p_dot) + if isinstance(resolved, SVD) + else self._ad_tangent_dense(Bt, residual_p_dot) + ) + # S = F_bar^{-1} is not self-adjoint, and a matrix-free factor may + # be opaque to JAX's transpose machinery, so declare its transpose + # explicitly: the identity matvec exposes nothing to AD and every rule + # routes through the declared solves. That keeps reverse mode working + # through a metric JAX could not transpose on its own. + theta_dot = jax.lax.custom_linear_solve( + lambda v: v, + u, + lambda _, b: whiten(b), + transpose_solve=lambda _, b: whiten_transpose(b), + ) + return unravel(theta_dot) + + def _ad_tangent_dense(self, Bt, residual_p_dot): + # Undamped Gauss-Newton tangent: u = -B^+ (dr/dp) p_dot through the + # smaller of the two normal systems. Requires full rank; a rank- + # deficient B needs SVD(), which selects the minimum-norm tangent. + n, m = Bt.shape + if n > m: + factor = jsp_linalg.cho_factor(Bt.T @ Bt) + return -Bt @ jsp_linalg.cho_solve(factor, residual_p_dot) + factor = jsp_linalg.cho_factor(Bt @ Bt.T) + return -jsp_linalg.cho_solve(factor, Bt @ residual_p_dot) + + def _ad_tangent_svd(self, Bt, residual_p_dot): + # Spectral filter: u = -B^+ (dr/dp) p_dot, the minimum-metric-norm + # tangent. This is the rule for the singular undamped systems that + # padded zero residuals produce by construction, where the dense and + # QR rules have no answer to give. The factors are constants in the + # tangent program, so the map stays linear in residual_p_dot. + U, sigma, Vt = jnp.linalg.svd(Bt.T, full_matrices=False) + cutoff = max(Bt.shape) * jnp.finfo(Bt.dtype).eps * sigma[0] + inverted = jnp.where(sigma > cutoff, 1.0 / jnp.maximum(sigma, cutoff), 0.0) + return -Vt.T @ (inverted * (U.T @ residual_p_dot)) + + def _ad_tangent_krylov( + self, config, theta, theta_jvp, residual_p_dot, whiten, whiten_transpose, ctx + ): + dtype = residual_p_dot.dtype + transpose_fn = jax.linear_transpose(theta_jvp, theta) + zero_damping = jnp.zeros((), dtype=dtype) + + def JT(cotangent): + return transpose_fn(cotangent)[0] + + def B(u): + return theta_jvp(whiten(u)) + + def Bt(w): + return whiten_transpose(JT(w)) + + apply_M = None + if self.ad_solver_preconditioner is not None: + # The AD system is undamped, so the preconditioner sees zero + # damping (requires_positive_damping hooks were rejected). + def apply_M(v): + return self.ad_solver_preconditioner.apply(v, zero_damping, ctx) + + def cg(matvec, rhs): + solution, _ = jsp_sparse_linalg.cg( + matvec, + rhs, + tol=self._ad_cg_tol(dtype), + atol=jnp.asarray(self.ad_solver_atol, dtype=dtype), + maxiter=self.ad_solver_maxiter, + M=apply_M, + ) + return solution + + if isinstance(config, GramCG): + # Dual: (B B') y = (dr/dp) p_dot, then u = -B' y. The right-hand + # side lies in range(B), so unpreconditioned CG from zero keeps the + # iterates selection-clean on rank-deficient problems. + def dual_matvec(y): + return B(Bt(y)) + + y = jax.lax.custom_linear_solve( + dual_matvec, + residual_p_dot, + lambda _, c: cg(dual_matvec, c), + symmetric=True, + ) + return -Bt(y) + + penalty = self.ad_solver_penalty + + def normal_matvec(u): + value = Bt(B(u)) + if penalty is not None: + value = value + jnp.asarray(penalty, dtype=dtype) * u + return value + + if penalty is not None: + # N = B'B + penalty I is SPD, so CG converges for any right-hand + # side and the symmetric operator is its own transpose. + transpose_solve = lambda _, c: cg(normal_matvec, c) # noqa: E731 + else: + # N = B'B is SINGULAR whenever B is (always, on the + # underdetermined problems this solver targets). The forward + # right-hand side lies in range(B') so CG converges there, but a + # reverse-mode cotangent does not, and plain CG on it diverges. + # Route the transpose through the push-through identity + # N^+ = B' (BB')^{+2} B instead: each dual solve sees a right-hand + # side in range(B), where BB' is invertible. + def transpose_solve(_, c): + return Bt(dual_solve(dual_solve(B(c)))) + + def dual_solve(y): + return cg(lambda w: B(Bt(w)), y) + + rhs = -Bt(residual_p_dot) + return jax.lax.custom_linear_solve( + normal_matvec, + rhs, + lambda _, c: cg(normal_matvec, c), + transpose_solve=transpose_solve, + ) diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index 9b8a5ed..e482c49 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -1,70 +1,82 @@ -"""Metric types for the package's two solvers. - -:class:`Metric` is the positive-definite metric ``W`` on the metric block of -:class:`~nlls_gram.RidgeLevenbergMarquardt`'s parameter vector, given through -factor callbacks for an invertible factor ``F`` with ``W = F'F`` -- -:class:`IdentityMetric` is the plain-ridge case and -:class:`RepeatedFactorMetric` the kernel workhorse (``repeats`` copies of one -block factor). Every callback receives a :class:`SolverContext` carrying the -solver's live state, so exotic metrics can key off the iterate. - -:class:`GramMetric` (with :func:`metric_from_cholesky`, -:func:`metric_from_diagonal`, and the ``repeated_shifted_*`` constructors) is -the damping metric of the classic :class:`~nlls_gram.LevenbergMarquardt` -solver -- an unrelated contract kept under its own name. +"""The positive-definite metric both solvers take, given through factor +callbacks. + +One contract serves two roles. For +:class:`~nlls_gram.RidgeLevenbergMarquardt` the metric ``W`` weights the +OBJECTIVE's penalty, ``ridge * ||x_m||_W^2``; for +:class:`~nlls_gram.LevenbergMarquardt` it is the damping geometry, so the +small-damping Gauss-Newton limit selects minimum-``W``-norm corrections. +Either way the solver runs in the whitened variable and never materializes +``W`` or its factor. """ -from collections.abc import Callable from dataclasses import dataclass, field import jax import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg -from nlls_gram import quasiseparable +from nlls_gram.lm_types import SolverContext + +__all__ = [ + "CholeskyMetric", + "DiagonalMetric", + "IdentityMetric", + "Metric", + "RepeatedFactorMetric", + "SolverContext", +] class Metric: - """Positive-definite metric ``W`` on the metric block, via factor callbacks. - - :class:`~nlls_gram.RidgeLevenbergMarquardt` minimizes - ``||r(x)||^2 + ridge * ||x_m||_W^2`` where ``x = [x_m; x_f]`` splits into - the metric block ``x_m`` (the leading ``size`` coordinates, covered by - ``W``) and the free block ``x_f`` (unpenalized). The metric is supplied - through callbacks for an invertible factor ``F`` with ``W = F'F``, the - whitened variable being ``x_hat_m = F x_m`` and + """Positive-definite metric ``W``, via factor callbacks. + + ``x = [x_m; x_f]`` splits into the metric block ``x_m`` -- the leading + ``size`` coordinates, covered by ``W`` -- and a free block ``x_f``. The + metric is supplied through callbacks for an invertible factor ``F`` with + ``W = F'F``, the whitened variable being ``F x_m`` and ``||v||_W = ||F v||_2``. ``F`` should be upper triangular; the canonical - example is the upper Cholesky factor, - ``F = jnp.linalg.cholesky(K, upper=True)``. The solver runs entirely in - the whitened variable and never materializes ``W`` or ``F``. + example is ``F = jnp.linalg.cholesky(K, upper=True)``. The solver extends + it to ``F_bar = blockdiag(F, sqrt(free_scale) I)`` over the whole vector + and never materializes either. Subclasses implement the ops on metric-block vectors (or matrices whose - LEADING axis is ``size``; columns are batched), each also receiving a - :class:`SolverContext` with the solver's live state: + LEADING axis is ``size``; columns are batched): - ``factor_apply(v, ctx)``: ``F v`` - ``factor_solve(v, ctx)``: ``F^{-1} v`` - ``factor_solve_transpose(v, ctx)``: ``F^{-T} v`` - ``norm(v, ctx)``: ``||v||_W`` (vectors only; the base default is - ``||factor_apply(v)||_2``, and an override must match it to - floating-point accuracy -- the solver compares objective values built - from both forms) + ``||factor_apply(v)||_2`` and an override must match it to + floating-point accuracy, since the solver compares objective values + built from both forms) + + Every callback receives a :class:`~nlls_gram.SolverContext` carrying the + solver's live state, so an exotic metric can key off the iterate; + :meth:`prepare` covers the iterate-dependent case. - Contracts: the factor must be EXACT -- the solver hardcodes the identity + ``free_scale`` weights the free block in the whitened variable: ``1.0`` + (the default) leaves it Euclidean. The ridge solver never penalizes the + free block whatever the scale -- ``free_scale`` only changes its + trust-region geometry -- while for the metric solver it IS that block's + damping weight. + + Contracts: the factor must be EXACT. The solver hardcodes the identity penalty block in the whitened variable, so an approximate factor silently changes the objective (unlike a CG preconditioner, which may be sloppy). The ridge weight never enters the factorization, so ridge continuation - composes unchanged. How a subclass fulfills the ops (prefactorized - storage, factorize-in-``__init__``, fully matrix-free) is its - constructor's business; the solver only sees the ops. + composes unchanged. How a subclass fulfills the ops -- prefactorized + storage, factorize-in-``__init__``, fully matrix-free -- is its + constructor's business. Metrics hash and compare by identity (``eq=False`` frozen dataclasses -- array fields make value-hashing impossible): construct one at setup scope - and reuse it, since rebuilding an equal-config metric per call would key - a fresh solver compilation. + and reuse it, since rebuilding an equal-config metric per call would key a + fresh solver compilation. """ size: int + free_scale: float = 1.0 def prepare(self, theta, ctx): """Build this metric's numeric state from the current iterate. @@ -103,14 +115,10 @@ def factor_solve_transpose(self, v, ctx): def norm(self, v, ctx): """``||v||_W = ||F v||_2`` for a metric-block vector.""" - if v.ndim != 1: - raise ValueError("Metric.norm requires a vector") return jnp.linalg.norm(self.factor_apply(v, ctx)) -def _validate_metric_input(v, size): - if v.ndim not in (1, 2): - raise ValueError("metric factor callbacks require a vector or matrix") +def _check_leading_size(v, size): if v.shape[0] != size: raise ValueError( f"metric factor input leading size must be {size}, got {v.shape[0]}" @@ -119,63 +127,121 @@ def _validate_metric_input(v, size): @dataclass(frozen=True, eq=False) class IdentityMetric(Metric): - """The identity metric ``W = I`` on ``size`` coordinates -- plain ridge. + """The identity metric ``W = I`` on ``size`` coordinates -- plain ridge for + the ridge solver, Euclidean damping for the metric solver. ``F = I``: every factor op is the identity and ``norm`` is the Euclidean - norm, so ``RidgeLevenbergMarquardt`` reduces to the classical - ``||r||^2 + ridge * ||x_m||^2`` objective with no special-casing. + norm, with no special-casing anywhere downstream. """ size: int - - def __post_init__(self): - if ( - isinstance(self.size, bool) - or not isinstance(self.size, int) - or self.size <= 0 - ): - raise ValueError("size must be a positive Python int") + free_scale: float = 1.0 def factor_apply(self, v, ctx): - _validate_metric_input(v, self.size) + _check_leading_size(v, self.size) return v def factor_solve(self, v, ctx): - _validate_metric_input(v, self.size) + _check_leading_size(v, self.size) return v def factor_solve_transpose(self, v, ctx): - _validate_metric_input(v, self.size) + _check_leading_size(v, self.size) return v def norm(self, v, ctx): - if v.ndim != 1: - raise ValueError("Metric.norm requires a vector") - _validate_metric_input(v, self.size) + _check_leading_size(v, self.size) return jnp.linalg.norm(v) +@dataclass(frozen=True, eq=False) +class CholeskyMetric(Metric): + """Dense metric ``W = L L'`` from its lower-triangular Cholesky factor. + + ``L`` is the factor as ``jnp.linalg.cholesky`` returns it, so the upper + factor this class works with is ``F = L'``. Triangularity and positive + definiteness are assumed, not validated -- the entries may be traced, and + a singular factor propagates NaN loudly through the triangular solves. + """ + + L: jax.Array + free_scale: float = 1.0 + size: int = field(init=False) + + def __post_init__(self): + L = jnp.asarray(self.L) + if L.ndim != 2 or L.shape[0] != L.shape[1] or L.shape[0] == 0: + raise ValueError("L must be a nonempty square matrix") + object.__setattr__(self, "L", L) + object.__setattr__(self, "size", L.shape[0]) + + def factor_apply(self, v, ctx): + _check_leading_size(v, self.size) + return self.L.T @ v + + def factor_solve(self, v, ctx): + _check_leading_size(v, self.size) + return jsp_linalg.solve_triangular(self.L.T, v, lower=False) + + def factor_solve_transpose(self, v, ctx): + _check_leading_size(v, self.size) + return jsp_linalg.solve_triangular(self.L, v, lower=True) + + +@dataclass(frozen=True, eq=False) +class DiagonalMetric(Metric): + """The diagonal metric ``W = diag(weights)``; ``F = diag(sqrt(weights))``. + + ``weights`` must be a positive 1-D array. Positivity is not validated + because the values may be traced. Every op is elementwise. + """ + + weights: jax.Array + free_scale: float = 1.0 + size: int = field(init=False) + + def __post_init__(self): + weights = jnp.asarray(self.weights) + if weights.ndim != 1: + raise ValueError("weights must be 1-D") + object.__setattr__(self, "weights", weights) + object.__setattr__(self, "size", weights.shape[0]) + + def _scaled(self, v, factor): + _check_leading_size(v, self.size) + return v * factor.reshape(factor.shape + (1,) * (v.ndim - 1)) + + def factor_apply(self, v, ctx): + return self._scaled(v, jnp.sqrt(self.weights)) + + def factor_solve(self, v, ctx): + return self._scaled(v, 1.0 / jnp.sqrt(self.weights)) + + def factor_solve_transpose(self, v, ctx): + return self.factor_solve(v, ctx) + + @dataclass(frozen=True, eq=False) class RepeatedFactorMetric(Metric): - """``repeats`` copies of one block factor on the metric block. - - The metric is ``W = blockdiag(F'F, ..., F'F)`` for an upper-triangular - invertible block factor ``F`` -- e.g. - ``F = jnp.linalg.cholesky(K, upper=True)`` for a positive-definite Gram - matrix ``K``, giving the repeated kernel seminorm - ``sum_j alpha_j' K alpha_j`` on ``repeats`` coefficient blocks. The - constructor takes the FACTOR, not ``K`` (callers typically already hold - it); triangularity and positive-definiteness are assumed, not validated - (the entries may be traced -- a singular factor propagates NaN loudly - through the triangular solves). + """``repeats`` copies of one block factor: ``W = blockdiag(F'F, ...)``. + + ``F`` is an upper-triangular invertible block factor -- e.g. + ``jnp.linalg.cholesky(K, upper=True)`` for a positive-definite Gram matrix + ``K``, giving the repeated kernel seminorm ``sum_j alpha_j' K alpha_j`` + over ``repeats`` coefficient blocks. The constructor takes the FACTOR, not + ``K`` (callers typically already hold it); :meth:`from_gram` shifts and + factors a ``K`` instead. Triangularity and positive definiteness are + assumed, not validated. All repeated blocks (and all batched columns) share a single triangular - product or solve: the ops reshape the metric block into the columns of - one ``(block, repeats * cols)`` matrix. ``size = repeats * F.shape[0]``. + product or solve: the ops reshape the metric block into the columns of one + ``(block, repeats * cols)`` matrix, so no repeated factor or full block + diagonal is ever formed. ``size = repeats * F.shape[0]``. """ F: jax.Array repeats: int = field(default=1, kw_only=True) + free_scale: float = field(default=1.0, kw_only=True) size: int = field(init=False) def __post_init__(self): @@ -185,17 +251,33 @@ def __post_init__(self): dtype = jnp.result_type(F, 1.0) if not jnp.issubdtype(dtype, jnp.floating): raise TypeError("F must have a real floating-point dtype") - if ( - isinstance(self.repeats, bool) - or not isinstance(self.repeats, int) - or self.repeats < 1 - ): + if self.repeats < 1: raise ValueError("repeats must be a positive integer") object.__setattr__(self, "F", F.astype(dtype)) object.__setattr__(self, "size", self.repeats * F.shape[0]) + @classmethod + def from_gram(cls, K, *, repeats=1, epsilon, free_scale=1.0): + """Factor ``K + epsilon I`` once and repeat it ``repeats`` times. + + The shift makes a positive-SEMIdefinite kernel Gram matrix invertible. + ``epsilon`` must be positive; non-positive values propagate NaN rather + than silently defining a singular factor. + """ + K = jnp.asarray(K) + if K.ndim != 2 or K.shape[0] != K.shape[1] or K.shape[0] == 0: + raise ValueError("K must be a nonempty square matrix") + epsilon = jnp.asarray(epsilon, dtype=jnp.result_type(K, 1.0)) + epsilon = jnp.where(epsilon > 0.0, epsilon, jnp.nan) + shifted = K + epsilon * jnp.eye(K.shape[0], dtype=K.dtype) + return cls( + jnp.linalg.cholesky(shifted, upper=True), + repeats=repeats, + free_scale=free_scale, + ) + def _map_blocks(self, block_op, v): - _validate_metric_input(v, self.size) + _check_leading_size(v, self.size) block_size = self.F.shape[0] trailing_shape = v.shape[1:] packed = jnp.moveaxis( @@ -219,342 +301,3 @@ def factor_solve_transpose(self, v, ctx): return self._map_blocks( lambda m: jsp_linalg.solve_triangular(self.F.T, m, lower=True), v ) - - -@dataclass(frozen=True) -class GramMetric: - """Positive-definite parameter-space metric ``M`` given through callbacks, - for the classic :class:`~nlls_gram.LevenbergMarquardt` solver. - - All callbacks act on the flattened parameter vector. With ``P = M^{-1}`` - and ``S`` satisfying ``S S' = M^{-1}``: - - - ``solve(x)``: ``M^{-1} x`` - - ``norm(x)``: ``sqrt(x' M x)`` - - ``inv_sqrt(x)``: ``S x`` - - ``inv_sqrt_transpose(x)``: ``S' x`` - - Fields left as ``None`` default to the identity metric. Which fields are - required depends on the solver configuration; see ``LevenbergMarquardt``. - """ - - solve: Callable | None = None - norm: Callable | None = None - inv_sqrt: Callable | None = None - inv_sqrt_transpose: Callable | None = None - - -def metric_from_cholesky(L): - """Build a dense ``GramMetric`` from a lower-triangular Cholesky factor. - - ``L`` is the factor of the metric matrix ``M = L @ L.T``, as returned by - ``jnp.linalg.cholesky``. - """ - - L = jnp.asarray(L) - if L.ndim != 2 or L.shape[0] != L.shape[1]: - raise ValueError("L must be a square matrix") - - def solve(x): - y = jsp_linalg.solve_triangular(L, x, lower=True) - return jsp_linalg.solve_triangular(L.T, y, lower=False) - - def norm(x): - return jnp.linalg.norm(L.T @ x) - - def inv_sqrt(x): - return jsp_linalg.solve_triangular(L.T, x, lower=False) - - def inv_sqrt_transpose(x): - return jsp_linalg.solve_triangular(L, x, lower=True) - - return GramMetric( - solve=solve, - norm=norm, - inv_sqrt=inv_sqrt, - inv_sqrt_transpose=inv_sqrt_transpose, - ) - - -def metric_from_diagonal(weights): - """Build a ``GramMetric`` for the diagonal metric ``M = diag(weights)``. - - ``weights`` must be a one-dimensional array of positive values. Positivity - is not validated because the values may be traced. Every callback is - elementwise. - """ - - weights = jnp.asarray(weights) - if weights.ndim != 1: - raise ValueError("weights must be 1-D") - sqrt_weights = jnp.sqrt(weights) - - def expand(v, x): - return v.reshape(v.shape + (1,) * (x.ndim - 1)) - - def solve(x): - return x / expand(weights, x) - - def norm(x): - return jnp.sqrt(x @ (weights * x)) - - def inv_sqrt(x): - return x / expand(sqrt_weights, x) - - return GramMetric( - solve=solve, - norm=norm, - inv_sqrt=inv_sqrt, - inv_sqrt_transpose=inv_sqrt, - ) - - -def _validate_repeated_shifted_layout(repeats, zero_pad_size): - if not isinstance(repeats, int) or isinstance(repeats, bool) or repeats < 1: - raise ValueError("repeats must be a positive integer") - if ( - not isinstance(zero_pad_size, int) - or isinstance(zero_pad_size, bool) - or zero_pad_size < 0 - ): - raise ValueError("zero_pad_size must be a nonnegative integer") - - -def _repeated_shifted_metric(block_metric, block_size, repeats, zero_pad_size, epsilon): - repeated_size = repeats * block_size - total_size = repeated_size + zero_pad_size - sqrt_epsilon = jnp.sqrt(epsilon) - - def check_input(x, *, norm=False): - expected_ndim = (1,) if norm else (1, 2) - if x.ndim not in expected_ndim: - kind = "a vector" if norm else "a vector or matrix" - raise ValueError(f"metric callback requires {kind}") - if x.shape[0] != total_size: - raise ValueError( - f"metric leading size must be {total_size}, got {x.shape[0]}" - ) - - def packed_head(x): - trailing_shape = x.shape[1:] - return jnp.moveaxis( - x[:repeated_size].reshape((repeats, block_size) + trailing_shape), - 0, - 1, - ).reshape(block_size, -1) - - def unpack_head(x, trailing_shape): - return jnp.moveaxis( - x.reshape((block_size, repeats) + trailing_shape), 0, 1 - ).reshape((repeated_size,) + trailing_shape) - - def apply(block_callback, tail_scale): - def callback(x): - check_input(x) - trailing_shape = x.shape[1:] - head = unpack_head(block_callback(packed_head(x)), trailing_shape) - tail = x[repeated_size:] / tail_scale - return jnp.concatenate([head, tail], axis=0) - - return callback - - def norm(x): - check_input(x, norm=True) - head_norm = block_metric.norm(packed_head(x)) - tail = x[repeated_size:] - return jnp.sqrt(head_norm**2 + epsilon * jnp.vdot(tail, tail)) - - return GramMetric( - solve=apply(block_metric.solve, epsilon), - norm=norm, - inv_sqrt=apply(block_metric.inv_sqrt, sqrt_epsilon), - inv_sqrt_transpose=apply(block_metric.inv_sqrt_transpose, sqrt_epsilon), - ) - - -def repeated_shifted_dense_metric(K, *, repeats: int, zero_pad_size: int, epsilon): - """Build a repeated shifted dense metric without repeating its factor. - - The metric is ``blockdiag(K, ..., K, 0) + epsilon * I``, with ``repeats`` - copies of the square positive-semidefinite matrix ``K`` and a trailing zero - block of size ``zero_pad_size``. ``epsilon`` must be a positive scalar. - - The constructor factors ``K + epsilon * I`` once, stores one dense - Cholesky factor and the scalar shift, and batches all repeated blocks into - the right-hand-side columns of each triangular solve. It never forms or - stores the full block diagonal, repeated factors, or a padding vector. - - The flattened parameter layout is the repeated ``K`` blocks followed by - the zero-padded coordinates. All four metric callbacks are provided; - ``solve``, ``inv_sqrt``, and ``inv_sqrt_transpose`` accept vectors or - matrices, while ``norm`` accepts a vector. - """ - - _validate_repeated_shifted_layout(repeats, zero_pad_size) - K = jnp.asarray(K) - if K.ndim != 2 or K.shape[0] != K.shape[1] or K.shape[0] == 0: - raise ValueError("K must be a nonempty square matrix") - - original_epsilon = epsilon - epsilon = jnp.asarray(epsilon) - if epsilon.ndim != 0: - raise ValueError("epsilon must be a scalar") - dtype = jnp.result_type(K, epsilon, 1.0) - if not jnp.issubdtype(dtype, jnp.floating): - raise TypeError("K and epsilon must have a real floating-point dtype") - if ( - not isinstance(original_epsilon, (jax.Array, jax.core.Tracer)) - and float(original_epsilon) <= 0.0 - ): - raise ValueError("epsilon must be positive") - K = K.astype(dtype) - epsilon = epsilon.astype(dtype) - epsilon = jnp.where(epsilon > 0.0, epsilon, jnp.nan) - - block_size = K.shape[0] - shifted = K + epsilon * jnp.eye(block_size, dtype=K.dtype) - block_metric = metric_from_cholesky(jnp.linalg.cholesky(shifted)) - return _repeated_shifted_metric( - block_metric, block_size, repeats, zero_pad_size, epsilon - ) - - -def _metric_from_quasiseparable(d, p, q, A, *, epsilon, parallel): - d = jnp.asarray(d) + epsilon - p = jnp.asarray(p) - q = jnp.asarray(q) - A = jnp.asarray(A) - n = d.shape[0] - if p.ndim != 2 or p.shape[0] != n: - raise ValueError("p must have shape (len(d), state_size)") - state_size = p.shape[1] - if q.shape != (n, state_size) or A.shape != (n, state_size, state_size): - raise ValueError( - "q must have shape (len(d), state_size) and A must have shape " - "(len(d), state_size, state_size)" - ) - if parallel is None: - parallel = jax.default_backend() != "cpu" and d.dtype == jnp.float64 - c, w = quasiseparable._cholesky(d, p, q, A) - - def solve(x): - y = quasiseparable._forward_substitution(c, p, w, A, x.reshape(n, -1), parallel) - return quasiseparable._backward_substitution(c, p, w, A, y, parallel).reshape( - x.shape - ) - - def norm(x): - y = quasiseparable._cholesky_transpose_matvec( - c, p, w, A, x.reshape(n, -1), parallel - ) - return jnp.linalg.norm(y) - - def inv_sqrt(x): - return quasiseparable._backward_substitution( - c, p, w, A, x.reshape(n, -1), parallel - ).reshape(x.shape) - - def inv_sqrt_transpose(x): - return quasiseparable._forward_substitution( - c, p, w, A, x.reshape(n, -1), parallel - ).reshape(x.shape) - - return GramMetric( - solve=solve, - norm=norm, - inv_sqrt=inv_sqrt, - inv_sqrt_transpose=inv_sqrt_transpose, - ) - - -def repeated_shifted_state_space_metric( - t, - h, - Pinf, - transition, - *, - repeats: int, - zero_pad_size: int, - epsilon, - parallel=None, -): - """Build a repeated shifted state-space kernel metric in linear storage. - - ``t`` is a strictly increasing one-dimensional coordinate. ``h``, - ``Pinf``, and ``transition`` define a stationary state-space kernel; the - convenience function ``matern_state_space`` supplies these objects for the - Matérn-1/2, Matérn-3/2, and Matérn-5/2 kernels. Non-increasing coordinates - propagate ``NaN`` rather than silently defining a nonstationary factor. - ``transition(dt)`` returns the transpose of the textbook state transition - for each gap in ``dt``. - - The resulting metric is ``blockdiag(K, ..., K, 0) + epsilon * I``, with - ``repeats`` copies of the implicit kernel Gram matrix ``K`` and a trailing - zero block of size ``zero_pad_size``. ``epsilon`` is added before the - quasiseparable Cholesky factorization. One structured factor is shared by - every repeated block, and all blocks are processed as batched right-hand - sides. No dense ``K``, repeated factor, full block diagonal, or padding - vector is formed. - - ``parallel`` selects sequential or associative scans. The default uses the - process backend and chooses associative scans only for float64 metrics off - CPU; pass it explicitly when arrays use nondefault device placement. All - four metric callbacks are provided; ``solve``, ``inv_sqrt``, and - ``inv_sqrt_transpose`` accept vectors or matrices, while ``norm`` accepts a - vector. - """ - - _validate_repeated_shifted_layout(repeats, zero_pad_size) - t = jnp.asarray(t) - if t.ndim != 1 or t.shape[0] == 0: - raise ValueError("t must be a nonempty 1-D array") - d, p, q, A = quasiseparable._state_space_generators(t, h, Pinf, transition) - - original_epsilon = epsilon - epsilon = jnp.asarray(epsilon) - if epsilon.ndim != 0: - raise ValueError("epsilon must be a scalar") - dtype = jnp.result_type(d, p, q, A, epsilon, 1.0) - if not jnp.issubdtype(dtype, jnp.floating): - raise TypeError( - "state-space generators and epsilon must have a real floating-point dtype" - ) - if ( - not isinstance(original_epsilon, (jax.Array, jax.core.Tracer)) - and float(original_epsilon) <= 0.0 - ): - raise ValueError("epsilon must be positive") - d = d.astype(dtype) - p = p.astype(dtype) - q = q.astype(dtype) - A = A.astype(dtype) - epsilon = epsilon.astype(dtype) - valid_coordinate = jnp.all(jnp.diff(t) > 0.0) - epsilon = jnp.where((epsilon > 0.0) & valid_coordinate, epsilon, jnp.nan) - - block_metric = _metric_from_quasiseparable( - d, p, q, A, epsilon=epsilon, parallel=parallel - ) - return _repeated_shifted_metric( - block_metric, d.shape[0], repeats, zero_pad_size, epsilon - ) - - -def _metric_with_compute_dtype(metric: GramMetric, dtype) -> GramMetric: - dtype = jnp.dtype(dtype) - - def wrap(callback): - if callback is None: - return None - - def apply(x): - return callback(x.astype(dtype)).astype(x.dtype) - - return apply - - return GramMetric( - solve=wrap(metric.solve), - norm=wrap(metric.norm), - inv_sqrt=wrap(metric.inv_sqrt), - inv_sqrt_transpose=wrap(metric.inv_sqrt_transpose), - ) diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index f5f6f3a..5dca700 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -13,7 +13,7 @@ changes the subproblem being solved, so approximations are safe. """ -from dataclasses import dataclass +from dataclasses import dataclass, field from typing import Any import jax @@ -230,287 +230,176 @@ def block_eigen_state(families, permutation): } -def identity_preconditioner(): - """The identity map as an explicit "no preconditioner" choice for the - ``LevenbergMarquardt`` hooks. - - ``linear_solver="gram_cg"`` requires ``dual_preconditioner``, and a - ``gram_cg``-resolved AD solve requires ``ad_solver_preconditioner`` (under - ``normal_cg`` the hook is optional) -- nobody should run Krylov methods - without thinking about preconditioning, so opting out is an explicit, - greppable decision rather than a silent default. The returned callable - accepts every hook signature: ``dual_preconditioner(v, damping)`` and - ``ad_solver_preconditioner(v)``. (The ridge solver's typed opt-out is - :class:`IdentityPreconditioner`.) - """ - - def preconditioner(v, damping=None): - return v - - return preconditioner - - -def identity_right_preconditioner(): - """The identity map as an explicit "no right-preconditioner" choice. - - Returns a :class:`WhitenedPreconditioner` whose ``solve`` and - ``solve_transpose`` are both the identity, so the metric solver's - ``linear_solver="lsmr"`` path runs unpreconditioned -- an explicit, - greppable opt-out rather than a silent default. - """ - - def solve(v, damping): - return v - - def solve_transpose(w, damping): - return w - - return WhitenedPreconditioner(solve, solve_transpose) - - -class WhitenedPreconditioner: - """Parameter-space right-preconditioner for ``linear_solver="lsmr"``: a - value-hashable pair ``(solve, solve_transpose)`` applying ``R^{-1}`` and - ``R^{-T}``. - - LSMR then runs in the preconditioned variable ``z = R u`` on the augmented - operator ``[B R^{-1}; sqrt(damping) R^{-1}]`` (``B = J S`` for - ``LevenbergMarquardt``), and the returned step un-preconditions the - final iterate as ``u = R^{-1} z``. A well-chosen ``R`` (a Schur-complement - factor of the parameter-space normal operator is the canonical - construction) clusters the spectrum of ``B R^{-1}`` and cuts the endgame - iteration count by orders of magnitude:: - - def solve(v, damping): - return jsp_linalg.solve_triangular(R, v) # R^{-1} v - - def solve_transpose(w, damping): - return jsp_linalg.solve_triangular(R.T, w) # R^{-T} w - - solver = LevenbergMarquardt( - residual_fn, linear_solver="lsmr", - whitened_preconditioner=WhitenedPreconditioner(solve, solve_transpose), - ) - - - ``solve(v, damping) -> vector`` applies ``R^{-1}`` on a parameter-space - vector; ``solve_transpose(w, damping) -> vector`` applies ``R^{-T}``. Both - receive the live ``damping`` (like ``dual_preconditioner(v, damping)``), so - a ``damping``-analytic ``R`` folds ``lambda`` in exactly. - - **Exact subproblem for any R**: the augmented damping row is - ``sqrt(damping) R^{-1} z = sqrt(damping) u``, so every ``damping > 0`` - subproblem is exactly the ``I``-damped - ``min_u ||r + B u||^2 + damping ||u||^2`` -- the computed step is - ``u = -(BᵀB + damping I)^{-1} Bᵀ r`` regardless of ``R``. The - preconditioner changes the iteration path, never the subproblem, and the - ``damping -> 0`` limit is the minimum-metric-norm step for ANY ``R``. - - LSMR stopping (``iterative_tol``/``iterative_atol``) is measured on the - preconditioned operator -- the well-conditioned ``z`` coordinates. - - ``None`` (the ``LevenbergMarquardt`` default) runs plain LSMR. - Value-hashable on ``(solve, solve_transpose)`` with jit's static-key - semantics: equal pairs share one compiled solve loop, so define the - callables once at setup scope. - """ - - def __init__(self, solve, solve_transpose): - if not callable(solve): - raise TypeError("WhitenedPreconditioner.solve must be callable") - if not callable(solve_transpose): - raise TypeError("WhitenedPreconditioner.solve_transpose must be callable") - self.solve = solve - self.solve_transpose = solve_transpose - - def __hash__(self): - return hash((self.solve, self.solve_transpose)) - - def __eq__(self, other): - return ( - isinstance(other, WhitenedPreconditioner) - and self.solve == other.solve - and self.solve_transpose == other.solve_transpose - ) - - -def sherman_morrison_preconditioner(solve, u, weight): - """Preconditioner for ``B = A + weight * u u'`` from a solve with ``A``. +@dataclass(frozen=True, eq=False) +class ShermanMorrisonPreconditioner(Preconditioner): + """Dual preconditioner for ``B = A + weight * u u'`` from a solve with ``A``. Applies ``B^{-1} v = y - A^{-1}u (u' y) / (1/weight + u' A^{-1} u)`` with - ``y = A^{-1} v`` by the Sherman-Morrison identity; ``A^{-1} u`` and the - scalar denominator are precomputed. This is the natural shape for - kernel-collocation dual operators, where a metric weight ``m`` on a scalar - parameter injects an exactly known rank-1 spike ``(c^2/m) u u'`` into - ``J M^{-1} J'``. The ``damping`` argument is accepted per the - ``dual_preconditioner`` contract and ignored -- spectral closeness to the - damped operator is all a preconditioner needs -- which also makes the - helper directly valid as ``ad_solver_preconditioner`` (the solver calls - two-argument callables with zero damping there). + ``y = A^{-1} v`` by the Sherman-Morrison identity; ``A^{-1}u`` and the + scalar denominator are precomputed at construction. This is the natural + shape for kernel-collocation dual operators, where a metric weight ``m`` + on a scalar parameter injects an exactly known rank-1 spike + ``(c^2/m) u u'`` into ``J M^{-1} J'``. The live ``damping`` is ignored -- + spectral closeness to the damped operator is all a preconditioner needs -- + which also makes it valid in the zero-damping ``ad_solver`` role. """ - solve_u = solve(u) - denominator = 1.0 / weight + u @ solve_u - - def dual_preconditioner(v, damping): - y = solve(v) - return y - solve_u * ((u @ y) / denominator) + solve: object + u: jax.Array + weight: float + _solve_u: jax.Array = field(init=False) + _denominator: jax.Array = field(init=False) - return dual_preconditioner + def __post_init__(self): + solve_u = self.solve(self.u) + object.__setattr__(self, "_solve_u", solve_u) + object.__setattr__(self, "_denominator", 1.0 / self.weight + self.u @ solve_u) + def apply(self, v, damping, ctx): + y = self.solve(v) + return y - self._solve_u * ((self.u @ y) / self._denominator) -def woodbury_preconditioner(solve, U, weights): - """Preconditioner for ``B = A + U diag(weights) U'`` from a solve with ``A``. - The rank-k generalization of ``sherman_morrison_preconditioner``: - applies ``B^{-1} v = y - A^{-1}U C^{-1} (U' y)`` with ``y = A^{-1} v`` - and capacitance ``C = diag(1/weights) + U' A^{-1} U`` by the Woodbury - identity; ``A^{-1} U`` (one matrix solve) and the Cholesky factor of the - k x k capacitance are precomputed. This is the natural shape when a - metric weight ``eps`` on a k-vector of scalar parameters injects the - exactly known rank-k spike ``(c^2/eps) U U'`` into ``J M^{-1} J'`` - (``U`` the corresponding Jacobian columns up to sign and scale). With - ``k = 1`` it reduces to ``sherman_morrison_preconditioner``. ``weights`` - must be positive -- not validated, since inputs may be traced. The - ``damping`` argument is accepted per the ``dual_preconditioner`` - contract and ignored, so the helper is directly valid as - ``ad_solver_preconditioner`` too. +@dataclass(frozen=True, eq=False) +class WoodburyPreconditioner(Preconditioner): + """Dual preconditioner for ``B = A + U diag(weights) U'``. + + The rank-k generalization of :class:`ShermanMorrisonPreconditioner`: + applies ``B^{-1} v = y - A^{-1}U C^{-1}(U' y)`` with ``y = A^{-1} v`` and + capacitance ``C = diag(1/weights) + U' A^{-1} U``; ``A^{-1}U`` (one matrix + solve) and the Cholesky factor of the k x k capacitance are precomputed. + ``weights`` must be positive -- not validated, since inputs may be traced. + Like Sherman-Morrison it ignores ``damping`` and so serves the AD role too. """ - U = jnp.asarray(U) - weights = jnp.asarray(weights) - if U.ndim != 2 or weights.shape != (U.shape[1],): - raise ValueError("U must have shape (n, k) and weights shape (k,)") - solve_U = solve(U) - capacitance = jnp.diag(1.0 / weights) + U.T @ solve_U - factor = jsp_linalg.cho_factor(capacitance) - - def dual_preconditioner(v, damping): - y = solve(v) - return y - solve_U @ jsp_linalg.cho_solve(factor, U.T @ y) + solve: object + U: jax.Array + weights: jax.Array + _solve_U: jax.Array = field(init=False) + _factor: tuple = field(init=False) + + def __post_init__(self): + U, weights = jnp.asarray(self.U), jnp.asarray(self.weights) + if U.ndim != 2 or weights.shape != (U.shape[1],): + raise ValueError("U must have shape (n, k) and weights shape (k,)") + object.__setattr__(self, "U", U) + object.__setattr__(self, "weights", weights) + solve_U = self.solve(U) + object.__setattr__(self, "_solve_U", solve_U) + capacitance = jnp.diag(1.0 / weights) + U.T @ solve_U + object.__setattr__(self, "_factor", jsp_linalg.cho_factor(capacitance)) - return dual_preconditioner + def apply(self, v, damping, ctx): + y = self.solve(v) + return y - self._solve_U @ jsp_linalg.cho_solve(self._factor, self.U.T @ y) -def pad_dual_preconditioner(base_preconditioner, n_real): +@dataclass(frozen=True, eq=False) +class PaddedPreconditioner(Preconditioner): """Extend a dual preconditioner to a residual padded with exact zeros. - The fixed-residual-shape pattern appends ``k`` identically-zero entries to - an ``n_real``-entry residual so the compiled shapes stay stable across - problem instances. The padded rows have zero Jacobian rows, so the dual - operator becomes exactly block diagonal:: + The fixed-residual-shape pattern appends identically-zero entries to an + ``n_real``-entry residual so compiled shapes stay stable across problem + instances. Padded rows have zero Jacobian rows, so the dual operator is + exactly block diagonal:: [ J P J' + damping I 0 ] [ 0 damping I ] - and the matching preconditioner applies ``base_preconditioner`` on the - first ``n_real`` coordinates and the exact ``1 / damping`` inverse on the - padded block -- the second block must NOT be zeroed (that would make the - preconditioner singular rather than SPD, even though zeros can appear to - work when the padded coordinates are never excited). Wrapping is needed - for shape-fixed bases (dense solves, ``nystrom_preconditioner``, - Sherman-Morrison/Woodbury built at the unpadded size); a shape-generic - base like ``identity_preconditioner()`` stays valid unwrapped, it just - forgoes the exact padded-block inverse. Like ``nystrom_preconditioner`` - this uses the live ``damping`` argument, and because the padded block - divides by it, the returned callback serves only the damped forward - solve -- never the ``ad_solver_preconditioner`` hook. Relatedly, padded - rows make the undamped dual ``J P J'`` singular; ``ad_solver="svd"`` - handles this exactly (its spectral filter computes the minimum-metric-norm - tangent, which equals the unpadded one), while ``ad_solver="qr"`` fails - loudly there. + and this applies ``base`` on the first ``n_real`` coordinates and the exact + ``1/damping`` inverse on the padded block. That second block must NOT be + zeroed -- that would make the preconditioner singular rather than SPD, even + though zeros can appear to work when the padded coordinates are never + excited. Because the padded block divides by the live damping, this serves + only the damped forward solve; the undamped dual is singular there, which + ``ad_solver=SVD()`` handles exactly. """ - if not isinstance(n_real, int) or isinstance(n_real, bool) or n_real <= 0: - raise ValueError("n_real must be a positive int") + base: Preconditioner + n_real: int + + requires_positive_damping = True - def dual_preconditioner(v, damping): + def apply(self, v, damping, ctx): # Static shapes, so this raises at trace time; without it a # shape-generic base would silently accept a too-short vector. - if v.ndim != 1 or v.shape[0] < n_real: + if v.ndim != 1 or v.shape[0] < self.n_real: raise ValueError( f"padded residual vector must be 1-D with at least " - f"n_real={n_real} entries; got shape {v.shape}" + f"n_real={self.n_real} entries; got shape {v.shape}" ) return jnp.concatenate( - (base_preconditioner(v[:n_real], damping), v[n_real:] / damping) + ( + self.base.apply(v[: self.n_real], damping, ctx), + v[self.n_real :] / damping, + ) ) - # The padded block divides by the live damping, so the zero-damping - # implicit hook must reject this helper at construction. - dual_preconditioner.requires_positive_damping = True - return dual_preconditioner - -def nystrom_preconditioner(matvec, n, rank, key, *, dtype=None): +@dataclass(frozen=True, eq=False) +class NystromPreconditioner(Preconditioner): """Randomized Nystrom preconditioner (Frangella-Tropp-Udell) for a PSD operator given only through ``matvec``. Sketches ``A`` with a rank-``rank`` Nystrom approximation - ``A_hat = U diag(lam) U'`` -- a thin-QR'd Gaussian test matrix, one - block application ``Y = A Omega``, and the shifted Cholesky/SVD recovery - of Frangella, Tropp, and Udell (arXiv:2110.02820, Algorithm 2.1); the - stabilization shift ``nu ~ eps * ||Y||_F`` is removed from the recovered - eigenvalues. The returned callback applies the FTU preconditioner - (their eq. 5.3, up to the positive scalar ``rho + damping``, which CG - ignores):: + ``A_hat = U diag(lam) U'`` -- a thin-QR'd Gaussian test matrix, one block + application ``Y = A Omega``, and the shifted Cholesky/SVD recovery of + arXiv:2110.02820 Algorithm 2.1 -- then applies their eq. 5.3:: v -> U ((U'v) / (lam + damping)) + (v - U U'v) / (rho + damping) - where ``rho`` is the smallest retained Nystrom eigenvalue: eigendirections - the sketch resolved are inverted against the live shift, and the - unresolved complement is treated as sitting at ``rho`` rather than at - zero -- that balance is what carries the FTU condition-number guarantee - for fast-decaying spectra. This is the one shipped base preconditioner - that uses the live ``damping`` argument (Sherman-Morrison/Woodbury ignore - it; the ``pad_dual_preconditioner`` wrapper also uses it): one - construction serves every LM damping value, and passed as - ``ad_solver_preconditioner`` it is called with zero damping and applies - the undamped inverse (valid only when the retained spectrum is strictly - positive). - - The target use is neural-network least squares under the identity - metric, where the dual operator is the m x m empirical NTK Gram - ``J J'`` -- fast spectral decay plus the LM damping shift is exactly the - FTU regime. ``matvec`` must apply a symmetric PSD operator and accept - ``(n, k)`` matrices (the same shape contract as ``Metric.solve``); an - indefinite operator silently produces NaN through the Cholesky square - root. The build costs ``rank`` operator applications plus an - ``O(n rank^2)`` QR/SVD, done once at construction -- like every - preconditioner it is frozen there, so for a nonlinear problem it + where ``rho`` is the smallest retained eigenvalue: directions the sketch + resolved are inverted against the live shift, and the unresolved + complement is treated as sitting at ``rho`` rather than at zero. That + balance is what carries the FTU condition-number guarantee for + fast-decaying spectra. + + The target use is neural-network least squares under the identity metric, + where the dual operator is the ``m x m`` empirical NTK Gram ``J J'`` -- + fast spectral decay plus the LM damping shift is exactly the FTU regime. + ``matvec`` must apply a symmetric PSD operator to ``(n, k)`` matrices; an + indefinite one silently produces NaN through the Cholesky square root. The + build costs ``rank`` operator applications plus an ``O(n rank^2)`` + QR/SVD, paid once at construction, so for a nonlinear problem it approximates the dual at the linearization point it was built from - (staleness is safe: preconditioner error never moves the converged - root). Each apply is two ``(n, rank)`` matvecs. + (staleness is safe). Each apply is two ``(n, rank)`` matvecs. ``key`` is an explicit PRNG key; the same key reproduces the same - preconditioner. ``dtype=None`` uses the JAX default float (respects - x64) -- pass the operator dtype explicitly for a float32 problem under - enabled x64. All operations are traceable; ``n`` and ``rank`` are static - Python ints. + preconditioner. ``dtype=None`` uses the JAX default float -- pass the + operator dtype explicitly for a float32 problem under enabled x64. """ - if not isinstance(n, int) or isinstance(n, bool) or n <= 0: - raise ValueError("n must be a positive int") - if not isinstance(rank, int) or isinstance(rank, bool) or not 0 < rank <= n: - raise ValueError("rank must be a positive int <= n") - if dtype is None: - dtype = jnp.result_type(float) - Omega = jnp.linalg.qr(jax.random.normal(key, (n, rank), dtype=dtype))[0] - Y = matvec(Omega) - # The floor keeps the shift usable for a (near-)zero operator, where - # eps * ||Y||_F alone would leave the core singular; tiny/eps stays clear - # of the subnormal range through the downstream products. - finfo = jnp.finfo(dtype) - nu = jnp.maximum(finfo.eps * jnp.linalg.norm(Y), finfo.tiny / finfo.eps) - Y_nu = Y + nu * Omega - core = Omega.T @ Y_nu - L = jnp.linalg.cholesky(0.5 * (core + core.T)) - B = jsp_linalg.solve_triangular(L, Y_nu.T, lower=True).T - U, sigma, _ = jnp.linalg.svd(B, full_matrices=False) - lam = jnp.maximum(sigma**2 - nu, 0.0) - rho = lam[-1] - - def preconditioner(v, damping=0.0): - # U (U'v)/(lam+damping) + (v - U U'v)/(rho+damping), regrouped so the - # apply is two (n, rank) matvecs instead of three. + matvec: object + n: int + rank: int + key: jax.Array + dtype: object = None + _basis: jax.Array = field(init=False) + _eigenvalues: jax.Array = field(init=False) + + def __post_init__(self): + if not 0 < self.rank <= self.n: + raise ValueError("rank must be a positive int <= n") + dtype = jnp.result_type(float) if self.dtype is None else self.dtype + shape = (self.n, self.rank) + Omega = jnp.linalg.qr(jax.random.normal(self.key, shape, dtype))[0] + Y = self.matvec(Omega) + # The floor keeps the shift usable for a (near-)zero operator, where + # eps * ||Y||_F alone would leave the core singular; tiny/eps stays + # clear of the subnormal range through the downstream products. + finfo = jnp.finfo(dtype) + nu = jnp.maximum(finfo.eps * jnp.linalg.norm(Y), finfo.tiny / finfo.eps) + Y_nu = Y + nu * Omega + core = Omega.T @ Y_nu + L = jnp.linalg.cholesky(0.5 * (core + core.T)) + B = jsp_linalg.solve_triangular(L, Y_nu.T, lower=True).T + U, sigma, _ = jnp.linalg.svd(B, full_matrices=False) + object.__setattr__(self, "_basis", U) + object.__setattr__(self, "_eigenvalues", jnp.maximum(sigma**2 - nu, 0.0)) + + def apply(self, v, damping, ctx): + # Regrouped so the apply is two (n, rank) matvecs instead of three. + U, lam = self._basis, self._eigenvalues + rho = lam[-1] Utv = U.T @ v return U @ (Utv / (lam + damping) - Utv / (rho + damping)) + v / (rho + damping) - - return preconditioner diff --git a/src/nlls_gram/recycled_cg.py b/src/nlls_gram/recycled_cg.py deleted file mode 100644 index ed589c1..0000000 --- a/src/nlls_gram/recycled_cg.py +++ /dev/null @@ -1,601 +0,0 @@ -# Copyright 2020 The JAX Authors. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# https://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. - -"""Forked conjugate-gradient core from ``jax.scipy.sparse.linalg``. - -``recycled_cg`` is a drop-in replacement for ``jax.scipy.sparse.linalg.cg``. -Only the Krylov loop is vendored here (from the installed jax's -``jax/_src/scipy/sparse/linalg.py``) -- it is the extension point for -deflated/recycled CG across LM steps. The surrounding plumbing (``x0``/ -``maxiter`` normalization and the ``lax.custom_linear_solve`` wrapper that -provides implicit derivatives) is imported from ``jax._src`` so upstream -improvements carry over; a jax release that moves those internals will fail -loudly at import time rather than silently diverge. -""" - -from dataclasses import dataclass -from typing import NamedTuple - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -from jax import lax -from jax.tree_util import tree_leaves - -# Compatibility policy: only the CG Krylov loop is vendored here; the surrounding -# plumbing (x0/maxiter normalization and the custom_linear_solve wrapper) is -# imported from jax's private jax._src so upstream fixes carry over. That module -# is not a public API -- a jax release that moves or renames it must fail loudly -# at import time rather than let this fork silently diverge, so the import is -# guarded and re-raised with actionable remediation. -try: - from jax._src.scipy.sparse.linalg import ( - _add, - _identity, - _isolve, - _mul, - _normalize_matvec, - _sub, - _vdot_real_tree, - ) -except ImportError as exc: # pragma: no cover - only on an upstream jax break - from importlib.metadata import version - - raise ImportError( - f"nlls-gram {version('nlls-gram')} tracks jax's private conjugate-gradient " - "plumbing (jax._src.scipy.sparse.linalg); this jax version appears to have " - "moved or renamed it. Pin jax to a known-good range or upgrade nlls-gram." - ) from exc - -_HIGHEST = lax.Precision.HIGHEST - - -def _apply_columns(matvec, X): - # Apply the operator to every column of ``X`` (m, k). The package's dual - # operators accept an ``(m, k)`` matrix directly (leading-axis batching) -- the - # hot path, one operator application -- so probe that and validate the shape; - # fall back to a per-column ``vmap`` for plain vector-only callables. The probe - # is a trace-time capability check: any failure (a vector-only callable can - # raise a shape/assert error of any type) just means "does not accept the - # batched shape", so fall back. Shapes are static -- the choice is made once. - m, k = X.shape - try: - out = matvec(X) - batched = getattr(out, "shape", None) == (m, k) - except Exception: - batched = False - if not batched: - out = jax.vmap(matvec, in_axes=1, out_axes=1)(X) - return out - - -def _sentinel(diag, valid, dtype): - # A finite diagonal placeholder for masked-out (invalid) rows of the harvest - # projection: larger than any valid Ritz value so they never rank among the k - # smallest, yet finite even when NO column is valid (the count==0 cold-start - # path, reachable by warm-starting at the solution) or when the *1e3 scaling - # would overflow -- an all -inf reduction would otherwise poison eigh. - max_valid = jnp.max(jnp.where(valid, diag, -jnp.inf)) - big = jnp.where(jnp.any(valid), max_valid * 1e3 + 1.0, jnp.ones((), dtype)) - return jnp.minimum(big, jnp.finfo(dtype).max) - - -def _recycled_cg_solve(A, b, x0=None, *, maxiter, tol=1e-5, atol=0.0, M=_identity): - # Verbatim fork of jax's _cg_solve, modulo formatting and public-API - # imports (jnp.result_type for dtypes.result_type); keep the structure - # diffable against upstream. Recycling state (deflation basis, Lanczos - # harvest buffers) will thread through this loop's carry. - - # tolerance handling uses the "non-legacy" behavior of - # scipy.sparse.linalg.cg - bs = _vdot_real_tree(b, b) - atol2 = jnp.maximum(jnp.square(tol) * bs, jnp.square(atol)) - - # preconditioned CG: - # en.wikipedia.org/wiki/Conjugate_gradient_method (preconditioned variant) - - def cond_fun(value): - _, r, gamma, _, k = value - rs = gamma.real if M is _identity else _vdot_real_tree(r, r) - return (rs > atol2) & (k < maxiter) - - def body_fun(value): - x, r, gamma, p, k = value - Ap = A(p) - alpha = gamma / _vdot_real_tree(p, Ap).astype(dtype) - x_ = _add(x, _mul(alpha, p)) - r_ = _sub(r, _mul(alpha, Ap)) - z_ = M(r_) - gamma_ = _vdot_real_tree(r_, z_).astype(dtype) - beta_ = gamma_ / gamma - p_ = _add(z_, _mul(beta_, p)) - return x_, r_, gamma_, p_, k + 1 - - r0 = _sub(b, A(x0)) - p0 = z0 = M(r0) - dtype = jnp.result_type(*tree_leaves(p0)) - gamma0 = _vdot_real_tree(r0, z0).astype(dtype) - initial_value = (x0, r0, gamma0, p0, 0) - - x_final, *_ = lax.while_loop(cond_fun, body_fun, initial_value) - - return x_final - - -def recycled_cg(A, b, x0=None, *, tol=1e-5, atol=0.0, maxiter=None, M=None): - """Upstream-parity fork of :func:`jax.scipy.sparse.linalg.cg` (no recycling). - - Despite the name this is the plain CG parity path: it does no recycling and - reproduces upstream CG exactly. Cross-step Krylov recycling / deflation lives - in :func:`deflated_pcg` and :class:`RecycleConfig`; this fork only vendors the - Krylov loop as their shared, upstream-tracking extension point. - - Semantics are identical to the upstream solver: ``A`` is a hermitian - positive-definite matvec callable (or matrix), convergence is - ``norm(residual) <= max(tol * norm(b), atol)``, ``M`` approximates - ``A^{-1}``, ``x0`` seeds the iteration, and derivatives are implicit - (another CG solve through ``lax.custom_linear_solve``) rather than - differentiated through the iterations. Returns ``(x, info)`` with - ``info=None``, matching upstream. - - The Krylov loop is vendored in this package as the extension point for - Krylov-subspace recycling across the LM solver's successive dual solves; - with no recycling state it reproduces upstream CG exactly. - """ - return _isolve( - _recycled_cg_solve, - A=A, - b=b, - x0=x0, - tol=tol, - atol=atol, - maxiter=maxiter, - M=M, - check_symmetric=True, - ) - - -# --- Deflated / recycled PCG ------------------------------------------------- -# -# A two-level additive-coarse-space PCG with an eigCG-style thick-restart -# harvest, kept entirely separate from the verbatim ``recycled_cg`` parity path -# above. The first-level preconditioner ``P`` (the user's structured dual -# preconditioner) is composed with a deflation coarse solve on a carried basis -# ``U`` whose columns approximately span the smallest-eigenvalue subspace of the -# P-preconditioned operator. Each solve harvests the next basis from the CG -# Lanczos trace so it can be recycled into the following (slowly drifting) solve -# at zero rebuild cost. -# -# Callers must NOT differentiate through this directly: the deflation basis and -# harvest are ``stop_gradient``'d and the solution carries implicit derivatives -# via ``lax.custom_linear_solve`` (the same wrapper the parity path reuses). - - -class HarvestState(NamedTuple): - """Diagnostics and the next deflation basis emitted by :func:`deflated_pcg`. - - A ``NamedTuple``: positional unpacking - (``basis, iterations, residual_norm = state``) is part of the stable API. - - Attributes: - basis: ``(m, k)`` orthonormal deflation basis harvested from the solve, - recycled into the next solve. ``stop_gradient``'d. - iterations: number of PCG iterations run (``()`` integer). - residual_norm: final ``||b - A x||`` (``()`` scalar). - """ - - basis: jax.Array - iterations: jax.Array - residual_norm: jax.Array - - -@dataclass(frozen=True) -class RecycleConfig: - """Static, value-hashable configuration for Krylov recycling across LM steps. - - All fields are ints/bools/None, so equal configs hash equal and share a - compiled program when this rides the solver's static key. ``rank`` and - ``window`` are shape-determining (they size the carried basis and the harvest - window), hence static -- not resettable mid-solve by a callback. - - Attributes: - rank: ``k``, the number of deflation vectors carried across steps. - window: ``w``, the harvest window; ``None`` selects - ``max(2 * rank, rank + 4)``. - warm_start: reuse the previous step's dual solution as the initial guess. - reorthogonalize: robust reorthonormalized ``Q'A Q`` harvest (vs the cheap - coefficient-tridiagonal route); see :func:`deflated_pcg`. - ridge: trace-scaled ridge fraction on ``E = U'A U``; ``None`` uses the - dtype-keyed default in :func:`build_coarse_operator`. - """ - - rank: int - window: int | None = None - warm_start: bool = True - reorthogonalize: bool = True - ridge: float | None = None - - def __post_init__(self): - # rank/window are shape-determining static ints (bool is an int subclass - # but is not a valid size, so reject it explicitly). - if isinstance(self.rank, bool) or not isinstance(self.rank, int): - raise TypeError( - f"RecycleConfig.rank must be an int, got {type(self.rank).__name__}" - ) - if self.rank <= 0: - raise ValueError(f"RecycleConfig.rank must be positive, got {self.rank}") - if self.window is not None: - if isinstance(self.window, bool) or not isinstance(self.window, int): - raise TypeError( - "RecycleConfig.window must be an int or None, got " - f"{type(self.window).__name__}" - ) - if self.window < self.rank: - raise ValueError( - f"RecycleConfig.window ({self.window}) must be >= " - f"rank ({self.rank})" - ) - if not isinstance(self.warm_start, bool): - raise TypeError( - "RecycleConfig.warm_start must be a bool, got " - f"{type(self.warm_start).__name__}" - ) - if not isinstance(self.reorthogonalize, bool): - raise TypeError( - "RecycleConfig.reorthogonalize must be a bool, got " - f"{type(self.reorthogonalize).__name__}" - ) - if self.ridge is not None: - if isinstance(self.ridge, bool) or not isinstance(self.ridge, (int, float)): - raise TypeError( - "RecycleConfig.ridge must be a float or None, got " - f"{type(self.ridge).__name__}" - ) - if self.ridge < 0: - raise ValueError( - f"RecycleConfig.ridge must be nonnegative, got {self.ridge}" - ) - - @property - def resolved_window(self): - """The concrete window, applying the ``max(2 * rank, rank + 4)`` default.""" - if self.window is not None: - return self.window - return max(2 * self.rank, self.rank + 4) - - -@jax.tree_util.register_dataclass -@dataclass(frozen=True) -class RecycleState: - """Carried recycling state on ``LMState``: the basis and warm starts. - - All fields are traced arrays of fixed shape (``rank`` and ``window`` are - static), so it vmaps cleanly for ``multi_start`` and rides the solve loop's - ``while_loop`` carry. Populated by ``init()`` (zeros, ``valid=False``) and - refreshed each accepted/rejected LM step; ``stop_gradient``'d so no AD path - flows through the harvest. - - Attributes: - U: ``(m, rank)`` deflation basis (zeros when ``valid`` is False). - dual_velocity: ``(m,)`` previous velocity dual solution (warm start). - dual_accel: ``(m,)`` previous geodesic-acceleration dual solution - (zeros when geodesic acceleration is off). - valid: ``()`` bool, whether the basis has been populated by a solve. - iterations: ``()`` int, PCG iterations of the last velocity solve - (0 before the first step); a diagnostic, not used by the algorithm. - residual_norm: ``()`` final velocity-solve residual norm (0 before the - first step); a diagnostic. - """ - - U: jax.Array - dual_velocity: jax.Array - dual_accel: jax.Array - valid: jax.Array - iterations: jax.Array - residual_norm: jax.Array - - -def build_coarse_operator(A, U, *, ridge=None): - """Precompute the deflation coarse operator ``W = A U`` and ``chol(U'A U)``. - - ``A`` is a hermitian positive-definite matvec callable (or square matrix) and - ``U`` an ``(m, k)`` deflation basis. Returns ``(W, E_factor)`` where - ``W = A U`` and ``E_factor`` is the :func:`jax.scipy.linalg.cho_factor` of the - ridged, symmetrized ``E = U'A U``. Built once per LM step and reused across - every right-hand side (velocity and geodesic acceleration share one operator). - - The ridge is a trace-scaled shift ``ridge`` (fraction ``gamma``; ``None`` uses - a dtype-keyed default, ``1e-12`` float64 / ``1e-6`` float32) with an absolute - floor, so the Cholesky factor stays finite even for a zero or rank-deficient - ``U``. It lives only inside a preconditioner and never moves the converged - root. - """ - Amv = _normalize_matvec(A) - W = _apply_columns(Amv, U) - E = jnp.matmul(U.T, W, precision=_HIGHEST) - E = 0.5 * (E + E.T) - dtype = E.dtype - k = E.shape[0] - finfo = jnp.finfo(dtype) - frac = ridge - if frac is None: - frac = 1e-12 if jnp.dtype(dtype) == jnp.dtype(jnp.float64) else 1e-6 - floor = finfo.tiny / finfo.eps - rho = jnp.maximum(jnp.asarray(frac, dtype) * jnp.trace(E) / k, floor) - E_reg = E + rho * jnp.eye(k, dtype=dtype) - return W, jsp_linalg.cho_factor(E_reg) - - -def _deflated_pcg_core( - A, b, x0, M, U, *, maxiter, tol, atol, window, rank, reorthogonalize, harvest -): - # Augmented PCG: the standard preconditioned recurrence (identical in the - # x/r/gamma/p carry to the parity loop, so U=0 reproduces it bitwise), plus a - # static (m, window) ring buffer of M-normalized Lanczos vectors and the - # CG-scalar tridiagonal (used only by the cheap harvest route). The harvest - # (deflation basis for the next solve) runs after the loop when ``harvest``. - m = b.shape[0] - w = window - bs = _vdot_real_tree(b, b) - atol2 = jnp.maximum(jnp.square(tol) * bs, jnp.square(atol)) - - r0 = _sub(b, A(x0)) - z0 = M(r0) - p0 = z0 - dtype = jnp.result_type(*tree_leaves(z0)) - gamma0 = _vdot_real_tree(r0, z0).astype(dtype) - V0 = jnp.zeros((m, w), dtype) - Tdiag0 = jnp.zeros((w,), dtype) - Toff0 = jnp.zeros((w,), dtype) - boa0 = jnp.zeros((), dtype) - - def cond_fun(value): - _, r, _, _, _, k, _, _, _, _ = value - return (_vdot_real_tree(r, r) > atol2) & (k < maxiter) - - def body_fun(value): - x, r, z, gamma, p, k, V, Tdiag, Toff, boa = value - Ap = A(p) - alpha = gamma / _vdot_real_tree(p, Ap).astype(dtype) - x_ = _add(x, _mul(alpha, p)) - r_ = _sub(r, _mul(alpha, Ap)) - z_ = M(r_) - gamma_ = _vdot_real_tree(r_, z_).astype(dtype) - beta = gamma_ / gamma - p_ = _add(z_, _mul(beta, p)) - # CG -> Lanczos of the P-preconditioned operator (Saad 6.7.3): the - # tridiagonal entries come free from the CG scalars, the window column is - # the M-normalized Lanczos vector z_k / sqrt(gamma_k). The window is a ring - # (slot = k mod w) keeping the last w vectors -- near convergence these are - # richest in the slow (small-eigenvalue) modes we want to deflate. Mapping - # V G back to the original space recovers eigenvectors of the - # preconditioned operator; Q'A Q equals the tridiagonal block exactly, so a - # windowed Rayleigh-Ritz reads off the ring's principal sub-block. - v_col = z / jnp.sqrt(gamma) - diag_k = jnp.ones((), dtype) / alpha + boa - # sqrt(beta) is real because beta = gamma_/gamma > 0 for an SPD - # preconditioner M (gamma = > 0). A non-SPD M is a contract - # violation and would surface here as a NaN rather than being masked. - off_k = jnp.sqrt(beta) / alpha - slot = k % w - V_ = V.at[:, slot].set(v_col) - Tdiag_ = Tdiag.at[slot].set(diag_k) - Toff_ = Toff.at[slot].set(off_k) - return x_, r_, z_, gamma_, p_, k + 1, V_, Tdiag_, Toff_, beta / alpha - - # int32 counter: LMState carries RecycleState.iterations as int32, and the - # x64 default of jnp.array(0) (int64) would break the solve-loop carry. - init = (x0, r0, z0, gamma0, p0, jnp.zeros((), jnp.int32), V0, Tdiag0, Toff0, boa0) - x_f, r_f, _, _, _, count, V, Tdiag, Toff, _ = lax.while_loop( - cond_fun, body_fun, init - ) - resid_norm = jnp.sqrt(_vdot_real_tree(r_f, r_f)) - - if not harvest: - # Shared-operator RHS (e.g. geodesic acceleration): reuse the carried basis - # unchanged and skip the Rayleigh-Ritz / QR / extra matvecs entirely. - return x_f, count, resid_norm, U - - # Unroll the ring into chronological order over the last min(count, w) Lanczos - # vectors. - idx = jnp.arange(w) - nvalid = jnp.minimum(count, w) - start = jnp.maximum(count - w, 0) - perm = (start + idx) % w - V_ord = V[:, perm] - - if reorthogonalize: - # Thick-restart / GCRO-DR harvest: Rayleigh-Ritz for A over the augmented - # recycle space [U, window]. Including the carried basis lets U PERSIST and - # refine even when deflation makes a solve converge in a few iterations - # (too few to re-harvest a full basis from the window alone). The explicit - # Q'A Q Rayleigh quotient on the reorthonormalized space is robust to the - # Lanczos orthogonality drift that pollutes the coefficient tridiagonal's - # near-converged Ritz vectors (design Hard 3), at k + w extra matvecs. - # Zero columns (cold U, unfilled window) are masked by column norm and - # sorted to the back before QR: a leading zero column would otherwise make - # QR orthogonalize the real columns against an arbitrary completion - # direction and corrupt their span. When fewer than rank columns are valid - # (cold start converging in < rank iterations), the surplus selected - # directions are QR completions -- non-Ritz but finite and orthonormal, and - # the ridge in build_coarse_operator keeps the next E factorable. - B = jnp.concatenate([U, V_ord], axis=1) - colnorm = jnp.linalg.norm(B, axis=0) - valid = colnorm > jnp.sqrt(jnp.finfo(dtype).eps) * jnp.max(colnorm) - order = jnp.argsort(~valid) - B = B[:, order] - valid = valid[order] - Q, _ = jnp.linalg.qr(B) - AQ = _apply_columns(A, Q) - H = jnp.matmul(Q.T, AQ, precision=_HIGHEST) - H = 0.5 * (H + H.T) - big = _sentinel(jnp.diag(H), valid, dtype) - mask = valid[:, None] & valid[None, :] - H = jnp.where(mask, H, 0.0) + jnp.diag(jnp.where(valid, 0.0, big)) - _, G = jnp.linalg.eigh(H) - U_next = jnp.matmul(Q, G[:, :rank], precision=_HIGHEST) - else: - # Free coefficient-tridiagonal route (no extra matvecs): cheaper, but - # window-only (no recycle-space augmentation, so it can starve when a - # deflated solve converges before the window refills) and its - # near-converged Ritz vectors can be polluted by orthogonality drift. - valid = idx < nvalid - d_ord = Tdiag[perm] - off_ord = Toff[perm] - big = _sentinel(d_ord, valid, dtype) - d_h = jnp.where(valid, d_ord, big) - off_h = jnp.where(idx < nvalid - 1, off_ord, jnp.zeros((), dtype)) - T = jnp.diag(d_h) + jnp.diag(off_h[: w - 1], 1) + jnp.diag(off_h[: w - 1], -1) - _, G = jnp.linalg.eigh(T) - U_raw = jnp.matmul(V_ord, G[:, :rank], precision=_HIGHEST) - U_next, _ = jnp.linalg.qr(U_raw) - return x_f, count, resid_norm, U_next - - -def deflated_pcg( - A, - b, - *, - U, - E_factor, - M=None, - x0=None, - tol=1e-5, - atol=0.0, - maxiter=None, - window=None, - rank=None, - reorthogonalize=True, - harvest=True, -): - """Two-level deflated PCG with an eigCG-style harvest of the next basis. - - Solves ``A y = b`` with a two-level additive preconditioner - ``M_defl(r) = P(r) + U (E^{-1} (U' r))`` (``P`` the first-level - preconditioner ``M``, ``U`` the carried deflation basis, ``E = U'A U`` - supplied pre-factored as ``E_factor``) started from a deflated, - warm-started initial guess, and harvests an orthonormal ``(m, rank)`` basis - from the CG Lanczos trace for the next solve. - - With ``U = 0`` the coarse correction and deflated init vanish exactly (the - ridge floor keeps ``E_factor`` finite while ``U' r = 0``), so the iterates - reduce bitwise to plain PCG with ``P`` -- the parity path of - :func:`recycled_cg`. - - Derivatives are implicit: the solution is wrapped in the same - ``lax.custom_linear_solve`` the parity path reuses (a second, differentiable - solve from zeros, deflation-accelerated by ``M_defl``, kept separate from the - harvest pass so higher-order AD stays correct), and the basis/harvest are - ``stop_gradient``'d. Callers must not differentiate through the harvest - directly. - - ``A`` is a hermitian positive-definite matvec callable (or square matrix) and - ``b`` the ``(m,)`` right-hand side. ``U`` is the ``(m, rank)`` deflation basis - (zeros for a cold start) and ``E_factor`` the ``cho_factor`` of the ridged - ``U'A U`` from :func:`build_coarse_operator`. ``M`` is the first-level - preconditioner ``P`` (``None`` is identity); ``x0`` the ``(m,)`` warm start - (previous dual solution; ``None`` is zeros). ``tol``/``atol`` are the relative - and absolute convergence tolerances on ``||b - A y||`` and ``maxiter`` the - iteration cap (``None`` uses ``10 * m``). - - ``rank`` (``k``, default ``U.shape[1]``) and ``window`` (``w``, default - ``max(2 * rank, rank + 4)``) are static shapes. ``reorthogonalize`` selects - the robust reorthonormalized ``Q'A Q`` harvest (vs the cheaper - coefficient-tridiagonal route). ``harvest=False`` (static) skips the - Rayleigh-Ritz / QR / extra matvecs and returns the carried ``U`` unchanged -- - for a right-hand side that shares the operator with an already harvested solve - (e.g. the geodesic-acceleration correction). - - Returns ``(y, harvest_state)`` with ``y`` the solution and ``harvest_state`` a - :class:`HarvestState`. - """ - Amv = _normalize_matvec(A) - P = _identity if M is None else _normalize_matvec(M) - dtype = b.dtype - m = b.shape[0] - k = U.shape[1] if rank is None else rank - w = window if window is not None else max(2 * k, k + 4) - if k <= 0: - raise ValueError(f"rank must be positive, got {k}") - if w < k: - raise ValueError(f"window ({w}) must be >= rank ({k})") - if k > m or w > m: - raise ValueError(f"rank ({k}) and window ({w}) must be <= problem size m ({m})") - if maxiter is None: - maxiter = 10 * m - tol = jnp.asarray(tol, dtype) - atol = jnp.asarray(atol, dtype) - - def M_defl(r): - c = jsp_linalg.cho_solve(E_factor, jnp.matmul(U.T, r, precision=_HIGHEST)) - return P(r) + jnp.matmul(U, c, precision=_HIGHEST) - - # Harvest pass: the augmented core solve (deflated + warm-started initial - # guess -- removes the range(U) component of the error, exact when U spans an - # invariant subspace, reduces to x0 when U = 0) produces the next basis and - # the velocity diagnostics. Skipped when harvest is off (the shared-operator - # RHS reuses the carried basis) so that solve costs only the differentiable - # pass below. - if harvest: - if x0 is None: - resid0 = b - warm = jnp.zeros(m, dtype) - else: - warm = x0 - resid0 = b - Amv(x0) - x_start = warm + jnp.matmul( - U, - jsp_linalg.cho_solve(E_factor, jnp.matmul(U.T, resid0, precision=_HIGHEST)), - precision=_HIGHEST, - ) - _, count, resid_norm, U_next = _deflated_pcg_core( - Amv, - b, - x_start, - M_defl, - U, - maxiter=maxiter, - tol=tol, - atol=atol, - window=w, - rank=k, - reorthogonalize=reorthogonalize, - harvest=True, - ) - else: - count = jnp.zeros((), jnp.int32) - resid_norm = jnp.zeros((), dtype) - U_next = U - - # Differentiable solution via the same custom_linear_solve wrapper the parity - # path reuses. Warm-started from zeros so the primal and every tangent / - # cotangent solve are correct-from-scratch (deflation-accelerated by M_defl): - # warm-starting at the harvested rough solution instead breaks higher-order AD - # (geodesic acceleration nests a jvp through the residual around this solve). - x_ws = jnp.zeros_like(b) - - def deflated_solve(matvec, rhs): - return _recycled_cg_solve( - matvec, rhs, x_ws, maxiter=maxiter, tol=tol, atol=atol, M=M_defl - ) - - y = lax.custom_linear_solve( - Amv, b, solve=deflated_solve, transpose_solve=deflated_solve, symmetric=True - ) - harvest_state = HarvestState( - basis=lax.stop_gradient(U_next), - iterations=lax.stop_gradient(count), - residual_norm=lax.stop_gradient(resid_norm), - ) - return y, harvest_state diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 9ed3a61..c5b9b46 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -36,7 +36,6 @@ ) from nlls_gram.lm_core import LevenbergMarquardtBase from nlls_gram.lm_types import ( - LMHyperparams, LMInfo, LMSolveAction, LMState, @@ -386,6 +385,12 @@ def __init__( raise ValueError("min_damping must be positive and at most init_damping") if max_damping is not None and max_damping < init_damping: raise ValueError("max_damping must be at least init_damping") + if getattr(linear_solver, "form", "normal") == "gram": + raise ValueError( + "Cholesky(form='gram') factors the dual J~J~', which never " + "sees the ridge penalty rows; the ridge objective needs the " + "normal form" + ) self.residual_fn = canonical_residual self.residual_arity = residual_arity self.metric = metric @@ -492,56 +497,6 @@ def __init__( ) self._static_hash = hash(self._static_key) - def hyperparams(self, dtype=None): - """``LMHyperparams`` built from the constructor values.""" - iterative_tol = self.iterative_tol - if iterative_tol is None: - # CG's tol=None: the _ad_cg_tol dtype-default convention. - resolved = jnp.result_type(float) if dtype is None else dtype - iterative_tol = 1e-10 if jnp.finfo(resolved).bits > 32 else 1e-6 - return LMHyperparams( - jnp.asarray(self.damping_decrease, dtype=dtype), - jnp.asarray(self.damping_increase, dtype=dtype), - _damping_floor(self.min_damping, dtype), - None - if self.max_damping is None - else jnp.asarray(self.max_damping, dtype=dtype), - jnp.asarray(self.geodesic_acceptance_ratio, dtype=dtype), - jnp.asarray(iterative_tol, dtype=dtype), - jnp.asarray(self.iterative_atol, dtype=dtype), - None - if self.iterative_maxiter is None - else jnp.asarray(self.iterative_maxiter, dtype=jnp.int32), - ) - - def _block_sizes(self, theta_size): - # The free-block size is inferred from the flattened iterate: the - # metric covers the leading metric.size coordinates, the rest is free. - n_f = theta_size - self.metric.size - if n_f < 0: - raise ValueError( - f"the metric covers {self.metric.size} leading coordinates " - f"but x flattens to only {theta_size}; the free block is " - "len(x) - metric.size and must be nonnegative" - ) - return self.metric.size, n_f - - # The solver-internal identity extension F_bar = blockdiag(F, I_{n_f}): - # the metric's factor op on the metric block, passthrough on the free - # block. Applied to vectors or leading-axis-batched matrices; F_bar - # itself is never materialized. - def _extended_solve(self, v, ctx): - n_m = self.metric.size - return jnp.concatenate( - [self.metric.factor_solve(v[:n_m], ctx), v[n_m:]], axis=0 - ) - - def _extended_solve_transpose(self, v, ctx): - n_m = self.metric.size - return jnp.concatenate( - [self.metric.factor_solve_transpose(v[:n_m], ctx), v[n_m:]], axis=0 - ) - def _resolve_ridge(self, dtype): if self.ridge is None: return jnp.asarray(jnp.sqrt(jnp.finfo(dtype).eps), dtype=dtype) @@ -586,61 +541,10 @@ def init(self, x0, args=None, *, p=None): Jt=jnp.zeros((p_dim, m), dtype=dtype), jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), aux=jax.tree.map(jnp.zeros_like, aux), - solver_cache=self.linear_solver.new_cache(m, p_dim, n_m, dtype), + solver_cache=self.linear_solver.new_cache(m, p_dim, n_m, dtype, True), **hooks, ) - def _hook_state(self, theta, lm_state, args, p): - """The metric's and preconditioner's prepared state for this step: - reused while still valid (a rejected step left ``x`` in place, or the - hook declined to rebuild), rebuilt from the live iterate otherwise.""" - bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) - metric_state = precond_state = None - if self._metric_prepares: - metric_state = jax.lax.cond( - lm_state.metric_valid | ~jnp.asarray(self.metric.rebuild(bare)), - lambda _: lm_state.metric_state, - lambda _: self.metric.prepare(theta, bare), - operand=None, - ) - if self._precond_prepares: - precond_state = jax.lax.cond( - lm_state.precond_valid - | ~jnp.asarray(self.preconditioner.rebuild(bare)), - lambda _: lm_state.precond, - lambda _: self.preconditioner.prepare(theta, bare), - operand=None, - ) - return metric_state, precond_state - - def _carried_ctx(self, theta, lm_state, args, p): - return SolverContext( - x=theta, - lm_state=lm_state, - args=args, - p=p, - metric_state=lm_state.metric_state, - preconditioner_state=lm_state.precond, - ) - - def _frozen_ctx(self, theta, lm_state, args, p, preconditioner): - # Under implicit AD the hooks are FROZEN at the returned solution: - # prepare runs once there and the state-dependence is not - # differentiated, the same contract as a fixed metric closing over - # constants. - bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) - metric_state = ( - self.metric.prepare(theta, bare) if self._metric_prepares else None - ) - precond_state = None - if preconditioner is not None and ( - type(preconditioner).prepare is not Preconditioner.prepare - ): - precond_state = preconditioner.prepare(theta, bare) - return dataclasses.replace( - bare, metric_state=metric_state, preconditioner_state=precond_state - ) - def _initial_info(self, x, lm_state, args, p): # grad_norm and penalty_grad_norm are +inf sentinels (computing them # would cost a Jacobian before the first step) and step_norm is zero; @@ -820,7 +724,7 @@ def first_jvp(th): ] f_vv = jax.jvp(first_jvp, (theta,), (velocity,))[1] - acceleration_sub = step_solver.solve(step_solver.accel_rhs(f_vv)) + acceleration_sub = step_solver.correction(f_vv) acceleration = jnp.asarray( self._extended_solve(acceleration_sub, ctx), dtype=resid.dtype ) @@ -1095,20 +999,6 @@ def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point) return self._ad_tangent_cholesky(x, args, p, p_dot, ridge, lm_state) return self._ad_tangent_normal_cg(x, args, p, p_dot, ridge, lm_state) - def _ad_linearization(self, x, args, p, p_dot): - theta, unravel = ravel_pytree(x) - - def residual_from_theta(theta_value): - return self._residual_and_aux(unravel(theta_value), args, p)[0] - - residual, theta_jvp = jax.linearize(residual_from_theta, theta) - - def residual_from_p(p_value): - return self._residual_and_aux(x, args, p_value)[0] - - residual_p_dot = jax.jvp(residual_from_p, (p,), (p_dot,))[1] - return theta, unravel, residual, theta_jvp, residual_p_dot - def _ad_tangent_cholesky(self, x, args, p, p_dot, ridge, lm_state): # The GN implicit rule posed on the whitened variable y = F_bar x: # (J~'J~ + ridge E) y_dot = -J~'(dr/dp) p_dot, then diff --git a/tests/test_ad_solver_methods.py b/tests/test_ad_solver_methods.py deleted file mode 100644 index 5e355cc..0000000 --- a/tests/test_ad_solver_methods.py +++ /dev/null @@ -1,150 +0,0 @@ -import jax -import jax.numpy as jnp -import pytest - -from nlls_gram import GramMetric, LevenbergMarquardt, identity_preconditioner - -A_SQUARE = jnp.array([[2.0, 1.0], [-1.0, 3.0]]) -P0 = jnp.array([1.0, -2.0]) -P_DOT = jnp.array([0.3, -0.7]) -X_BAR = jnp.array([0.4, -0.2]) - - -def square_residual(x, _, p): - return A_SQUARE @ x - p - - -def solved_x(solver, p): - return solver.solve(jnp.zeros(2), p=p, max_steps=40, atol=1e-6).x - - -@pytest.mark.parametrize("ad_solver", ["auto", "direct"]) -def test_square_direct_jvp_and_vjp_match_general_solve(ad_solver): - solver = LevenbergMarquardt(square_residual, ad_solver=ad_solver) - value, tangent = jax.jvp( - lambda p: solved_x(solver, p), - (P0,), - (P_DOT,), - ) - _, pullback = jax.vjp(lambda p: solved_x(solver, p), P0) - - assert solver._ad_solver_at(value, None, P0) == "direct" - assert jnp.allclose(value, jnp.linalg.solve(A_SQUARE, P0), atol=1e-6) - assert jnp.allclose(tangent, jnp.linalg.solve(A_SQUARE, P_DOT), atol=1e-6) - assert jnp.allclose( - pullback(X_BAR)[0], - jnp.linalg.solve(A_SQUARE.T, X_BAR), - atol=1e-6, - ) - - -def test_direct_supports_higher_order_ad(): - def residual(x, _, p): - return x**2 - p - - solver = LevenbergMarquardt(residual, ad_solver="direct") - - def root(p): - return solver.solve(jnp.ones(1), p=p, max_steps=40, atol=1e-6).x[0] - - p = jnp.asarray(4.0) - assert jnp.allclose(jax.grad(root)(p), 0.25, atol=1e-6) - assert jnp.allclose(jax.grad(jax.grad(root))(p), -0.03125, atol=1e-6) - - -def test_direct_rejects_non_square_system_at_trace_time(): - def residual(x, _, p): - return jnp.array([x[0] - p, 2.0 * x[0] - p]) - - solver = LevenbergMarquardt(residual, ad_solver="direct") - with pytest.raises(ValueError, match="requires a square residual Jacobian"): - jax.jvp( - lambda p: solver.solve(jnp.zeros(1), p=p, max_steps=40).x, - (jnp.asarray(1.0),), - (jnp.asarray(1.0),), - ) - - -def test_direct_singular_square_system_fails_loudly(): - matrix = jnp.array([[1.0, 0.0], [0.0, 0.0]]) - - def residual(x, _, p): - return matrix @ x - p - - solver = LevenbergMarquardt(residual, ad_solver="direct") - tangent = jax.jvp( - lambda p: solver.solve(jnp.zeros(2), p=p, max_steps=1, atol=0.0).x, - (jnp.zeros(2),), - (jnp.ones(2),), - )[1] - assert not jnp.all(jnp.isfinite(tangent)) - - -def test_auto_dispatches_by_shape_before_forward_solver(): - square_cg = LevenbergMarquardt( - square_residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ) - assert square_cg._ad_solver_at(jnp.zeros(2), None, P0) == "direct" - - def tall_residual(x, _, p): - return jnp.array([x[0] - p, 2.0 * x[0] - 2.0 * p]) - - tall_dense = LevenbergMarquardt(tall_residual) - tall_cg = LevenbergMarquardt( - tall_residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - ) - assert tall_dense._ad_solver_at(jnp.zeros(1), None, jnp.asarray(1.0)) == "svd" - assert tall_cg._ad_solver_at(jnp.zeros(1), None, jnp.asarray(1.0)) == "gram_cg" - - -def test_direct_does_not_require_metric_whitening_callbacks(): - metric = GramMetric(solve=lambda value: value) - solver = LevenbergMarquardt( - square_residual, - metric=metric, - linear_solver="gram_cholesky", - geodesic_acceleration=False, - ad_solver="direct", - ) - tangent = jax.jvp( - lambda p: solved_x(solver, p), - (P0,), - (P_DOT,), - )[1] - assert jnp.allclose(tangent, jnp.linalg.solve(A_SQUARE, P_DOT), atol=1e-6) - - -@pytest.mark.parametrize( - ("ad_solver", "penalty"), - [ - ("auto", 1e-6), - ("direct", 1e-6), - ("svd", 1e-6), - ("qr", 0.0), - ("gram_cg", 1e-6), - ("normal_cg", 1e-6), - ], -) -def test_penalty_does_not_select_an_ad_algorithm(ad_solver, penalty): - with pytest.raises(ValueError, match="accepted only"): - LevenbergMarquardt( - square_residual, - ad_solver=ad_solver, - ad_solver_penalty=penalty, - ) - - -@pytest.mark.parametrize("ad_solver", ["augmented_qr", "regularized_normal_cg"]) -@pytest.mark.parametrize("penalty", [None, 0.0, -1e-6]) -def test_regularized_ad_algorithms_require_positive_penalty(ad_solver, penalty): - with pytest.raises(ValueError, match="requires a positive"): - LevenbergMarquardt( - square_residual, - ad_solver=ad_solver, - ad_solver_penalty=penalty, - ) diff --git a/tests/test_augmented_qr.py b/tests/test_augmented_qr.py deleted file mode 100644 index bd2366f..0000000 --- a/tests/test_augmented_qr.py +++ /dev/null @@ -1,184 +0,0 @@ -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import pytest - -from nlls_gram import LevenbergMarquardt, LMStatus, metric_from_cholesky - - -def augmented_qr_solver(residual, *, has_aux=False): - return LevenbergMarquardt( - residual, - linear_solver="augmented_qr", - ad_solver="svd", - geodesic_acceleration=False, - cache_jacobian=False, - has_aux=has_aux, - ) - - -@pytest.mark.parametrize("use_metric", [False, True], ids=["identity", "cholesky"]) -def test_qr_tall_branch_step_matches_closed_form(use_metric): - # m = 3 > n = 2 takes the qr solver's tall sub-branch (the reduced QR of - # the n x m whitened transpose); the step must equal the damped whitened - # normal solution theta0 - S (B'B + lam I)^{-1} B' r with B = J S. - A = jnp.array([[1.0, 0.5], [0.3, 2.0], [-1.0, 1.0]]) - b = jnp.array([1.0, -2.0, 0.5]) - L = jnp.array([[1.3, 0.0], [0.5, 0.8]]) - lam = 1e-2 - - def residual(theta, args, p): - return A @ theta - b - - solver = LevenbergMarquardt( - residual, - init_damping=lam, - linear_solver="qr", - metric=metric_from_cholesky(L) if use_metric else None, - geodesic_acceleration=False, - ) - theta0 = jnp.array([0.4, -0.3]) - theta1, _, info = solver.update(theta0, solver.init(theta0)) - - S = ( - jsp_linalg.solve_triangular(L.T, jnp.eye(2), lower=False) - if use_metric - else jnp.eye(2) - ) - B = A @ S - r0 = A @ theta0 - b - u = jnp.linalg.solve(B.T @ B + lam * jnp.eye(2), -(B.T @ r0)) - assert bool(info.accepted) - assert jnp.allclose(theta1, theta0 + S @ u, atol=1e-5) - - -def test_nonlinear_algebraic_root_matches_closed_form(): - solver = augmented_qr_solver(lambda x, args, p: x**2 - p) - result = solver.solve(jnp.array([1.0]), p=jnp.asarray(4.0), max_steps=50, atol=1e-6) - - assert int(result.status) == LMStatus.CONVERGED - assert jnp.allclose(result.x, jnp.array([2.0]), atol=1e-5) - assert float(jnp.sqrt(result.info.loss)) < 1e-6 - - -def test_dae_style_pytree_root(): - def residual(z, args, p): - y, t, theta = p - return jnp.array([z["a"] + z["b"] - y * t, theta * z["a"] - z["b"]]) - - solver = augmented_qr_solver(residual) - y, t, theta = jnp.asarray(2.0), jnp.asarray(0.5), jnp.asarray(3.0) - result = solver.solve( - {"a": jnp.zeros(()), "b": jnp.zeros(())}, - p=(y, t, theta), - max_steps=50, - atol=1e-6, - ) - a_expected = y * t / (1.0 + theta) - - assert int(result.status) == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], a_expected, atol=1e-6) - assert jnp.allclose(result.x["b"], theta * a_expected, atol=1e-6) - - -def test_warm_start_at_root_exits_in_zero_steps(): - solver = augmented_qr_solver(lambda x, args, p: x**2 - p) - p = jnp.asarray(4.0) - first = solver.solve(jnp.array([1.0]), p=p, max_steps=50, atol=1e-6) - warm = solver.solve(first.x, p=p, max_steps=50, atol=1e-6) - - assert int(warm.status) == LMStatus.CONVERGED - assert int(warm.steps) == 0 - assert jnp.allclose(warm.x, first.x) - - -def test_jit_python_and_vmap_solve_paths_agree(): - W = 0.1 * jax.random.normal(jax.random.key(64), (3, 3)) - - def residual(z, _, p): - return z + jnp.tanh(W @ z) - p - - solver = augmented_qr_solver(residual) - ps = jax.random.normal(jax.random.key(65), (4, 3)) - z0 = jnp.zeros(3) - - compiled = solver.solve(z0, p=ps[0], max_steps=50, atol=1e-6) - eager = solver.solve(z0, p=ps[0], max_steps=50, atol=1e-6, jit=False) - batched = jax.vmap(lambda p: solver.solve(z0, p=p, max_steps=50, atol=1e-6))(ps) - - assert int(compiled.status) == int(eager.status) - assert int(compiled.steps) == int(eager.steps) - assert jnp.allclose(compiled.x, eager.x, atol=1e-6) - for i in range(ps.shape[0]): - lane = solver.solve(z0, p=ps[i], max_steps=50, atol=1e-6) - assert int(batched.status[i]) == int(lane.status) - assert jnp.allclose(batched.x[i], lane.x, atol=1e-5) - - -def test_linear_root_jvp_and_vjp_match_closed_form(): - A = jnp.array([[2.0, 0.5], [-0.3, 1.5]]) - B = jnp.array([[1.0, -0.5, 0.2], [0.3, 1.0, -0.7]]) - - def residual(x, _, p): - return A @ x - B @ p - - solver = augmented_qr_solver(residual) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=50, atol=1e-6).x - - p = jnp.array([1.0, -0.5, 0.25]) - p_dot = jnp.array([0.2, -0.1, 0.3]) - x_bar = jnp.array([0.7, -0.4]) - x, x_dot = jax.jvp(solved_x, (p,), (p_dot,)) - _, pullback = jax.vjp(solved_x, p) - (p_bar,) = pullback(x_bar) - - assert jnp.allclose(x, jnp.linalg.solve(A, B @ p), atol=1e-5) - assert jnp.allclose(x_dot, jnp.linalg.solve(A, B @ p_dot), atol=2e-5) - assert jnp.allclose(p_bar, B.T @ jnp.linalg.solve(A.T, x_bar), atol=2e-5) - assert jnp.allclose(x_dot @ x_bar, p_dot @ p_bar, atol=1e-6) - - -def test_second_order_derivatives_compose(): - solver = augmented_qr_solver(lambda x, args, p: x**2 - p) - - def scalar_root(p): - return solver.solve(jnp.array([1.0]), p=p, max_steps=60, atol=1e-7).x[0] - - p = jnp.asarray(4.0) - expected_second = -1.0 / (4.0 * p**1.5) - - assert jnp.allclose(jax.hessian(scalar_root)(p), expected_second, atol=1e-5) - assert jnp.allclose( - jax.jacrev(jax.jacfwd(scalar_root))(p), expected_second, atol=1e-5 - ) - - -def test_has_aux_reports_and_differentiates_aux(): - def residual(x, args, p): - return x**2 - p, {"scaled_root": x[0] * p} - - solver = augmented_qr_solver(residual, has_aux=True) - - def solved_aux(p): - return solver.solve(jnp.array([1.0]), p=p, max_steps=50, atol=1e-6).aux[ - "scaled_root" - ] - - p = jnp.asarray(4.0) - value, tangent = jax.jvp(solved_aux, (p,), (jnp.asarray(1.0),)) - - assert jnp.allclose(value, p * jnp.sqrt(p), atol=1e-4) - assert jnp.allclose(tangent, 1.5 * jnp.sqrt(p), atol=2e-5) - - -def test_solve_composes_inside_outer_jit(): - solver = augmented_qr_solver(lambda x, args, p: x**2 - p) - - @jax.jit - def stage(p): - root = solver.solve(jnp.array([1.0]), p=p, max_steps=50, atol=1e-6).x[0] - return root + p - - assert jnp.allclose(stage(jnp.asarray(4.0)), 6.0, atol=1e-5) diff --git a/tests/test_failed_implicit_ad.py b/tests/test_failed_implicit_ad.py index 69d9337..ae9a538 100644 --- a/tests/test_failed_implicit_ad.py +++ b/tests/test_failed_implicit_ad.py @@ -3,16 +3,38 @@ import pytest from nlls_gram import ( + SVD, + DiagonalMetric, + GramCG, + IdentityPreconditioner, LevenbergMarquardt, LMSolveAction, LMStatus, - MetricFactory, + Metric, MultiStart, - PreconditionerFactory, - metric_from_diagonal, ) +class AuxWeightedMetric(Metric): + """An iterate-dependent metric: the diagonal weights ride on prepare's + traced state, rebuilt from the live iterate and frozen at the solution + under implicit AD.""" + + size = 1 + + def prepare(self, theta, ctx): + return 1.0 + jnp.sqrt(jnp.abs(theta)) + + def factor_apply(self, v, ctx): + return jnp.sqrt(ctx.metric_state) * v + + def factor_solve(self, v, ctx): + return v / jnp.sqrt(ctx.metric_state) + + def factor_solve_transpose(self, v, ctx): + return self.factor_solve(v, ctx) + + def test_failed_lane_uses_initial_point_under_vmap_jvp_and_vjp(): def residual(x, _, p): return x - p @@ -63,20 +85,16 @@ def solve_one(parameter, atol): assert jnp.allclose(cotangent, jnp.asarray([1.0, 0.0]), atol=1e-6) -def test_invalid_failed_result_uses_initial_aux_for_metric_factory(): +def test_invalid_failed_result_uses_initial_point_for_a_prepared_metric(): def residual(x, _, p): root = jnp.sqrt(x) return root - p, {"weight": 1.0 + root} - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["weight"], - build=metric_from_diagonal, - ) solver = LevenbergMarquardt( residual, has_aux=True, - metric_factory=factory, - ad_solver="svd", + metric=AuxWeightedMetric(), + ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) @@ -117,15 +135,10 @@ def residual(x, _, p): value = jnp.asarray([jnp.sum(x) - p]) return value, {"scale": 1.0 + 0.1 * jnp.sum(x**2)} - factory = PreconditionerFactory( - prepare=lambda x, args, p, aux: aux["scale"], - apply=lambda state, value, damping: value / (state + damping), - ) solver = LevenbergMarquardt( residual, has_aux=True, - linear_solver="gram_cg", - preconditioner_factory=factory, + linear_solver=GramCG(IdentityPreconditioner(), maxiter=8), cache_jacobian=False, geodesic_acceleration=False, ) @@ -235,8 +248,8 @@ def residual(x, _, p): solver = LevenbergMarquardt( residual, - metric=metric_from_diagonal(jnp.asarray([2.0, 3.0])), - ad_solver="svd", + metric=DiagonalMetric(jnp.asarray([2.0, 3.0])), + ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) @@ -263,14 +276,10 @@ def residual(x, _, p): jax.debug.callback(lambda _: calls.append(None), x, ordered=True) return x - p, {"value": x + p} - factory = MetricFactory( - prepare=lambda x, args, p, aux: jnp.ones_like(x), - build=metric_from_diagonal, - ) solver = LevenbergMarquardt( residual, has_aux=True, - metric_factory=factory, + metric=DiagonalMetric(jnp.ones(1)), cache_jacobian=False, geodesic_acceleration=False, ) diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index 7269b17..25bf3a5 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -3,746 +3,6 @@ import textwrap -def test_float64_plain_and_nnx_paths_do_not_use_float32(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp -from flax import nnx - -from nlls_gram import ( - LevenbergMarquardt, - identity_preconditioner, - nystrom_preconditioner, -) - - -def assert_float64_tree(tree): - leaves = jax.tree.leaves(tree) - assert leaves - for leaf in leaves: - assert leaf.dtype == jnp.float64, (leaf.dtype, leaf) - - -def residual_fn(x, args, p): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -ts = jnp.linspace(0.0, 2.0, 20, dtype=jnp.float64) -ys = 2.0 * jnp.exp(-1.0 * ts) -x = { - "a": jnp.asarray(1.0, dtype=jnp.float64), - "b": jnp.asarray(0.0, dtype=jnp.float64), -} -solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) -lm_state = solver.init(x, (ts, ys)) -for _ in range(5): - x, lm_state, info = solver.update(x, lm_state, (ts, ys)) - -assert_float64_tree(x) -assert lm_state.damping.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -assert info.loss_old.dtype == jnp.float64 -assert info.loss_candidate.dtype == jnp.float64 -assert info.damping.dtype == jnp.float64 -assert info.damping_factor.dtype == jnp.float64 -assert info.acceleration_ratio.dtype == jnp.float64 -assert info.grad_norm.dtype == jnp.float64 -assert info.step_norm.dtype == jnp.float64 -jaxpr = str(jax.make_jaxpr(lambda p, s: solver.update(p, s, (ts, ys)))(x, lm_state)) -assert "f32" not in jaxpr, jaxpr -solve_jaxpr = str( - jax.make_jaxpr( - lambda p: solver.solve( - p, (ts, ys), max_steps=20, atol=1e-8, gtol=1e-10, xtol=1e-10 - ).x - )(x) -) -assert "f32" not in solve_jaxpr, solve_jaxpr - - -def quadratic_residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - -theta = jnp.asarray([1.9], dtype=jnp.float64) -target = jnp.asarray(4.0, dtype=jnp.float64) -solver = LevenbergMarquardt( - quadratic_residual, - init_damping=1e-12, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, -) -lm_state = solver.init(theta, target) -theta, lm_state, info = solver.update(theta, lm_state, target) - -assert theta.dtype == jnp.float64 -assert lm_state.damping.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -assert info.loss_old.dtype == jnp.float64 -assert info.loss_candidate.dtype == jnp.float64 -assert info.damping.dtype == jnp.float64 -assert info.damping_factor.dtype == jnp.float64 -assert info.acceleration_ratio.dtype == jnp.float64 -assert info.grad_norm.dtype == jnp.float64 -assert info.step_norm.dtype == jnp.float64 -jaxpr = str(jax.make_jaxpr(lambda p, s: solver.update(p, s, target))(theta, lm_state)) -assert "f32" not in jaxpr, jaxpr -solve_jaxpr = str( - jax.make_jaxpr( - lambda p: solver.solve(p, target, max_steps=20, atol=1e-10).x - )(theta) -) -assert "f32" not in solve_jaxpr, solve_jaxpr - - -def linear_residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - -matrix = jnp.asarray([[1.0, 2.0], [3.0, -1.0], [2.0, 0.5]], dtype=jnp.float64) -target = jnp.asarray([1.0, 2.0, -1.0], dtype=jnp.float64) -theta = jnp.asarray([0.0, 0.0], dtype=jnp.float64) -solver = LevenbergMarquardt( - linear_residual, - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-10, - iterative_maxiter=20, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), -) -lm_state = solver.init(theta, (matrix, target)) -theta, lm_state, info = solver.update(theta, lm_state, (matrix, target)) - -assert theta.dtype == jnp.float64 -assert lm_state.damping.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -assert info.loss_old.dtype == jnp.float64 -assert info.loss_candidate.dtype == jnp.float64 -assert info.damping.dtype == jnp.float64 -assert info.damping_factor.dtype == jnp.float64 -assert info.acceleration_ratio.dtype == jnp.float64 -assert info.grad_norm.dtype == jnp.float64 -assert info.step_norm.dtype == jnp.float64 -jaxpr = str( - jax.make_jaxpr(lambda p, s: solver.update(p, s, (matrix, target)))(theta, lm_state) -) -assert "f32" not in jaxpr, jaxpr - - -matrix = jnp.asarray( - [[1.0, 2.0, 0.5, -1.0], [0.0, 1.0, 3.0, 2.0]], - dtype=jnp.float64, -) -target = jnp.asarray([1.0, -2.0], dtype=jnp.float64) -theta = jnp.zeros(matrix.shape[1], dtype=jnp.float64) -solver = LevenbergMarquardt( - linear_residual, - init_damping=1e-2, - linear_solver="qr", -) -lm_state = solver.init(theta, (matrix, target)) -theta, lm_state, info = solver.update(theta, lm_state, (matrix, target)) - -assert theta.dtype == jnp.float64 -assert lm_state.damping.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -assert info.loss_old.dtype == jnp.float64 -assert info.loss_candidate.dtype == jnp.float64 -assert info.damping.dtype == jnp.float64 -assert info.damping_factor.dtype == jnp.float64 -assert info.acceleration_ratio.dtype == jnp.float64 -assert info.grad_norm.dtype == jnp.float64 -assert info.step_norm.dtype == jnp.float64 -jaxpr = str( - jax.make_jaxpr(lambda p, s: solver.update(p, s, (matrix, target)))(theta, lm_state) -) -assert "f32" not in jaxpr, jaxpr - - -# Nystrom build + apply traced end to end: the sketch, Cholesky, and SVD must -# all stay float64. -n_dual = 6 -G_psd = jax.random.normal(jax.random.PRNGKey(0), (n_dual, n_dual), dtype=jnp.float64) -A_psd = G_psd @ G_psd.T + jnp.eye(n_dual) - - -def build_and_apply(A, v): - preconditioner = nystrom_preconditioner( - lambda X: A @ X, n_dual, n_dual, jax.random.PRNGKey(1) - ) - return preconditioner(v, jnp.asarray(1e-3, v.dtype)) - - -v_dual = jnp.ones(n_dual, dtype=jnp.float64) -assert build_and_apply(A_psd, v_dual).dtype == jnp.float64 -jaxpr = str(jax.make_jaxpr(build_and_apply)(A_psd, v_dual)) -assert "f32" not in jaxpr, jaxpr - -# An explicit float32 dtype stays float32 even with x64 enabled. -pre32 = nystrom_preconditioner( - lambda X: A_psd.astype(jnp.float32) @ X, - n_dual, - 3, - jax.random.PRNGKey(2), - dtype=jnp.float32, -) -assert pre32(jnp.ones(n_dual, jnp.float32), jnp.float32(0.5)).dtype == jnp.float32 - -# A cg solver whose dual preconditioner is a (float64) Nystrom sketch of -# J J' keeps the whole update float64. -solver = LevenbergMarquardt( - linear_residual, - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-10, - iterative_maxiter=20, - dual_preconditioner=nystrom_preconditioner( - lambda V: matrix @ (matrix.T @ V), - matrix.shape[0], - matrix.shape[0], - jax.random.PRNGKey(3), - ), - ad_solver_preconditioner=identity_preconditioner(), -) -lm_state = solver.init(theta, (matrix, target)) -theta_nystrom, lm_state, info = solver.update(theta, lm_state, (matrix, target)) - -assert theta_nystrom.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -jaxpr = str( - jax.make_jaxpr(lambda p, s: solver.update(p, s, (matrix, target)))(theta, lm_state) -) -assert "f32" not in jaxpr, jaxpr - - -class LinearModel(nnx.Module): - def __init__(self): - self.linear = nnx.Linear( - 1, - 1, - use_bias=False, - dtype=jnp.float64, - param_dtype=jnp.float64, - rngs=nnx.Rngs(0), - ) - - def __call__(self, x): - return jnp.ravel(self.linear(x)) - - -model = LinearModel() -graphdef, nnx_params = nnx.split(model, nnx.Param) -assert_float64_tree(nnx_params) - -x_nnx = jnp.linspace(0.0, 2.0, 20, dtype=jnp.float64).reshape(-1, 1) -y_nnx = 2.0 * jnp.ravel(x_nnx) - - -def nnx_residual_fn(x, args, p): - ts, ys = args - model = nnx.merge(graphdef, x) - return model(ts) - ys - - -solver = LevenbergMarquardt(nnx_residual_fn, init_damping=1e-12) -lm_state = solver.init(nnx_params, (x_nnx, y_nnx)) -nnx_params, lm_state, info = solver.update(nnx_params, lm_state, (x_nnx, y_nnx)) -trained = nnx.merge(graphdef, nnx_params) - -assert_float64_tree(nnx_params) -assert trained.linear.kernel[...].dtype == jnp.float64 -assert jnp.allclose(trained.linear.kernel[...], jnp.asarray([[2.0]], dtype=jnp.float64)) -assert lm_state.damping.dtype == jnp.float64 -assert info.loss.dtype == jnp.float64 -assert info.loss_old.dtype == jnp.float64 -assert info.loss_candidate.dtype == jnp.float64 -assert info.damping.dtype == jnp.float64 -assert info.damping_factor.dtype == jnp.float64 -assert info.acceleration_ratio.dtype == jnp.float64 -assert info.grad_norm.dtype == jnp.float64 -assert info.step_norm.dtype == jnp.float64 -jaxpr = str( - jax.make_jaxpr(lambda p, s: solver.update(p, s, (x_nnx, y_nnx)))( - nnx_params, lm_state - ) -) -assert "f32" not in jaxpr, jaxpr -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_linear_solve_dtype_promotes_dense_dual_solve(): - # A 1e-7 metric weight injects a 1/eps spike into the dual, driving - # cond(J P J') ~ 1e7: the float32 cholesky paths lose the step and the - # implicit derivative, while linear_solve_dtype=jnp.float64 recovers the - # float64 reference on the SAME float32-representable data to ~1e-6, - # with every output still float32. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import LevenbergMarquardt, metric_from_diagonal - -n, m, eps = 12, 4, 1e-7 -A32 = jax.random.normal(jax.random.PRNGKey(0), (m, n), dtype=jnp.float32) -b32 = jax.random.normal(jax.random.PRNGKey(1), (m,), dtype=jnp.float32) -w32 = jnp.concatenate([jnp.array([eps], jnp.float32), jnp.ones(n - 1, jnp.float32)]) -# The reference solves the SAME problem (float32 values are exactly -# representable in float64), isolating solve error from data rounding. -A64, b64, w64 = (v.astype(jnp.float64) for v in (A32, b32, w32)) - - -def make(matrix, target, weights, dual_dtype): - def residual(theta, _, p): - return matrix @ theta - p * target - - return LevenbergMarquardt( - residual, - init_damping=1e-3, - metric=metric_from_diagonal(weights), - geodesic_acceleration=False, - linear_solve_dtype=dual_dtype, - ) - - -plain32 = make(A32, b32, w32, None) -promoted = make(A32, b32, w32, jnp.float64) -reference = make(A64, b64, w64, None) -p32, p64 = jnp.float32(1.0), jnp.float64(1.0) -t032, t064 = jnp.zeros(n, jnp.float32), jnp.zeros(n, jnp.float64) - - -def rel(value, ref): - difference = value.astype(jnp.float64) - ref - return float(jnp.linalg.norm(difference) / jnp.linalg.norm(ref)) - - -# Forward step. -x_plain = plain32.update(t032, plain32.init(t032, p=p32), p=p32)[0] -x_promoted = promoted.update(t032, promoted.init(t032, p=p32), p=p32)[0] -x_reference = reference.update(t064, reference.init(t064, p=p64), p=p64)[0] -assert x_promoted.dtype == jnp.float32 -assert rel(x_promoted, x_reference) < 1e-6, rel(x_promoted, x_reference) -assert rel(x_plain, x_reference) > 1e-3, rel(x_plain, x_reference) - - -# Implicit JVP and VJP through the (auto-resolved) dense implicit rule. -def solved_x(solver, theta0, p_value): - return solver.solve(theta0, p=p_value, max_steps=80, atol=0.0, gtol=1e-5).x - - -def tangent(solver, theta0, p_value): - return jax.jvp( - lambda q: solved_x(solver, theta0, q), - (p_value,), - (jnp.ones((), p_value.dtype),), - )[1] - - -t_promoted = tangent(promoted, t032, p32) -t_reference = tangent(reference, t064, p64) -assert t_promoted.dtype == jnp.float32 -assert rel(t_promoted, t_reference) < 1e-6, rel(t_promoted, t_reference) -# Unlike the forward step (whose float32 cholesky forms B'B and pays the -# squared-assembly floor, > 1e-3 above), the SVD AD method factors B itself: -# the UNPROMOTED float32 tangent already tracks the float64 reference on -# this cond ~ 1e3 fixture (measured 3.9e-7), so promotion is a no-op here. -assert rel(tangent(plain32, t032, p32), t_reference) < 1e-5 - - -def summed_gradient(solver, theta0, p_value): - return jax.grad(lambda q: jnp.sum(solved_x(solver, theta0, q)))(p_value) - - -g_promoted = float(summed_gradient(promoted, t032, p32)) -g_reference = float(summed_gradient(reference, t064, p64)) -g_plain = float(summed_gradient(plain32, t032, p32)) -assert abs(g_promoted - g_reference) / abs(g_reference) < 1e-5 -# Same cond(B)-not-cond(B)^2 story in reverse mode (measured 1.1e-6). -assert abs(g_plain - g_reference) / abs(g_reference) < 1e-4 - - -# On a well-conditioned problem the flag changes nothing beyond float32 -# rounding, and the qr-forward + dense-implicit consumer combination is -# accepted. -well = jnp.ones(n, jnp.float32) -plain_well = make(A32, b32, well, None) -promoted_well = make(A32, b32, well, jnp.float64) -x_plain_well = plain_well.update(t032, plain_well.init(t032, p=p32), p=p32)[0] -x_promoted_well = promoted_well.update( - t032, promoted_well.init(t032, p=p32), p=p32 -)[0] -assert jnp.allclose(x_promoted_well, x_plain_well, rtol=1e-5, atol=1e-6) - -qr_dense_implicit = LevenbergMarquardt( - lambda theta, _, p: A32 @ theta - p * b32, - linear_solver="qr", - geodesic_acceleration=False, - linear_solve_dtype=jnp.float64, -) -qr_tangent = tangent(qr_dense_implicit, t032, p32) -assert qr_tangent.dtype == jnp.float32 -assert bool(jnp.all(jnp.isfinite(qr_tangent))) - - -# Geodesic acceleration reuses the promoted solve_step: a nonlinear promoted -# update matches the float64 reference, and the diagnostics stay float32. -def make_geodesic(matrix, target, weights, dual_dtype): - def residual(theta, _, p): - linear = matrix @ theta - return linear + 0.05 * linear**2 - p * target - - return LevenbergMarquardt( - residual, - init_damping=1e-3, - metric=metric_from_diagonal(weights), - geodesic_acceleration=True, - geodesic_acceptance_ratio=10.0, - linear_solve_dtype=dual_dtype, - ) - - -geo_promoted = make_geodesic(A32, b32, w32, jnp.float64) -geo_reference = make_geodesic(A64, b64, w64, None) -xg_promoted, _, info_promoted = geo_promoted.update( - t032, geo_promoted.init(t032, p=p32), p=p32 -) -xg_reference, _, info_reference = geo_reference.update( - t064, geo_reference.init(t064, p=p64), p=p64 -) -assert xg_promoted.dtype == jnp.float32 -assert info_promoted.acceleration_ratio.dtype == jnp.float32 -assert bool(info_promoted.used_geodesic) == bool(info_reference.used_geodesic) -assert rel(xg_promoted, xg_reference) < 1e-5, rel(xg_promoted, xg_reference) - - -# Direct differentiation THROUGH update (no implicit rule) on the promoted -# path stays valid in both modes and matches the float64 reference. -def update_x(solver, theta0, p_value): - return solver.update(theta0, solver.init(theta0, p=p_value), p=p_value)[0] - - -_, u_dot_promoted = jax.jvp( - lambda q: update_x(promoted, t032, q), (p32,), (jnp.float32(1.0),) -) -_, u_dot_reference = jax.jvp( - lambda q: update_x(reference, t064, q), (p64,), (jnp.float64(1.0),) -) -assert u_dot_promoted.dtype == jnp.float32 -assert rel(u_dot_promoted, u_dot_reference) < 1e-5, rel(u_dot_promoted, u_dot_reference) - -_, pull_promoted = jax.vjp(lambda q: update_x(promoted, t032, q), p32) -_, pull_reference = jax.vjp(lambda q: update_x(reference, t064, q), p64) -cotangent_promoted = float(pull_promoted(jnp.ones(n, jnp.float32))[0]) -cotangent_reference = float(pull_reference(jnp.ones(n, jnp.float64))[0]) -assert abs(cotangent_promoted - cotangent_reference) / abs(cotangent_reference) < 1e-5 -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_linear_solve_dtype_normal_forms_and_metric_solve_dtype_jaxpr(): - # The normal-form twin of the promoted-dual test. A metric spike does NOT - # stress this form (the graded B'B factors its huge pivot first, stably), - # so the float32 fragility is driven the way it actually arises: columns - # with cond(A) ~ 1e3 square to cond(B'B) ~ 1e6, and the solution's - # small-singular-direction components lose eps32 * cond^2 ~ O(0.1) while - # linear_solve_dtype=jnp.float64 recovers the float64 reference on the - # SAME float32-representable data, with float32 outputs. Then the jaxpr - # policy: float64 problems stay f32-free through the normal forward and - # implicit paths, and metric_solve_dtype injects f64 casts into an - # otherwise-f32 update. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import ( - LevenbergMarquardt, - identity_preconditioner, - metric_from_cholesky, -) - -m, n = 12, 4 -U, _ = jnp.linalg.qr(jax.random.normal(jax.random.PRNGKey(0), (m, n))) -V, _ = jnp.linalg.qr(jax.random.normal(jax.random.PRNGKey(1), (n, n))) -A32 = ((U * jnp.logspace(0.0, -3.0, n)) @ V.T).astype(jnp.float32) -b32 = (A32.astype(jnp.float64) @ jnp.arange(1.0, n + 1.0)).astype(jnp.float32) -A64, b64 = A32.astype(jnp.float64), b32.astype(jnp.float64) - - -def make(matrix, target, solve_dtype): - def residual(theta, _, p): - return matrix @ theta - p * target - - return LevenbergMarquardt( - residual, - init_damping=1e-8, - linear_solver="normal_cholesky", - geodesic_acceleration=False, - linear_solve_dtype=solve_dtype, - ) - - -plain32 = make(A32, b32, None) -promoted = make(A32, b32, jnp.float64) -reference = make(A64, b64, None) -p32, p64 = jnp.float32(1.0), jnp.float64(1.0) -t032, t064 = jnp.zeros(n, jnp.float32), jnp.zeros(n, jnp.float64) - - -def rel(value, ref): - difference = value.astype(jnp.float64) - ref - return float(jnp.linalg.norm(difference) / jnp.linalg.norm(ref)) - - -x_plain = plain32.update(t032, plain32.init(t032, p=p32), p=p32)[0] -x_promoted = promoted.update(t032, promoted.init(t032, p=p32), p=p32)[0] -x_reference = reference.update(t064, reference.init(t064, p=p64), p=p64)[0] -assert x_promoted.dtype == jnp.float32 -assert rel(x_promoted, x_reference) < 1e-6, rel(x_promoted, x_reference) -assert rel(x_plain, x_reference) > 1e-3, rel(x_plain, x_reference) - - -def tangent(solver, theta0, p_value): - return jax.jvp( - lambda q: solver.solve(theta0, p=q, max_steps=80, atol=0.0, gtol=1e-5).x, - (p_value,), - (jnp.ones((), p_value.dtype),), - )[1] - - -t_promoted = tangent(promoted, t032, p32) -t_reference = tangent(reference, t064, p64) -assert t_promoted.dtype == jnp.float32 -assert rel(t_promoted, t_reference) < 1e-6, rel(t_promoted, t_reference) -# The default spectral-filter (eigh) implicit is sturdier in float32 than the -# forward Cholesky, so its degradation is milder -- measured ~6e-4 here. -assert rel(tangent(plain32, t032, p32), t_reference) > 1e-4 - - -# jaxpr policy on float64 data: no f32 anywhere through the normal forward -# paths or the normal-resolved implicit tangents. -def residual64(theta, _, p): - return A64 @ theta - p * b64 - - -normal_dense = LevenbergMarquardt( - residual64, - init_damping=1e-3, - linear_solver="normal_cholesky", - geodesic_acceleration=False, -) -state64 = normal_dense.init(t064, p=p64) -jaxpr = str( - jax.make_jaxpr(lambda th, s, q: normal_dense.update(th, s, p=q))( - t064, state64, p64 - ) -) -assert "f32" not in jaxpr, jaxpr - -normal_cg = LevenbergMarquardt( - residual64, - init_damping=1e-3, - linear_solver="normal_cg", - normal_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-10, - iterative_maxiter=30, - geodesic_acceleration=False, -) -state_cg = normal_cg.init(t064, p=p64) -jaxpr = str( - jax.make_jaxpr(lambda th, s, q: normal_cg.update(th, s, p=q))( - t064, state_cg, p64 - ) -) -assert "f32" not in jaxpr, jaxpr - -for solver in (normal_dense, normal_cg): - jaxpr = str(jax.make_jaxpr(lambda q: tangent(solver, t064, q))(p64)) - assert "f32" not in jaxpr, jaxpr - -implicit_normal_cg = LevenbergMarquardt( - residual64, - init_damping=1e-3, - linear_solver="normal_cholesky", - ad_solver="normal_cg", - ad_solver_preconditioner=identity_preconditioner(), - ad_solver_maxiter=30, - geodesic_acceleration=False, -) -jaxpr = str(jax.make_jaxpr(lambda q: tangent(implicit_normal_cg, t064, q))(p64)) -assert "f32" not in jaxpr, jaxpr - - -# metric_solve_dtype on a float32 problem: the update jaxpr gains f64 casts -# around the metric callbacks (absent without the knob) while every output -# stays float32. -L32 = jnp.array([[1.3, 0.0], [0.5, 0.8]], dtype=jnp.float32) -A_t32 = jnp.array([[1.0, 0.5], [0.3, 2.0], [-1.0, 1.0]], dtype=jnp.float32) -b_t32 = jnp.array([1.0, -2.0, 0.5], dtype=jnp.float32) -t02 = jnp.zeros(2, jnp.float32) - - -def residual32(theta, _, p): - return A_t32 @ theta - p * b_t32 - - -def make_metric_solver(solve_dtype): - return LevenbergMarquardt( - residual32, - init_damping=1e-3, - linear_solver="normal_cholesky", - metric=metric_from_cholesky(L32), - metric_solve_dtype=solve_dtype, - geodesic_acceleration=False, - ) - - -wide_metric = make_metric_solver(jnp.float64) -plain_metric = make_metric_solver(None) -state32 = wide_metric.init(t02, p=jnp.float32(1.0)) -jaxpr_wide = str( - jax.make_jaxpr(lambda th, s, q: wide_metric.update(th, s, p=q))( - t02, state32, jnp.float32(1.0) - ) -) -jaxpr_plain = str( - jax.make_jaxpr(lambda th, s, q: plain_metric.update(th, s, p=q))( - t02, plain_metric.init(t02, p=jnp.float32(1.0)), jnp.float32(1.0) - ) -) -assert "f64" in jaxpr_wide, jaxpr_wide -assert "f64" not in jaxpr_plain, jaxpr_plain -x1, state1, info1 = wide_metric.update(t02, state32, p=jnp.float32(1.0)) -assert x1.dtype == jnp.float32 -assert state1.damping.dtype == jnp.float32 -assert info1.loss.dtype == jnp.float32 -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_augmented_qr_float64_and_dtype_policy(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import LMStatus, LevenbergMarquardt - -W = 0.1 * jax.random.normal(jax.random.PRNGKey(0), (3, 3), dtype=jnp.float64) - - -def residual(z, args, p): - return z + jnp.tanh(W @ z) - p - - -solver = LevenbergMarquardt( - residual, - linear_solver="augmented_qr", - ad_solver="svd", - geodesic_acceleration=False, - cache_jacobian=False, -) -p = jax.random.normal(jax.random.PRNGKey(1), (3,), dtype=jnp.float64) -result = solver.solve( - jnp.zeros(3, dtype=jnp.float64), p=p, max_steps=50, atol=1e-10 -) - -assert int(result.status) == LMStatus.CONVERGED -assert result.x.dtype == jnp.float64 -assert result.info.loss.dtype == jnp.float64 -assert float(jnp.sqrt(result.info.loss)) < 1e-10 - -jaxpr = str( - jax.make_jaxpr( - lambda q: solver.solve( - jnp.zeros(3, dtype=jnp.float64), p=q, max_steps=50, atol=1e-10 - ).x - )(p) -) -assert "f32" not in jaxpr, jaxpr - -jvp_jaxpr = str( - jax.make_jaxpr( - lambda q, q_dot: jax.jvp( - lambda r: solver.solve( - jnp.zeros(3, dtype=jnp.float64), p=r, max_steps=50, atol=1e-10 - ).x, - (q,), - (q_dot,), - )[1] - )(p, p) -) -assert "f32" not in jvp_jaxpr, jvp_jaxpr - -x, x_dot = jax.jvp( - lambda q: solver.solve( - jnp.zeros(3, dtype=jnp.float64), p=q, max_steps=50, atol=1e-10 - ).x, - (p,), - (jnp.ones(3, dtype=jnp.float64),), -) -assert x.dtype == jnp.float64 and x_dot.dtype == jnp.float64 -J = jax.jacfwd(lambda z: residual(z, None, p))(x) -assert jnp.allclose(x_dot, jnp.linalg.solve(J, jnp.ones(3)), atol=1e-10) - -# A float32 problem under enabled x64 stays float32. -W32 = W.astype(jnp.float32) - - -def residual32(z, args, p): - return z + jnp.tanh(W32 @ z) - p - - -solver32 = LevenbergMarquardt( - residual32, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, -) -result32 = solver32.solve( - jnp.zeros(3, dtype=jnp.float32), - p=p.astype(jnp.float32), - max_steps=50, - atol=1e-6, -) -assert int(result32.status) == LMStatus.CONVERGED -assert result32.x.dtype == jnp.float32 -assert result32.info.loss.dtype == jnp.float32 -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - def test_failed_implicit_ad_float64_is_finite_and_exactly_zero(): script = r""" import jax @@ -825,288 +85,6 @@ def solved_x(values): assert result.returncode == 0, result.stderr + result.stdout -def test_repeated_shifted_state_space_float64_parallel_matches_sequential(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg - -from nlls_gram import ( - matern_state_space, - repeated_shifted_state_space_metric, -) - - -def rel(a, b): - return float(jnp.linalg.norm(jnp.ravel(a - b)) / jnp.linalg.norm(jnp.ravel(a))) - - -n, repeats, zero_pad_size = 3000, 3, 2 -sigma, ell, epsilon = 1.3, 0.8, 1e-8 -well = jnp.cumsum( - jax.random.uniform(jax.random.PRNGKey(2), (n,), minval=0.6, maxval=1.4) -) -stiff = jnp.linspace(0.0, 5.0, n) -total = repeats * n + zero_pad_size -x = jax.random.normal(jax.random.PRNGKey(0), (total,)) -X = jax.random.normal(jax.random.PRNGKey(1), (total, 3)) - -for (name, t), tol in ((("well", well), 1e-12), (("stiff", stiff), 1e-6)): - for nu in (0.5, 1.5, 2.5): - model = matern_state_space(sigma, ell, nu) - seq = repeated_shifted_state_space_metric( - t, - *model, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - parallel=False, - ) - par = repeated_shifted_state_space_metric( - t, - *model, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - parallel=True, - ) - for callback in ("solve", "norm", "inv_sqrt", "inv_sqrt_transpose"): - a = getattr(seq, callback)(x) - b = getattr(par, callback)(x) - assert bool(jnp.all(jnp.isfinite(b))), (name, nu, callback) - assert rel(a, b) < tol, (name, nu, callback, rel(a, b)) - assert rel(seq.solve(X), par.solve(X)) < tol, (name, nu, "matrix") - - -def dense_matern_gram(t, sigma, ell): - tau = jnp.abs(t[:, None] - t[None, :]) - ft = jnp.sqrt(3.0) * tau / ell - return sigma**2 * (1.0 + ft) * jnp.exp(-ft) - - -n, repeats, zero_pad_size = 150, 2, 1 -t = jnp.cumsum( - jax.random.uniform(jax.random.PRNGKey(3), (n,), minval=0.6, maxval=1.4) -) -v = jax.random.normal(jax.random.PRNGKey(4), (repeats * n + zero_pad_size,)) - - -def structured_loss(params): - sigma, ell, epsilon = params - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma, ell, 1.5), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - return v @ metric.solve(v) + metric.norm(v) - - -def dense_loss(params): - sigma, ell, epsilon = params - K = dense_matern_gram(t, sigma, ell) - blocks = [K + epsilon * jnp.eye(n)] * repeats - blocks.append(epsilon * jnp.eye(zero_pad_size)) - M = jsp_linalg.block_diag(*blocks) - return v @ jnp.linalg.solve(M, v) + jnp.sqrt(v @ M @ v) - - -params = jnp.array([1.3, 0.8, 1e-4]) -grad_structured = jax.jit(jax.grad(structured_loss))(params) -grad_dense = jax.grad(dense_loss)(params) -assert rel(grad_dense, grad_structured) < 1e-9 - -sigma, ell, epsilon = params -metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma, ell, 1.5), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - parallel=False, -) -K = dense_matern_gram(t, sigma, ell) -blocks = [K + epsilon * jnp.eye(n)] * repeats -blocks.append(epsilon * jnp.eye(zero_pad_size)) -M = jsp_linalg.block_diag(*blocks) -total = M.shape[0] -x = jax.random.normal(jax.random.PRNGKey(5), (total,)) -X = jax.random.normal(jax.random.PRNGKey(6), (total, 3)) -assert rel(jnp.linalg.solve(M, x), metric.solve(x)) < 1e-9 -assert rel(jnp.linalg.solve(M, X), metric.solve(X)) < 1e-9 -assert rel(jnp.sqrt(x @ M @ x), metric.norm(x)) < 1e-10 -S = metric.inv_sqrt(jnp.eye(total)) -assert rel(jnp.linalg.inv(M), S @ S.T) < 1e-9 -assert rel(S.T, metric.inv_sqrt_transpose(jnp.eye(total))) < 1e-10 - -for callback in ("solve", "norm", "inv_sqrt", "inv_sqrt_transpose"): - value = x if callback == "norm" else X - shapes = [ - constant.shape - for constant in jax.make_jaxpr(getattr(metric, callback))(value).consts - ] - assert (n, n) not in shapes, (callback, shapes) - assert (total, total) not in shapes, (callback, shapes) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_repeated_shifted_dense_metric_float64_matches_explicit_matrix(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg - -from nlls_gram import repeated_shifted_dense_metric - - -def rel(a, b): - denominator = jnp.maximum(jnp.linalg.norm(jnp.ravel(a)), 1.0) - return float(jnp.linalg.norm(jnp.ravel(a - b)) / denominator) - - -n, repeats, zero_pad_size, epsilon = 4, 3, 2, 0.2 -K = jnp.array( - [ - [2.0, 0.2, 0.1, 0.0], - [0.2, 1.8, 0.0, 0.1], - [0.1, 0.0, 1.5, 0.2], - [0.0, 0.1, 0.2, 1.2], - ], - dtype=jnp.float64, -) -metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, -) -blocks = [K + epsilon * jnp.eye(n)] * repeats -blocks.append(epsilon * jnp.eye(zero_pad_size)) -M = jsp_linalg.block_diag(*blocks) -total = M.shape[0] -x = jax.random.normal(jax.random.PRNGKey(0), (total,)) -X = jax.random.normal(jax.random.PRNGKey(1), (total, 5)) - -for callback in ("solve", "inv_sqrt", "inv_sqrt_transpose"): - for value in (x, X): - actual = jax.jit(getattr(metric, callback))(value) - if callback == "solve": - expected = jnp.linalg.solve(M, value) - assert rel(expected, actual) < 1e-12 - assert actual.dtype == jnp.float64 - -assert rel(jnp.sqrt(x @ M @ x), metric.norm(x)) < 1e-12 -S = metric.inv_sqrt(jnp.eye(total)) -assert rel(jnp.linalg.inv(M), S @ S.T) < 1e-12 -assert rel(S.T, metric.inv_sqrt_transpose(jnp.eye(total))) < 1e-12 - -dx = jax.random.normal(jax.random.PRNGKey(2), (total,)) -_, tangent = jax.jvp(metric.norm, (x,), (dx,)) -expected_tangent = (x @ M @ dx) / jnp.sqrt(x @ M @ x) -assert rel(expected_tangent, tangent) < 1e-12 -assert rel(jax.grad(metric.norm)(x), M @ x / jnp.sqrt(x @ M @ x)) < 1e-12 - -for callback in ("solve", "norm", "inv_sqrt", "inv_sqrt_transpose"): - value = x if callback == "norm" else X - constants = jax.make_jaxpr(getattr(metric, callback))(value).consts - shapes = [constant.shape for constant in constants] - assert (n, n) in shapes, (callback, shapes) - assert (total, total) not in shapes, (callback, shapes) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_repeated_shifted_dense_metric_eps_limit_matches_kkt(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import LevenbergMarquardt, repeated_shifted_dense_metric - -n, k, m = 12, 2, 4 -t = jnp.arange(n, dtype=jnp.float64) -ft = jnp.sqrt(3.0) * jnp.abs(t[:, None] - t[None, :]) / 0.8 -K = 1.3**2 * (1.0 + ft) * jnp.exp(-ft) + 1e-8 * jnp.eye(n) -J_alpha = jax.random.normal(jax.random.PRNGKey(0), (m, n)) -J_beta = jax.random.normal(jax.random.PRNGKey(1), (m, k)) -J = jnp.concatenate([J_alpha, J_beta], axis=1) -b = jax.random.normal(jax.random.PRNGKey(2), (m,)) - -kkt = jnp.block( - [ - [2.0 * K, jnp.zeros((n, k)), J_alpha.T], - [jnp.zeros((k, n)), jnp.zeros((k, k)), J_beta.T], - [J_alpha, J_beta, jnp.zeros((m, m))], - ] -) -rhs = jnp.concatenate([jnp.zeros(n + k), b]) -theta_kkt = jnp.linalg.solve(kkt, rhs)[: n + k] -assert jnp.allclose(J @ theta_kkt, b, atol=1e-9) - - -def residual(theta, _, p): - return J @ theta - p * b - - -def solved_x(epsilon, p): - metric = repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=k, epsilon=epsilon - ) - solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - metric=metric, - geodesic_acceleration=False, - ad_solver="qr", - ) - return solver.solve(jnp.zeros(n + k), p=p, max_steps=200, atol=1e-12).x - - -errors = {} -for epsilon in (1e-3, 1e-5, 1e-7): - theta = solved_x(epsilon, jnp.asarray(1.0)) - assert jnp.allclose(J @ theta, b, atol=1e-8), epsilon - errors[epsilon] = float(jnp.linalg.norm(theta - theta_kkt)) - -assert errors[1e-7] < 1e-5, errors -rate = errors[1e-3] / errors[1e-5] -assert 30.0 < rate < 300.0, (errors, rate) - -epsilon = 1e-5 -p, p_dot = jnp.asarray(1.0), jnp.asarray(1.0) -theta, theta_dot = jax.jvp(lambda q: solved_x(epsilon, q), (p,), (p_dot,)) -assert jnp.allclose(theta_dot, theta, atol=1e-8) - -x_bar = jnp.linspace(-1.0, 1.0, n + k) -_, pullback = jax.vjp(lambda q: solved_x(epsilon, q), p) -assert jnp.allclose(pullback(x_bar)[0], x_bar @ theta, atol=1e-8) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - def test_solve_with_float32_problem_under_x64_keeps_lm_state_dtype_consistent(): # solve(lm_state=None) must carry the damping in the residual dtype, not # the default float, or the while_loop carry mismatches update()'s output @@ -1172,7 +150,7 @@ def test_float64_svd_ad_solver_near_duplicate_rows(): jax.config.update("jax_enable_x64", True) import jax.numpy as jnp -from nlls_gram import LevenbergMarquardt +from nlls_gram import SVD, LevenbergMarquardt w = jnp.array([1.0, 2.0, 3.0]) wiggles = 1.0 + 1e-13 * jnp.arange(40.0) @@ -1183,7 +161,7 @@ def residual_fn(x, args, p): x0 = jnp.zeros(3) -solver = LevenbergMarquardt(residual_fn, ad_solver="svd") +solver = LevenbergMarquardt(residual_fn, ad_solver=SVD()) def sum_x_star(target): @@ -1206,121 +184,6 @@ def sum_x_star(target): ) -def test_float64_deflated_pcg_build_and_harvest(): - # In genuine float64: build_coarse_operator, deflated_pcg, and the eigCG - # harvest stay float64 end to end (no f32 in the jaxpr); U=0 reproduces - # recycled_cg bitwise; an exact-eigenvector basis cuts the iteration count; - # the harvested basis matches the true smallest eigenvectors to a tight f64 - # bound; and the implicit gradient matches the dense linear solve. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram.recycled_cg import build_coarse_operator, deflated_pcg, recycled_cg - -n, k = 50, 4 -Q, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (n, n))) -small = jnp.array([0.01, 0.02, 0.04, 0.08]) -bulk = 1.0 + 1e-4 * jax.random.uniform(jax.random.key(2), (n - k,)) -eigs = jnp.concatenate([small, bulk]) -A = (Q * eigs) @ Q.T -A = 0.5 * (A + A.T) -b = jax.random.normal(jax.random.key(1), (n,)) -w = 3 * k - - -def matvec(v): - return A @ v - - -# dtypes stay float64 -U0 = jnp.zeros((n, k)) -W, E_factor = build_coarse_operator(matvec, U0) -assert W.dtype == jnp.float64 -assert E_factor[0].dtype == jnp.float64 -y, harvest = deflated_pcg( - matvec, b, U=U0, E_factor=E_factor, tol=1e-10, atol=0.0, - maxiter=200, window=w, rank=k, -) -assert y.dtype == jnp.float64 -assert harvest.basis.dtype == jnp.float64 -assert harvest.residual_norm.dtype == jnp.float64 -assert jnp.allclose(y, jnp.linalg.solve(A, b), rtol=1e-8, atol=1e-8) - -# no f32 anywhere in the traced program -jaxpr = str( - jax.make_jaxpr( - lambda rhs: deflated_pcg( - matvec, rhs, U=U0, E_factor=E_factor, tol=1e-10, atol=0.0, - maxiter=200, window=w, rank=k, - )[0] - )(b) -) -assert "f32" not in jaxpr, jaxpr - -# U=0 reproduces recycled_cg bitwise (non-identity first-level P) -weights = jnp.diag(A) - - -def P(v): - return v / weights - - -yd, _ = deflated_pcg( - matvec, b, U=U0, E_factor=E_factor, M=P, - tol=1e-10, atol=0.0, maxiter=300, window=w, rank=k, -) -yr, _ = recycled_cg(matvec, b, tol=1e-10, atol=0.0, maxiter=300, M=P) -assert bool(jnp.array_equal(yd, yr)) - -# exact-eigenvector basis cuts iterations -order = jnp.argsort(eigs) -U_exact = Q[:, order[:k]] -_, cold = deflated_pcg( - matvec, b, U=U0, E_factor=E_factor, tol=1e-10, atol=0.0, - maxiter=300, window=w, rank=k, -) -_, defl = deflated_pcg( - matvec, b, U=U_exact, E_factor=build_coarse_operator(matvec, U_exact)[1], - tol=1e-10, atol=0.0, maxiter=300, window=w, rank=k, -) -assert int(defl.iterations) < int(cold.iterations) - -# harvested basis matches the true smallest eigenvectors to a tight f64 bound -_, evecs = jnp.linalg.eigh(A) -cos_angles = jnp.linalg.svd(harvest.basis.T @ evecs[:, :k], compute_uv=False) -assert float(jnp.min(cos_angles)) > 1.0 - 1e-8, float(jnp.min(cos_angles)) -assert float(jnp.max(jnp.abs(harvest.basis.T @ harvest.basis - jnp.eye(k)))) < 1e-12 - -# implicit gradient matches the dense solve to a tight f64 bound -A_inv = jnp.linalg.inv(A) - - -def loss(rhs): - x, _ = deflated_pcg( - matvec, rhs, U=U_exact, - E_factor=build_coarse_operator(matvec, U_exact)[1], - tol=1e-12, atol=0.0, maxiter=300, window=w, rank=k, - ) - return jnp.sum(x**2) - - -got = jax.grad(loss)(b) -expected = jax.grad(lambda rhs: jnp.sum((A_inv @ rhs) ** 2))(b) -assert jnp.allclose(got, expected, rtol=1e-9, atol=1e-9), float( - jnp.max(jnp.abs(got - expected)) -) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - def test_float64_multi_start_modes_and_float32_data_under_x64(): script = r""" import jax @@ -1422,57 +285,6 @@ def sum_x(pv, ms=ms): ) -def test_float64_recycled_solve_carry_dtypes(): - # Regression: under x64 the deflated-PCG loop counter defaulted to int64 - # while LMState carried RecycleState.iterations as int32, breaking the - # solve-loop carry on every recycled cg solve. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import ( - LevenbergMarquardt, - LMStatus, - RecycleConfig, - identity_preconditioner, -) - -A = jax.random.normal(jax.random.key(0), (20, 6)) -b = jax.random.normal(jax.random.key(1), (20,)) - - -def residual(theta): - return A @ theta - b + 0.1 * jnp.sum(theta**2) - - -solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - iterative_maxiter=30, - iterative_tol=1e-10, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - recycle=RecycleConfig(rank=3), -) -# gtol is set above the solver's attainable gradient floor for this -# cg/recycle problem (~2e-8 under the locked jaxlib) so CONVERGED is a -# platform-stable outcome; the regression this guards is the dtype carry -# below, not the exact endgame accuracy. -result = solver.solve(jnp.zeros(6), max_steps=60, gtol=1e-7) -assert int(result.status) == LMStatus.CONVERGED, int(result.status) -assert result.lm_state.recycle.iterations.dtype == jnp.int32 -assert result.lm_state.recycle.residual_norm.dtype == jnp.float64 -assert float(result.info.grad_norm) < 1e-6, float(result.info.grad_norm) -""" - subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=True, - capture_output=True, - text=True, - ) - - def test_float64_default_min_damping_uses_float64_normal_floor(): script = r""" import jax @@ -1673,7 +485,6 @@ def test_ridge_continuation_matches_metric_lm_min_seminorm_float64(): LevenbergMarquardt, RepeatedFactorMetric, RidgeLevenbergMarquardt, - repeated_shifted_dense_metric, ridge_continuation, ) @@ -1702,8 +513,10 @@ def residual(theta): x_dagger = np.linalg.solve(kkt, np.concatenate([np.zeros(p_dim), b_np]))[:p_dim] # Metric-damped LM with a small epsilon shift selects x_dagger + O(eps). -metric = repeated_shifted_dense_metric( - K, repeats=repeats, zero_pad_size=pad, epsilon=1e-8 +# free_scale weights the zero-padded tail, the role epsilon used to play +# there; the metric block carries K + epsilon I. +metric = RepeatedFactorMetric.from_gram( + K, repeats=repeats, epsilon=1e-8, free_scale=1e-8 ) metric_solver = LevenbergMarquardt(residual, metric=metric) metric_result = metric_solver.solve(jnp.zeros(p_dim), max_steps=200, atol=1e-12) diff --git a/tests/test_gpu.py b/tests/test_gpu.py index 0ad07ba..26e98eb 100644 --- a/tests/test_gpu.py +++ b/tests/test_gpu.py @@ -3,11 +3,14 @@ import pytest from nlls_gram import ( + CG, + QR, + Cholesky, + GramCG, + IdentityPreconditioner, LevenbergMarquardt, - identity_preconditioner, - matern_state_space, - repeated_shifted_state_space_metric, ) +from nlls_gram.experimental import StateSpaceMetric, matern_state_space def _gpu_devices(): @@ -24,22 +27,18 @@ def _gpu_devices(): ) -# Matrix-free params (cg with an explicit identity preconditioner, plain lsmr) -# ride alongside the dense ones; they auto-skip without a GPU like the rest. -_MATRIX_FREE_GPU_KWARGS = { - "gram_cg": { - "iterative_tol": 1e-7, - "iterative_maxiter": 10, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - }, - "lsmr": {"iterative_tol": 1e-8, "iterative_maxiter": 10}, -} +# The matrix-free configs ride alongside the dense ones; all auto-skip +# without a GPU. +GPU_SOLVERS = [ + Cholesky(form="gram"), + Cholesky(form="normal"), + QR(), + CG(IdentityPreconditioner(), tol=1e-7, maxiter=10), + GramCG(IdentityPreconditioner(), tol=1e-7, maxiter=10), +] -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "qr", "augmented_qr", "gram_cg", "lsmr"] -) +@pytest.mark.parametrize("linear_solver", GPU_SOLVERS) def test_jitted_geodesic_update_runs_on_gpu(linear_solver): def residual(theta, target, p): return jnp.array([theta[0] ** 2 - target]) @@ -51,7 +50,6 @@ def residual(theta, target, p): linear_solver=linear_solver, geodesic_acceleration=True, geodesic_acceptance_ratio=1.0, - **_MATRIX_FREE_GPU_KWARGS.get(linear_solver, {}), ) with jax.default_device(gpu): @@ -75,9 +73,7 @@ def step(theta, lm_state, target): assert jnp.isfinite(info.acceleration_ratio) -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "qr", "augmented_qr", "gram_cg", "lsmr"] -) +@pytest.mark.parametrize("linear_solver", GPU_SOLVERS) def test_jitted_geodesic_update_does_not_transfer_to_host(linear_solver): def residual(theta, target, p): return jnp.array([theta[0] ** 2 - target]) @@ -89,7 +85,6 @@ def residual(theta, target, p): linear_solver=linear_solver, geodesic_acceleration=True, geodesic_acceptance_ratio=1.0, - **_MATRIX_FREE_GPU_KWARGS.get(linear_solver, {}), ) with jax.default_device(gpu): @@ -110,39 +105,28 @@ def step(theta, lm_state, target): assert next(iter(leaf.devices())).platform == "gpu" -def test_repeated_shifted_state_space_metric_runs_on_gpu(): - # The parallel and sequential apply paths must both run and agree on - # the GPU backend (float32 here, so the dtype-aware default picks the +def test_state_space_metric_runs_on_gpu(): + # The parallel and sequential apply paths must both run and agree on the + # GPU backend (float32 here, so the dtype-aware default picks the # sequential path; parallel=True forces the associative scans). gpu = _gpu_devices()[0] with jax.default_device(gpu): - n, repeats, zero_pad_size = 512, 3, 2 + n, repeats = 512, 3 t = jnp.cumsum(jnp.ones(n)) - x = jnp.sin(jnp.linspace(0.0, 6.0, repeats * n + zero_pad_size)) + x = jnp.sin(jnp.linspace(0.0, 6.0, repeats * n)) model = matern_state_space(1.3, 0.8, 2.5) - default = repeated_shifted_state_space_metric( - t, - *model, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=1e-6, - ) - parallel = repeated_shifted_state_space_metric( - t, - *model, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=1e-6, - parallel=True, + default = StateSpaceMetric(t, *model, repeats=repeats, epsilon=1e-6) + parallel = StateSpaceMetric( + t, *model, repeats=repeats, epsilon=1e-6, parallel=True ) - out = jax.jit(default.solve)(x) - out_parallel = jax.jit(parallel.solve)(x) + out = jax.jit(lambda v: default.factor_solve(v, None))(x) + out_parallel = jax.jit(lambda v: parallel.factor_solve(v, None))(x) jax.block_until_ready((out, out_parallel)) assert next(iter(out.devices())).platform == "gpu" assert bool(jnp.all(jnp.isfinite(out))) assert jnp.allclose(out, out_parallel, rtol=1e-4, atol=1e-5) - assert jnp.allclose(default.norm(x), parallel.norm(x), rtol=1e-4) + assert jnp.allclose(default.norm(x, None), parallel.norm(x, None), rtol=1e-4) def multi_start_residual(theta, args, p): diff --git a/tests/test_gram_lm.py b/tests/test_gram_lm.py deleted file mode 100644 index 74e1536..0000000 --- a/tests/test_gram_lm.py +++ /dev/null @@ -1,4697 +0,0 @@ -import dataclasses - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import pytest -from jax.flatten_util import ravel_pytree - -from nlls_gram import ( - GramMetric, - LevenbergMarquardt, - LMSolveAction, - LMState, - LMStatus, - identity_preconditioner, - matern_state_space, - metric_from_cholesky, - metric_from_diagonal, - nystrom_preconditioner, - pad_dual_preconditioner, - repeated_shifted_dense_metric, - repeated_shifted_state_space_metric, - sherman_morrison_preconditioner, - woodbury_preconditioner, -) - - -def residual_fn(x, args, p): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -REGRESSION_ATOL = 5e-5 -REGRESSION_RTOL = 1e-5 - - -def _solve_2x2(matrix, rhs): - determinant = matrix[0, 0] * matrix[1, 1] - matrix[0, 1] * matrix[1, 0] - return jnp.stack( - ( - (matrix[1, 1] * rhs[0] - matrix[0, 1] * rhs[1]) / determinant, - (-matrix[1, 0] * rhs[0] + matrix[0, 0] * rhs[1]) / determinant, - ) - ) - - -def test_recovers_known_parameters_with_jitted_step(): - a_true, b_true = 2.0, -1.0 - ts = jnp.linspace(0.0, 2.0, 20) - ys = a_true * jnp.exp(b_true * ts) - - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - lm_state = solver.init(x, (ts, ys)) - - @jax.jit - def train_step(x, lm_state, args): - return solver.update(x, lm_state, args) - - info = None - for _ in range(50): - x, lm_state, info = train_step(x, lm_state, (ts, ys)) - - assert float(info.loss) < 1e-8 - assert jnp.allclose(x["a"], a_true, atol=1e-4) - assert jnp.allclose(x["b"], b_true, atol=1e-4) - - -def test_default_metric_matches_explicit_identity_metric_solve(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - default_solver = LevenbergMarquardt( - residual_fn, init_damping=1e-2, linear_solver="gram_cholesky" - ) - identity_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cholesky", - metric=GramMetric( - solve=lambda x: x, - norm=jnp.linalg.norm, - inv_sqrt=lambda x: x, - inv_sqrt_transpose=lambda x: x, - ), - ) - - default_x, default_state, default_info = default_solver.update( - x, default_solver.init(x, (ts, ys)), (ts, ys) - ) - identity_x, identity_state, identity_info = identity_solver.update( - x, identity_solver.init(x, (ts, ys)), (ts, ys) - ) - - assert jnp.allclose(default_x["a"], identity_x["a"]) - assert jnp.allclose(default_x["b"], identity_x["b"]) - assert jnp.allclose(default_state.damping, identity_state.damping) - assert jnp.allclose(default_info.loss, identity_info.loss) - - -def test_flat_array_x(): - def residual(theta, args, p): - ts, ys = args - return theta[0] * jnp.exp(theta[1] * ts) - ys - - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - - x = jnp.array([1.0, 0.0]) - solver = LevenbergMarquardt(residual, init_damping=1e-2) - lm_state = solver.init(x, (ts, ys)) - - for _ in range(50): - x, lm_state, _ = solver.update(x, lm_state, (ts, ys)) - - assert x.shape == (2,) - assert jnp.allclose(x, jnp.array([2.0, -1.0]), atol=1e-4) - - -def test_linear_problem_matches_closed_form_solution(): - def residual(x, args, p): - ts, ys = args - return x["a"] * ts - ys - - ts = jnp.array([1.0, 2.0, 3.0]) - ys = 2.0 * ts - x = {"a": 0.0} - init_damping = 1e-4 - - solver = LevenbergMarquardt(residual, init_damping=init_damping) - new_x, _, info = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - expected_a = jnp.sum(ts * ys) / (jnp.sum(ts**2) + init_damping) - expected_loss = jnp.sum((expected_a * ts - ys) ** 2) - - assert bool(info.accepted) - assert jnp.allclose(new_x["a"], expected_a, atol=1e-6) - assert jnp.allclose(info.loss, expected_loss, atol=1e-10) - assert float(info.loss_old) == pytest.approx(56.0) - assert jnp.allclose(info.loss_candidate, expected_loss, atol=1e-10) - assert float(info.damping_factor) == pytest.approx(0.5) - assert not bool(info.used_geodesic) - assert float(info.acceleration_ratio) == pytest.approx(0.0) - - -def test_update_calls_residual_and_uses_values(): - calls = {"count": 0} - - def residual(x, args, p): - calls["count"] += 1 - ts, ys = args - return x["a"] * ts - ys - - ts = jnp.array([1.0, 2.0, 3.0]) - ys = 2.0 * ts - x = {"a": 0.0} - - solver = LevenbergMarquardt(residual, init_damping=1e-4) - new_x, _, info = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - - assert calls["count"] >= 2 - assert bool(info.accepted) - assert jnp.allclose(new_x["a"], 2.0, atol=1e-4) - - -def test_defaults_enable_geodesic_and_jacobian_cache(): - solver = LevenbergMarquardt(lambda x: x) - assert solver.geodesic_acceleration - assert solver.cache_jacobian - - -def test_geodesic_off_uses_minimal_residual_evaluations(): - calls = {"count": 0} - - def residual(x, args, p): - calls["count"] += 1 - ts, ys = args - return x["a"] * ts - ys - - ts = jnp.array([1.0, 2.0, 3.0]) - ys = 2.0 * ts - x = {"a": 0.0} - - solver = LevenbergMarquardt( - residual, init_damping=1e-4, geodesic_acceleration=False, cache_jacobian=False - ) - lm_state = solver.init(x, (ts, ys)) - calls["count"] = 0 - solver.update(x, lm_state, (ts, ys)) - - assert calls["count"] == 2 - - -def test_rejected_step_leaves_x_unchanged(): - ts = jnp.linspace(0.0, 2.0, 5) - ys = jnp.ones_like(ts) - x = {"a": 1.0, "b": 0.0} - - solver = LevenbergMarquardt(residual_fn) - lm_state = solver.init(x, (ts, ys)) - new_x, new_lm_state, info = solver.update(x, lm_state, (ts, ys)) - - assert not bool(info.accepted) - assert jnp.allclose(new_x["a"], x["a"]) - assert jnp.allclose(new_x["b"], x["b"]) - assert float(new_lm_state.damping) > float(lm_state.damping) - assert float(info.loss) == pytest.approx(0.0) - assert float(info.loss_old) == pytest.approx(0.0) - assert float(info.loss_candidate) == pytest.approx(0.0) - assert float(info.damping_factor) == pytest.approx(4.0) - assert not bool(info.used_geodesic) - assert float(info.acceleration_ratio) == pytest.approx(0.0) - - -def test_unknown_linear_solver_raises(): - with pytest.raises(ValueError, match="unknown linear_solver"): - LevenbergMarquardt(residual_fn, linear_solver="svd") - - -def test_init_damping_must_be_positive(): - with pytest.raises(ValueError, match="init_damping must be positive"): - LevenbergMarquardt(residual_fn, init_damping=0.0) - - -def test_damping_update_factors_must_be_positive(): - with pytest.raises(ValueError, match="damping_decrease must be positive"): - LevenbergMarquardt(residual_fn, damping_decrease=0.0) - with pytest.raises(ValueError, match="damping_increase must be positive"): - LevenbergMarquardt(residual_fn, damping_increase=0.0) - - -def test_min_damping_must_be_positive_and_not_exceed_initial_damping(): - with pytest.raises(ValueError, match="min_damping must be positive or None"): - LevenbergMarquardt(residual_fn, min_damping=0.0) - with pytest.raises(ValueError, match="min_damping must not exceed"): - LevenbergMarquardt(residual_fn, init_damping=1e-3, min_damping=1e-2) - - -def test_iterative_options_must_be_valid(): - with pytest.raises(ValueError, match="iterative_tol must be nonnegative"): - LevenbergMarquardt(residual_fn, linear_solver="gram_cg", iterative_tol=-1.0) - with pytest.raises(ValueError, match="iterative_atol must be nonnegative"): - LevenbergMarquardt(residual_fn, linear_solver="gram_cg", iterative_atol=-1.0) - with pytest.raises(ValueError, match="iterative_maxiter must be positive or None"): - LevenbergMarquardt(residual_fn, linear_solver="gram_cg", iterative_maxiter=0) - with pytest.raises(ValueError, match="iterative_maxiter must be set"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=None, - ) - - -def test_ad_solver_options_must_be_valid(): - with pytest.raises(ValueError, match="unknown ad_solver"): - LevenbergMarquardt(residual_fn, ad_solver="lu") - with pytest.raises(ValueError, match="ad_solver_tol must be nonnegative"): - LevenbergMarquardt(residual_fn, ad_solver_tol=-1.0) - with pytest.raises(ValueError, match="ad_solver_atol must be nonnegative"): - LevenbergMarquardt(residual_fn, ad_solver_atol=-1.0) - with pytest.raises(ValueError, match="ad_solver_maxiter must be positive or None"): - LevenbergMarquardt(residual_fn, ad_solver_maxiter=0) - with pytest.raises(ValueError, match="requires a positive"): - LevenbergMarquardt( - residual_fn, - ad_solver="augmented_qr", - ad_solver_penalty=-1e-8, - ) - # The zero-tolerance guard is a cg stopping control: it fires only for a - # CG stopping controls apply only to an explicitly selected CG method. - with pytest.raises(ValueError, match="ad_solver_maxiter must be set"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - ad_solver_tol=0.0, - ad_solver_atol=0.0, - ad_solver_maxiter=None, - ) - with pytest.raises(ValueError, match="accepted only"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - ad_solver="gram_cg", - ad_solver_penalty=1e-6, - ) - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - LevenbergMarquardt(residual_fn, ad_solver_preconditioner=lambda v: v) - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - LevenbergMarquardt( - residual_fn, - linear_solver="qr", - ad_solver="auto", - ad_solver_preconditioner=lambda v: v, - ) - - auto_cg = LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=lambda v: v, - ) - explicit_cg = LevenbergMarquardt( - residual_fn, - ad_solver="gram_cg", - ad_solver_preconditioner=lambda v: v, - ) - assert auto_cg.ad_solver == "auto" - assert explicit_cg.ad_solver == "gram_cg" - - -def test_linear_solve_dtype_validation(): - with pytest.raises(ValueError, match="None or jnp.float64"): - LevenbergMarquardt(residual_fn, linear_solve_dtype=jnp.float32) - with pytest.raises(ValueError, match="dense linear-solve pipelines"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - iterative_tol=1e-7, - iterative_maxiter=20, - dual_preconditioner=identity_preconditioner(), - ad_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - linear_solve_dtype=jnp.float64, - ) - # x64 is disabled in this test process, so float64 is unavailable and - # requesting it raises rather than silently downcasting. - with pytest.raises(ValueError, match="requires x64"): - LevenbergMarquardt(residual_fn, linear_solve_dtype=jnp.float64) - - -def test_default_float32_x_keeps_float32_outputs(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - new_x, new_lm_state, info = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - - assert new_x["a"].dtype == jnp.float32 - assert new_x["b"].dtype == jnp.float32 - assert new_lm_state.damping.dtype == jnp.float32 - assert info.loss.dtype == jnp.float32 - assert info.loss_old.dtype == jnp.float32 - assert info.loss_candidate.dtype == jnp.float32 - assert info.damping.dtype == jnp.float32 - assert info.damping_factor.dtype == jnp.float32 - assert info.acceleration_ratio.dtype == jnp.float32 - assert info.grad_norm.dtype == jnp.float32 - assert info.step_norm.dtype == jnp.float32 - - -def test_max_damping_below_init_damping_raises(): - with pytest.raises(ValueError, match="max_damping must be at least"): - LevenbergMarquardt(residual_fn, init_damping=1e-2, max_damping=1e-3) - - -@pytest.mark.parametrize("jit", [False, True]) -@pytest.mark.parametrize("linear_solver", ["auto", "lsmr"]) -def test_default_min_damping_repairs_zero_and_prevents_float32_underflow( - jit, linear_solver -): - def residual(theta): - return theta - - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver=linear_solver, - cache_jacobian=False, - geodesic_acceleration=False, - ) - state = LMState(jnp.asarray(0.0, dtype=jnp.float32)) - update = solver.update if not jit else jax.jit(lambda x, s: solver.update(x, s)) - x, state, info = update(jnp.ones(1, dtype=jnp.float32), state) - floor = jnp.asarray(jnp.finfo(jnp.float32).tiny, dtype=jnp.float32) - - assert bool(info.accepted) - assert jnp.all(jnp.isfinite(x)) - assert state.damping == floor - assert info.damping == floor - - -@pytest.mark.parametrize("jit", [False, True]) -def test_explicit_min_damping_is_used_by_step_and_update(jit): - def residual(theta): - return theta - - min_damping = 1e-4 - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - min_damping=min_damping, - cache_jacobian=False, - geodesic_acceleration=False, - ) - state = LMState(jnp.asarray(0.0, dtype=jnp.float32)) - update = solver.update if not jit else jax.jit(lambda x, s: solver.update(x, s)) - x, state, info = update(jnp.ones(1, dtype=jnp.float32), state) - expected_x = min_damping / (1.0 + min_damping) - - assert bool(info.accepted) - assert jnp.allclose(x, expected_x, rtol=1e-4, atol=1e-7) - assert float(state.damping) == pytest.approx(min_damping) - assert float(info.damping) == pytest.approx(min_damping) - - -def test_metric_requirements_per_linear_solver(): - with pytest.raises(ValueError, match="metric.solve"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cholesky", - metric=GramMetric(norm=jnp.linalg.norm), - ) - for linear_solver in ("qr", "augmented_qr"): - with pytest.raises(ValueError, match="metric.inv_sqrt"): - LevenbergMarquardt( - residual_fn, - linear_solver=linear_solver, - metric=GramMetric(solve=lambda x: x), - ) - with pytest.raises(ValueError, match="metric.norm"): - LevenbergMarquardt( - residual_fn, - geodesic_acceleration=True, - metric=GramMetric(solve=lambda x: x), - ) - - -def test_cg_step_matches_cholesky_identity_step(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - cholesky_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - cg_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ) - - cholesky_x, cholesky_state, cholesky_info = cholesky_solver.update( - x, cholesky_solver.init(x, (ts, ys)), (ts, ys) - ) - cg_x, cg_state, cg_info = cg_solver.update(x, cg_solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(cg_info.accepted) == bool(cholesky_info.accepted) - assert not bool(cg_info.used_geodesic) - assert jnp.allclose(cg_x["a"], cholesky_x["a"], rtol=1e-5, atol=1e-5) - assert jnp.allclose(cg_x["b"], cholesky_x["b"], rtol=1e-5, atol=1e-5) - assert jnp.allclose(cg_state.damping, cholesky_state.damping) - assert jnp.allclose( - cg_info.loss, - cholesky_info.loss, - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert cg_x["a"].dtype == jnp.float32 - assert cg_info.loss.dtype == jnp.float32 - - -@pytest.mark.parametrize("linear_solver", ["qr", "augmented_qr"]) -def test_qr_steps_match_cholesky_identity_step(linear_solver): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - cholesky_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - ) - qr_solver = LevenbergMarquardt( - residual_fn, init_damping=1e-2, linear_solver=linear_solver - ) - - cholesky_x, cholesky_state, cholesky_info = cholesky_solver.update( - x, cholesky_solver.init(x, (ts, ys)), (ts, ys) - ) - qr_x, qr_state, qr_info = qr_solver.update(x, qr_solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(qr_info.accepted) == bool(cholesky_info.accepted) - assert not bool(qr_info.used_geodesic) - assert jnp.allclose( - qr_x["a"], - cholesky_x["a"], - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert jnp.allclose( - qr_x["b"], - cholesky_x["b"], - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert jnp.allclose(qr_state.damping, cholesky_state.damping) - assert jnp.allclose( - qr_info.loss, - cholesky_info.loss, - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert qr_x["a"].dtype == jnp.float32 - assert qr_info.loss.dtype == jnp.float32 - - -@pytest.mark.parametrize("linear_solver", ["qr", "augmented_qr"]) -def test_qr_steps_match_closed_form_underdetermined_damped_solution(linear_solver): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 2.0, 0.5, -1.0], [0.0, 1.0, 3.0, 2.0]]) - target = jnp.array([1.0, -2.0]) - theta0 = jnp.zeros(matrix.shape[1]) - init_damping = 0.1 - - solver = LevenbergMarquardt( - residual, - init_damping=init_damping, - linear_solver=linear_solver, - ) - theta, lm_state, info = solver.update( - theta0, solver.init(theta0, (matrix, target)), (matrix, target) - ) - - expected_step = jnp.linalg.solve( - matrix.T @ matrix + init_damping * jnp.eye(matrix.shape[1]), - matrix.T @ target, - ) - expected_loss = jnp.sum((matrix @ expected_step - target) ** 2) - - assert bool(info.accepted) - assert not bool(info.used_geodesic) - assert jnp.allclose(theta, expected_step, rtol=1e-5, atol=1e-5) - assert jnp.allclose(info.loss, expected_loss, rtol=1e-5, atol=1e-5) - assert jnp.allclose(lm_state.damping, init_damping * 0.5) - assert theta.dtype == jnp.float32 - assert info.loss.dtype == jnp.float32 - - -@pytest.mark.parametrize( - "matrix", - [ - jnp.array([[1.0, 2.0], [0.5, -1.0]]), - jnp.array([[1.0, 2.0], [0.5, -1.0], [2.0, 0.25]]), - ], -) -def test_augmented_qr_matches_closed_form_for_square_and_overdetermined(matrix): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - target = jnp.arange(1, matrix.shape[0] + 1, dtype=matrix.dtype) - theta0 = jnp.zeros(matrix.shape[1]) - damping = 0.1 - solver = LevenbergMarquardt( - residual, - init_damping=damping, - linear_solver="augmented_qr", - geodesic_acceleration=False, - ) - theta, _, info = solver.update( - theta0, - solver.init(theta0, (matrix, target)), - (matrix, target), - ) - expected = jnp.linalg.solve( - matrix.T @ matrix + damping * jnp.eye(matrix.shape[1]), - matrix.T @ target, - ) - - assert bool(info.accepted) - assert jnp.allclose(theta, expected, rtol=1e-5, atol=1e-5) - - -def test_augmented_qr_rank_deficient_jacobian_has_finite_damped_step(): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 0.0], [2.0, 0.0]]) - target = jnp.array([1.0, 2.0]) - theta0 = jnp.zeros(2) - damping = 1e-3 - solver = LevenbergMarquardt( - residual, - init_damping=damping, - linear_solver="augmented_qr", - geodesic_acceleration=False, - ) - theta, _, info = solver.update( - theta0, - solver.init(theta0, (matrix, target)), - (matrix, target), - ) - expected = jnp.linalg.solve( - matrix.T @ matrix + damping * jnp.eye(2), matrix.T @ target - ) - - assert bool(info.accepted) - assert bool(jnp.all(jnp.isfinite(theta))) - assert jnp.allclose(theta, expected, rtol=1e-5, atol=1e-5) - - -def test_qr_float32_handles_ill_conditioned_case_where_cholesky_fails(): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 0.0, 0.0, 0.0], [1.0, 1e-4, 0.0, 0.0]]) - theta_true = jnp.array([1.0, 1.0, 0.0, 0.0]) - target = matrix @ theta_true - theta0 = jnp.zeros(matrix.shape[1]) - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-12, - linear_solver="gram_cholesky", - ) - qr_solver = LevenbergMarquardt( - residual, - init_damping=1e-12, - linear_solver="qr", - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, (matrix, target)), (matrix, target) - ) - qr_theta, _, qr_info = qr_solver.update( - theta0, qr_solver.init(theta0, (matrix, target)), (matrix, target) - ) - - assert jnp.all(jnp.isfinite(qr_theta)) - assert jnp.isfinite(qr_info.loss_candidate) - assert bool(qr_info.accepted) - assert not bool(jnp.all(jnp.isfinite(cholesky_theta))) or not bool( - jnp.isfinite(cholesky_info.loss_candidate) - ) - assert qr_info.loss_candidate < 1e-12 - - -def test_cg_update_jits(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(lm_state.damping) - assert x["a"].dtype == jnp.float32 - assert x["b"].dtype == jnp.float32 - - -@pytest.mark.parametrize("linear_solver", ["qr", "augmented_qr"]) -def test_qr_updates_jit(linear_solver): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver=linear_solver, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(lm_state.damping) - assert x["a"].dtype == jnp.float32 - assert x["b"].dtype == jnp.float32 - - -def test_geodesic_acceptance_ratio_zero_falls_back_to_velocity_step(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=0.0, - ) - new_theta, _, info = solver.update(theta0, solver.init(theta0, target), target) - - jacobian = 2.0 * theta0[0] - velocity = -jacobian * (theta0[0] ** 2 - target) / (jacobian**2 + 1e-6) - expected_theta = theta0 + jnp.array([velocity]) - - assert bool(info.accepted) - assert not bool(info.used_geodesic) - assert float(info.acceleration_ratio) > 0.0 - assert jnp.allclose(new_theta, expected_theta, rtol=1e-6, atol=1e-6) - - -def test_geodesic_acceleration_matches_closed_form_quadratic_step(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - new_theta, _, info = solver.update(theta0, solver.init(theta0, target), target) - - jacobian = 2.0 * theta0[0] - linear_denominator = jacobian**2 + 1e-6 - velocity = -jacobian * (theta0[0] ** 2 - target) / linear_denominator - f_vv = 2.0 * velocity**2 - acceleration = -jacobian * f_vv / linear_denominator - expected_theta = theta0 + jnp.array([velocity + 0.5 * acceleration]) - expected_ratio = ( - 2.0 * jnp.abs(acceleration) / (jnp.abs(velocity) + jnp.finfo(theta0.dtype).eps) - ) - - assert bool(info.accepted) - assert bool(info.used_geodesic) - assert new_theta.dtype == jnp.float32 - assert info.loss.dtype == jnp.float32 - assert info.loss_old.dtype == jnp.float32 - assert info.loss_candidate.dtype == jnp.float32 - assert info.damping.dtype == jnp.float32 - assert info.damping_factor.dtype == jnp.float32 - assert info.acceleration_ratio.dtype == jnp.float32 - assert jnp.allclose(new_theta, expected_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose(info.acceleration_ratio, expected_ratio, rtol=1e-6) - - -def test_cg_geodesic_acceleration_matches_cholesky(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - cg_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=10, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, target), target - ) - cg_theta, _, cg_info = cg_solver.update( - theta0, cg_solver.init(theta0, target), target - ) - - assert bool(cg_info.accepted) - assert bool(cg_info.used_geodesic) - assert jnp.allclose(cg_theta, cholesky_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose( - cg_info.acceleration_ratio, - cholesky_info.acceleration_ratio, - rtol=1e-6, - atol=1e-6, - ) - - -def test_qr_geodesic_acceleration_matches_cholesky(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - qr_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="qr", - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, target), target - ) - qr_theta, _, qr_info = qr_solver.update( - theta0, qr_solver.init(theta0, target), target - ) - - assert bool(qr_info.accepted) - assert bool(qr_info.used_geodesic) - assert jnp.allclose(qr_theta, cholesky_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose( - qr_info.acceleration_ratio, - cholesky_info.acceleration_ratio, - rtol=1e-6, - atol=1e-6, - ) - - -def test_geodesic_acceleration_jits(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - - @jax.jit - def step(theta, lm_state, target): - return solver.update(theta, lm_state, target) - - theta, lm_state, info = step( - jnp.array([1.9]), solver.init(jnp.array([1.9]), 4.0), 4.0 - ) - - assert bool(info.accepted) - assert bool(info.used_geodesic) - assert jnp.isfinite(theta[0]) - assert jnp.isfinite(lm_state.damping) - - -def test_geodesic_acceleration_reduces_iterations_on_gsl_rosenbrock_example(): - def residual(theta, _, p): - return jnp.array([100.0 * (theta[1] - theta[0] ** 2), 1.0 - theta[0]]) - - def iterations_to_threshold(geodesic_acceleration): - theta = jnp.array([-0.5, 1.75]) - solver = LevenbergMarquardt( - residual, - init_damping=1.0, - geodesic_acceleration=geodesic_acceleration, - ) - lm_state = solver.init(theta) - used_geodesic = 0 - for iteration in range(1, 101): - theta, lm_state, info = solver.update(theta, lm_state, None) - used_geodesic += int(bool(info.used_geodesic)) - if float(info.loss) < 1e-12: - return iteration, used_geodesic - return 101, used_geodesic - - plain_iterations, plain_used_geodesic = iterations_to_threshold(False) - geodesic_iterations, geodesic_used_geodesic = iterations_to_threshold(True) - - assert plain_used_geodesic == 0 - assert geodesic_used_geodesic > 0 - assert geodesic_iterations < plain_iterations / 2 - - -def test_jitted_residual_with_jitted_geodesic_update(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt( - jax.jit(residual_fn), - init_damping=1e-2, - geodesic_acceleration=True, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(info.acceleration_ratio) - assert jnp.isfinite(lm_state.damping) - assert x["a"].dtype == jnp.float32 - assert x["b"].dtype == jnp.float32 - - -def test_metric_from_cholesky_matches_dense_metric(): - L = jnp.array( - [ - [2.0, 0.0, 0.0], - [0.3, 1.5, 0.0], - [-0.2, 0.4, 1.2], - ] - ) - metric_matrix = L @ L.T - metric = metric_from_cholesky(L) - vector = jnp.array([0.5, -1.0, 2.0]) - matrix = jnp.array([[1.0, -0.5], [0.2, 2.0], [-1.0, 0.25]]) - - expected_solve_vector = jnp.linalg.solve(metric_matrix, vector) - expected_solve_matrix = jnp.linalg.solve(metric_matrix, matrix) - expected_norm = jnp.sqrt(vector @ metric_matrix @ vector) - expected_inv_sqrt = jsp_linalg.solve_triangular(L.T, matrix, lower=False) - expected_inv_sqrt_transpose = jsp_linalg.solve_triangular(L, matrix, lower=True) - - assert jnp.allclose(metric.solve(vector), expected_solve_vector) - assert jnp.allclose(metric.solve(matrix), expected_solve_matrix) - assert jnp.allclose(metric.norm(vector), expected_norm) - assert jnp.allclose(metric.inv_sqrt(matrix), expected_inv_sqrt) - assert jnp.allclose( - metric.inv_sqrt_transpose(matrix), - expected_inv_sqrt_transpose, - ) - - -def test_metric_selects_minimum_norm_interpolating_step(): - # r(theta) = theta_0 + theta_1 - 1 at theta = 0: every interpolating step - # satisfies s_0 + s_1 = 1, and with tiny damping the update is the metric - # Gauss-Newton step — the minimum-M-norm solution (docs worked example). - def residual(theta, _, __): - return jnp.array([theta[0] + theta[1] - 1.0]) - - theta0 = jnp.zeros(2) - - identity_solver = LevenbergMarquardt(residual, init_damping=1e-9) - x_identity, _, _ = identity_solver.update(theta0, identity_solver.init(theta0)) - assert jnp.allclose(x_identity, jnp.array([0.5, 0.5]), atol=1e-5) - - L = jnp.linalg.cholesky(jnp.diag(jnp.array([1.0, 4.0]))) - metric_solver = LevenbergMarquardt( - residual, init_damping=1e-9, metric=metric_from_cholesky(L) - ) - x_metric, _, _ = metric_solver.update(theta0, metric_solver.init(theta0)) - assert jnp.allclose(x_metric, jnp.array([0.8, 0.2]), atol=1e-5) - - -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "gram_cg", "qr", "augmented_qr"] -) -def test_metric_step_matches_closed_form_solution(linear_solver): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 2.0, -0.5], [0.3, -1.0, 1.5]]) - target = jnp.array([1.0, -2.0]) - theta0 = jnp.zeros(matrix.shape[1]) - init_damping = 0.1 - L = jnp.array( - [ - [2.0, 0.0, 0.0], - [0.3, 1.5, 0.0], - [-0.2, 0.4, 1.2], - ] - ) - metric_matrix = L @ L.T - solver_kwargs = {} - if linear_solver == "gram_cg": - solver_kwargs = { - "iterative_tol": 1e-7, - "iterative_maxiter": 30, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - - solver = LevenbergMarquardt( - residual, - init_damping=init_damping, - linear_solver=linear_solver, - metric=metric_from_cholesky(L), - **solver_kwargs, - ) - theta, lm_state, info = solver.update( - theta0, solver.init(theta0, (matrix, target)), (matrix, target) - ) - - expected_step = jnp.linalg.solve( - matrix.T @ matrix + init_damping * metric_matrix, - matrix.T @ target, - ) - expected_loss = jnp.sum((matrix @ expected_step - target) ** 2) - - assert bool(info.accepted) - assert not bool(info.used_geodesic) - assert jnp.allclose(theta, expected_step, rtol=1e-5, atol=1e-5) - assert jnp.allclose(info.loss, expected_loss, rtol=1e-5, atol=1e-5) - assert jnp.allclose(lm_state.damping, init_damping * 0.5) - - -def test_geodesic_step_matches_regression_values(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - geodesic_acceleration=True, - geodesic_acceptance_ratio=10.0, - ) - - new_x, lm_state, info = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(info.accepted) - assert bool(info.used_geodesic) - assert jnp.allclose( - new_x["a"], - jnp.asarray(1.9073810577392578), - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert jnp.allclose( - new_x["b"], - jnp.asarray(-0.9168586730957031), - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert float(info.loss) == pytest.approx(0.029626082628965378, abs=REGRESSION_ATOL) - assert float(info.loss_old) == pytest.approx(5.599210739135742, abs=REGRESSION_ATOL) - assert float(info.loss_candidate) == pytest.approx( - 0.029626082628965378, abs=REGRESSION_ATOL - ) - assert float(lm_state.damping) == pytest.approx(0.004999999888241291) - assert float(info.damping_factor) == pytest.approx(0.5) - assert float(info.acceleration_ratio) == pytest.approx( - 0.8667416572570801, abs=REGRESSION_ATOL - ) - - -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "gram_cg", "qr", "augmented_qr"] -) -def test_metric_geodesic_acceleration_ratio_uses_metric_norm(linear_solver): - def residual(theta, _, p): - return jnp.array( - [ - theta[0] ** 2 + theta[1] - 1.0, - theta[0] + theta[1] ** 2 - 1.0, - ] - ) - - theta0 = jnp.array([0.4, 1.2]) - init_damping = 0.1 - L = jnp.array([[3.0, 0.0], [0.2, 0.5]]) - metric_matrix = L @ L.T - metric = metric_from_cholesky(L) - solver_kwargs = {} - if linear_solver == "gram_cg": - solver_kwargs = { - "iterative_tol": 1e-7, - "iterative_maxiter": 30, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - solver = LevenbergMarquardt( - residual, - init_damping=init_damping, - linear_solver=linear_solver, - geodesic_acceleration=True, - geodesic_acceptance_ratio=100.0, - metric=metric, - **solver_kwargs, - ) - - _, _, info = solver.update(theta0, solver.init(theta0, None), None) - - resid = residual(theta0, None, None) - jacobian = jnp.array([[2.0 * theta0[0], 1.0], [1.0, 2.0 * theta0[1]]]) - normal_matrix = jacobian.T @ jacobian + init_damping * metric_matrix - velocity = -jnp.linalg.solve(normal_matrix, jacobian.T @ resid) - f_vv = jnp.array([2.0 * velocity[0] ** 2, 2.0 * velocity[1] ** 2]) - acceleration = -jnp.linalg.solve(normal_matrix, jacobian.T @ f_vv) - metric_ratio = ( - 2.0 - * metric.norm(acceleration) - / (metric.norm(velocity) + jnp.finfo(theta0.dtype).eps) - ) - euclidean_ratio = ( - 2.0 - * jnp.linalg.norm(acceleration) - / (jnp.linalg.norm(velocity) + jnp.finfo(theta0.dtype).eps) - ) - - assert jnp.allclose(info.acceleration_ratio, metric_ratio, rtol=1e-5, atol=1e-5) - assert not jnp.allclose(metric_ratio, euclidean_ratio, rtol=1e-3, atol=1e-3) - - -def test_custom_metric_update_jits_and_matches_closed_form_solution(): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 2.0, -0.5], [0.3, -1.0, 1.5]]) - target = jnp.array([1.0, -2.0]) - theta0 = jnp.zeros(matrix.shape[1]) - L = jnp.array( - [ - [2.0, 0.0, 0.0], - [0.3, 1.5, 0.0], - [-0.2, 0.4, 1.2], - ] - ) - metric_matrix = L @ L.T - init_damping = 0.1 - solver = LevenbergMarquardt( - residual, - init_damping=init_damping, - metric=metric_from_cholesky(L), - ) - - @jax.jit - def train_step(theta, lm_state): - return solver.update(theta, lm_state, (matrix, target)) - - theta, lm_state, info = train_step(theta0, solver.init(theta0, (matrix, target))) - expected_step = jnp.linalg.solve( - matrix.T @ matrix + init_damping * metric_matrix, - matrix.T @ target, - ) - - assert bool(info.accepted) - assert jnp.allclose(theta, expected_step, rtol=1e-5, atol=1e-5) - assert jnp.isfinite(lm_state.damping) - assert jnp.isfinite(info.loss) - - -def test_init_lm_state_matches_update_signature(): - # init() and update() must produce the same jit signature for `damping` - # (strongly typed, matching dtype), or the second step recompiles. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - - lm_state0 = solver.init(x, (ts, ys)) - _, lm_state1, _ = solver.update(x, lm_state0, (ts, ys)) - d0, d1 = lm_state0.damping, lm_state1.damping - assert (d0.dtype, d0.weak_type, d0.shape) == (d1.dtype, d1.weak_type, d1.shape) - assert d0.weak_type is False - assert d0.dtype == jnp.result_type(float) - - -def test_solve_converges_with_args_and_p_jit_modes(): - def residual(theta, args, p): - return theta - (args + p) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - theta0 = jnp.array([0.0]) - args = jnp.array([1.25]) - p = jnp.array([0.75]) - - jit_result = solver.solve(theta0, args, p=p, max_steps=40, atol=1e-6) - python_result = solver.solve(theta0, args, p=p, max_steps=40, atol=1e-6, jit=False) - - assert int(jit_result.status) == LMStatus.CONVERGED - assert int(python_result.status) == LMStatus.CONVERGED - assert jnp.allclose(jit_result.x, jnp.array([2.0]), atol=1e-5) - assert jnp.allclose(jit_result.x, python_result.x, atol=1e-6) - assert jnp.allclose(jit_result.p, p) - assert jit_result.steps <= 40 - - -def test_solve_reports_max_steps_without_atol_convergence(): - def residual(theta, args, p): - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve(jnp.array([0.0]), jnp.array([1.0]), max_steps=3, atol=0.0) - - assert int(result.status) == LMStatus.MAX_STEPS - assert int(result.steps) == 3 - assert jnp.isfinite(result.info.loss) - - with pytest.raises(TypeError, match="max_steps_is_success must be a bool"): - solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=3, - max_steps_is_success=1, - ) - - -def test_solve_callback_can_abort_on_nonfinite_candidate(): - def residual(theta, _, __): - return jnp.where(theta[0] > 0.0, theta + 1.0, jnp.asarray([jnp.nan])) - - def callback(ctx): - nonfinite = ~jnp.isfinite(ctx.info.loss_candidate) - return LMSolveAction(stop=nonfinite, status=LMStatus.NONFINITE) - - solver = LevenbergMarquardt(residual, init_damping=1e-3) - theta0 = jnp.array([0.1]) - result = solver.solve(theta0, max_steps=5, callback=callback) - - assert int(result.status) == LMStatus.NONFINITE - assert int(result.steps) == 1 - assert jnp.allclose(result.x, theta0) - assert jnp.isfinite(result.info.loss) - assert not jnp.isfinite(result.info.loss_candidate) - - -def test_solve_callback_updates_args_and_user_state(): - def residual(theta, args, _): - return theta - args - - def callback(ctx): - next_args = jnp.where(ctx.step == 1, jnp.asarray([2.0]), ctx.args) - return LMSolveAction(args=next_args, user_state=ctx.user_state + ctx.info.loss) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=2, - callback=callback, - user_state=jnp.asarray(0.0), - ) - - assert int(result.status) == LMStatus.MAX_STEPS - assert int(result.steps) == 2 - assert jnp.allclose(result.args, jnp.array([2.0])) - assert result.x[0] > 1.0 - assert result.user_state > 0.0 - - -def test_solve_save_steps_matches_manual_update_loop(): - a_true, b_true = 2.0, -1.0 - ts = jnp.linspace(0.0, 2.0, 20) - ys = a_true * jnp.exp(b_true * ts) - x0 = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - - result = solver.solve(x0, (ts, ys), max_steps=8, save_steps=True) - assert int(result.steps) == 8 - assert result.aux_history is None - # args never change: every args_history row repeats the initial pytree. - assert result.args_history[0].shape == (9, *ts.shape) - assert jnp.all(result.args_history[0] == ts) - assert jnp.all(result.args_history[1] == ys) - - x, lm_state = x0, solver.init(x0, (ts, ys)) - iterates = [x0] - for _ in range(8): - x, lm_state, _ = solver.update(x, lm_state, (ts, ys)) - iterates.append(x) - for s, expected in enumerate(iterates): - assert jnp.allclose(result.x_history["a"][s], expected["a"]) - assert jnp.allclose(result.x_history["b"][s], expected["b"]) - assert jnp.allclose(result.x_history["a"][-1], result.x["a"]) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_save_steps_pads_rows_beyond_steps(jit): - def residual(theta, args): - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - theta0 = jnp.array([0.0]) - result = solver.solve( - theta0, jnp.array([1.0]), max_steps=20, atol=1e-6, save_steps=True, jit=jit - ) - - steps = int(result.steps) - assert int(result.status) == LMStatus.CONVERGED - assert 0 < steps < 20 - assert result.x_history.shape == (21, 1) - assert jnp.array_equal(result.x_history[0], theta0) - assert jnp.allclose(result.x_history[steps], result.x) - assert jnp.all(result.x_history[steps + 1 :] == 0.0) - assert result.args_history.shape == (21, 1) - assert jnp.all(result.args_history[: steps + 1] == 1.0) - assert jnp.all(result.args_history[steps + 1 :] == 0.0) - - -def test_solve_save_steps_aux_history_aligns_with_iterates(): - def residual(theta, args): - return theta - args, {"total": jnp.sum(theta), "sq": theta**2} - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - result = solver.solve( - jnp.array([0.0, 0.5]), - jnp.array([1.0, -1.0]), - max_steps=15, - atol=1e-6, - save_steps=True, - ) - - steps = int(result.steps) - for s in range(steps + 1): - x_s = result.x_history[s] - assert jnp.allclose(result.aux_history["total"][s], jnp.sum(x_s)) - assert jnp.allclose(result.aux_history["sq"][s], x_s**2) - assert jnp.allclose(result.aux_history["total"][steps], result.aux["total"]) - - -def test_solve_save_steps_composes_with_callback_and_user_state(): - def residual(theta, args): - return theta - args - - def callback(ctx): - replaced = jnp.where(ctx.step == 1, jnp.asarray([5.0]), ctx.x) - return LMSolveAction(x=replaced, user_state=ctx.user_state + 1.0) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=3, - callback=callback, - user_state=jnp.asarray(0.0), - save_steps=True, - ) - - # x_history records the kept post-action iterate. - assert jnp.allclose(result.x_history[1], jnp.array([5.0])) - assert int(result.user_state) == int(result.steps) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_save_steps_records_args_replacement(jit): - def residual(theta, args): - return theta - args - - def callback(ctx): - replaced = jnp.where(ctx.step == 2, jnp.asarray([3.0]), ctx.args) - return LMSolveAction(args=replaced) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=4, - callback=callback, - save_steps=True, - jit=jit, - ) - - assert int(result.steps) == 4 - # Row s holds the kept post-action args after step s: the original args - # through step 1, the replacement from step 2 onward. - assert jnp.array_equal(result.args_history[0], jnp.array([1.0])) - assert jnp.array_equal(result.args_history[1], jnp.array([1.0])) - for s in range(2, 5): - assert jnp.array_equal(result.args_history[s], jnp.array([3.0])) - assert jnp.array_equal(result.args_history[-1], result.args) - - -def test_solve_save_steps_args_history_none_without_args(): - def residual(theta): - return theta - 1.0 - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve(jnp.array([0.0]), max_steps=5, atol=1e-6, save_steps=True) - - assert result.args_history is None - assert result.x_history.shape == (6, 1) - - -def test_vmap_over_solve_save_steps_keeps_per_lane_padding(): - def residual(theta, _, p): - return theta - p["target"] - - def callback(ctx): - return LMSolveAction(stop=ctx.step >= ctx.p["stop_after"]) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - x0s = jnp.zeros((3, 1)) - p = { - "target": jnp.arange(1.0, 4.0)[:, None], - "stop_after": jnp.arange(1, 4, dtype=jnp.int32), - } - - def solve_one(x0, p_one): - return solver.solve( - x0, p=p_one, max_steps=6, callback=callback, save_steps=True - ) - - batched = jax.vmap(solve_one)(x0s, p) - assert batched.x_history.shape == (3, 7, 1) - for i in range(3): - single = solve_one(x0s[i], jax.tree.map(lambda leaf, i=i: leaf[i], p)) - assert int(batched.steps[i]) == int(single.steps) - # Lanes that stop early must keep their rows frozen while other lanes - # continue, so the padding beyond each lane's steps stays zero. - assert jnp.allclose(batched.x_history[i], single.x_history, atol=1e-6) - assert jnp.all(batched.x_history[i, int(batched.steps[i]) + 1 :] == 0.0) - - -def test_solve_save_steps_histories_are_differentiation_inert(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]), {"s": jnp.sum(theta)} - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - theta0 = jnp.zeros(2) - - def solved(p): - result = solver.solve(theta0, p=p, max_steps=80, atol=1e-8, save_steps=True) - return result.x, result.x_history, result.aux_history - - p, p_dot = jnp.asarray(3.0), jnp.asarray(0.7) - (_, x_hist, _), (x_dot, x_hist_dot, aux_hist_dot) = jax.jvp(solved, (p,), (p_dot,)) - assert jnp.allclose(x_dot, jnp.array([p_dot / 5.0, 2.0 * p_dot / 5.0]), atol=1e-6) - assert jnp.all(x_hist_dot == 0.0) - assert jnp.all(aux_hist_dot["s"] == 0.0) - - # Reverse mode: cotangents on the histories pull back to zero, while the - # solution cotangent still flows through the implicit rule. - grad_p = jax.grad(lambda p_: jnp.sum(solved(p_)[0]) + jnp.sum(solved(p_)[1]))(p) - assert jnp.allclose(grad_p, 3.0 / 5.0, atol=1e-6) - - -def test_vmap_over_solve_callback_stops_per_lane(): - def residual(theta, _, p): - return theta - p["target"] - - def callback(ctx): - stop = ctx.step >= ctx.p["stop_after"] - return LMSolveAction(stop=stop, status=100 + ctx.p["stop_after"]) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - x0s = jnp.zeros((4, 1)) - p = { - "target": jnp.arange(1.0, 5.0)[:, None], - "stop_after": jnp.arange(1, 5, dtype=jnp.int32), - } - - def solve_one(x0, p_one): - return solver.solve(x0, p=p_one, max_steps=8, atol=0.0, callback=callback) - - batched = jax.vmap(solve_one)(x0s, p) - loop = jax.tree.map( - lambda *xs: jnp.stack(xs), - *[ - solve_one(x0s[i], jax.tree.map(lambda leaf, i=i: leaf[i], p)) - for i in range(x0s.shape[0]) - ], - ) - - assert jnp.array_equal(batched.steps, p["stop_after"]) - assert jnp.array_equal(batched.steps, loop.steps) - assert jnp.array_equal(batched.status, loop.status) - assert jnp.allclose(batched.x, loop.x, atol=1e-6) - - -@pytest.mark.parametrize("save_steps", [False, True]) -def test_vmap_over_solve_heterogeneous_convergence_matches_sequential(save_steps): - def residual(theta, _, p): - return theta - p["target"] - - solver = LevenbergMarquardt(residual, init_damping=1.0) - x0s = jnp.zeros((2, 1)) - p = {"target": jnp.array([[1e-4], [3.0]])} - atol = 1e-5 - - def solve_one(x0, p_one): - return solver.solve(x0, p=p_one, max_steps=60, atol=atol, save_steps=save_steps) - - batched = jax.vmap(solve_one)(x0s, p) - for i in range(2): - single = solve_one(x0s[i], jax.tree.map(lambda leaf, i=i: leaf[i], p)) - assert int(batched.steps[i]) == int(single.steps) - assert int(batched.status[i]) == int(single.status) == LMStatus.CONVERGED - assert jnp.allclose(batched.x[i], single.x, atol=1e-6) - assert jnp.linalg.norm(batched.x[i] - p["target"][i]) < atol - if save_steps: - assert jnp.allclose(batched.x_history[i], single.x_history, atol=1e-6) - # A lane whose convergence fired must never keep writing rows while - # the slower lane continues, so its padding stays exactly zero. - assert jnp.all(batched.x_history[i, int(batched.steps[i]) + 1 :] == 0.0) - assert int(batched.steps[0]) < int(batched.steps[1]) - - -@pytest.mark.parametrize("save_steps", [False, True]) -def test_vmap_over_solve_epoch_conditional_callback_early_stop(save_steps): - steps_per_epoch = 3 - init_damping = 1.0 - - def residual(theta, _, p): - return theta - p["target"] - - solver = LevenbergMarquardt(residual, init_damping=init_damping) - - # Epoch-boundary early stopping: the expensive check runs only every - # steps_per_epoch steps behind a lax.cond, which under vmap lowers to a - # select that evaluates both branches for every lane; per-lane stops must - # still bind exactly as in the sequential solves. - def callback(ctx): - def epoch_boundary(_): - r = ctx.x - ctx.p["target"] - stop = jnp.sum(r * r) < ctx.p["threshold"] - status = jnp.where(stop, LMStatus.CONVERGED, LMStatus.RUNNING) - return ( - stop, - status.astype(jnp.int32), - jnp.asarray(init_damping, ctx.lm_state.damping.dtype), - ) - - def mid_epoch(_): - # RUNNING is the no-op status: solve only reads it when stop fires. - return ( - jnp.asarray(False), - jnp.asarray(LMStatus.RUNNING, dtype=jnp.int32), - ctx.lm_state.damping, - ) - - stop, status, damping = jax.lax.cond( - ctx.step % steps_per_epoch == 0, epoch_boundary, mid_epoch, None - ) - return LMSolveAction( - stop=stop, - status=status, - lm_state=dataclasses.replace(ctx.lm_state, damping=damping), - ) - - x0s = jnp.zeros((2, 1)) - p = { - "target": jnp.full((2, 1), 2.0), - "threshold": jnp.array([1e-2, 1e-7]), - } - - def solve_one(x0, p_one): - return solver.solve( - x0, - p=p_one, - max_steps=30, - atol=0.0, - callback=callback, - save_steps=save_steps, - ) - - batched = jax.vmap(solve_one)(x0s, p) - for i in range(2): - single = solve_one(x0s[i], jax.tree.map(lambda leaf, i=i: leaf[i], p)) - assert int(batched.steps[i]) == int(single.steps) - assert int(batched.status[i]) == int(single.status) == LMStatus.CONVERGED - assert int(batched.steps[i]) % steps_per_epoch == 0 - assert jnp.allclose(batched.x[i], single.x, atol=1e-6) - assert jnp.sum((batched.x[i] - p["target"][i]) ** 2) < p["threshold"][i] - if save_steps: - assert jnp.allclose(batched.x_history[i], single.x_history, atol=1e-6) - assert jnp.all(batched.x_history[i, int(batched.steps[i]) + 1 :] == 0.0) - assert int(batched.steps[0]) < int(batched.steps[1]) - - -def test_vmap_over_solve_tolerances(): - def residual(theta, _, p): - return theta - p - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - x0 = jnp.zeros(1) - target = jnp.array([2.0]) - atols = jnp.array([5e-2, 1e-5]) - - def solve_one(atol): - return solver.solve(x0, p=target, max_steps=100, atol=atol) - - batched = jax.vmap(solve_one)(atols) - for i in range(2): - single = solve_one(atols[i]) - assert int(batched.steps[i]) == int(single.steps) - assert int(batched.status[i]) == int(single.status) == LMStatus.CONVERGED - assert jnp.allclose(batched.x[i], single.x, atol=1e-6) - # The tight-tolerance lane keeps iterating after the loose lane stopped. - assert int(batched.steps[1]) > int(batched.steps[0]) - - -def test_svd_and_augmented_qr_handle_redundant_rows_explicitly(): - # Two identical residual rows: the undamped implicit dual J J' is singular - # (rank 1) everywhere, but the system is consistent and x*(p) is smooth - # with minimum-norm derivative d x* / d target = w / ||w||^2 from x0 = 0. - # The default eps * trace ridge resolves it to that min-norm tangent. - w = jnp.array([1.0, 2.0, 3.0]) - - def duplicated_rows_residual(x, args, p): - row = jnp.dot(w, x) - p["target"] - return jnp.stack([row, row]) - - x0 = jnp.zeros(3) - p = {"target": 1.0} - expected = jnp.sum(w) / jnp.dot(w, w) - - def sum_x_star(solver, p): - return jnp.sum(solver.solve(x0, p=p, max_steps=50).x) - - svd = LevenbergMarquardt(duplicated_rows_residual, ad_solver="svd") - vjp_grad = jax.jacobian(lambda p: sum_x_star(svd, p))(p)["target"] - assert jnp.allclose(vjp_grad, expected, rtol=1e-4) - _, jvp_grad = jax.jvp(lambda t: sum_x_star(svd, {"target": t}), (1.0,), (1.0,)) - assert jnp.allclose(jvp_grad, expected, rtol=1e-4) - - # An explicit (larger) penalty is plumbed through and still resolves the - # singular dual; the bias grows with the penalty but stays O(penalty * m). - blunt = LevenbergMarquardt( - duplicated_rows_residual, - ad_solver="augmented_qr", - ad_solver_penalty=1e-4, - ) - blunt_grad = jax.jacobian(lambda p: sum_x_star(blunt, p))(p)["target"] - assert jnp.isfinite(blunt_grad) - assert jnp.allclose(blunt_grad, expected, rtol=1e-3) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_implicit_jvp_and_vjp_wrt_p_match_underdetermined_root(jit): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - theta0 = jnp.zeros(2) - - def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6, jit=jit).x - - p = jnp.asarray(3.0) - p_dot = jnp.asarray(0.7) - x, x_dot = jax.jvp(solved_x, (p,), (p_dot,)) - expected_x = jnp.array([3.0 / 5.0, 6.0 / 5.0]) - expected_x_dot = jnp.array([p_dot / 5.0, 2.0 * p_dot / 5.0]) - - _, pullback = jax.vjp(solved_x, p) - (p_cotangent,) = pullback(jnp.array([3.0, 4.0])) - expected_p_cotangent = (3.0 + 2.0 * 4.0) / 5.0 - - assert jnp.allclose(x, expected_x, atol=1e-5) - assert jnp.allclose(x_dot, expected_x_dot, atol=1e-6) - assert jnp.allclose(p_cotangent, expected_p_cotangent, atol=1e-6) - - -def test_implicit_cg_jvp_and_vjp_match_cholesky_with_metric(): - with jax.default_device(jax.devices("cpu")[0]): - matrix = jnp.array([[1.0, 2.0, -0.5, 0.3], [0.2, -1.0, 1.5, 2.0]]) - target_matrix = jnp.array([[1.0, -0.5, 0.7], [0.3, 1.2, -1.0]]) - L = jnp.array( - [ - [2.0, 0.0, 0.0, 0.0], - [0.3, 1.5, 0.0, 0.0], - [-0.2, 0.4, 1.2, 0.0], - [0.1, -0.1, 0.2, 1.7], - ] - ) - - def residual(theta, _, p): - return matrix @ theta - target_matrix @ p - - common = dict( - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-7, - iterative_maxiter=30, - dual_preconditioner=identity_preconditioner(), - metric=metric_from_cholesky(L), - geodesic_acceleration=False, - ) - dense_implicit = LevenbergMarquardt(residual, ad_solver="svd", **common) - cg_implicit = LevenbergMarquardt( - residual, - ad_solver="gram_cg", - ad_solver_tol=1e-7, - ad_solver_preconditioner=identity_preconditioner(), - **common, - ) - theta0 = jnp.zeros(matrix.shape[1]) - - def solved_x(solver, p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - p = jnp.array([1.0, -0.5, 0.25]) - p_dot = jnp.array([0.2, -0.1, 0.3]) - _, dense_dot = jax.jvp(lambda q: solved_x(dense_implicit, q), (p,), (p_dot,)) - _, cg_dot = jax.jvp(lambda q: solved_x(cg_implicit, q), (p,), (p_dot,)) - - theta_bar = jnp.array([0.4, -0.2, 0.7, 0.1]) - _, dense_pullback = jax.vjp(lambda q: solved_x(dense_implicit, q), p) - _, cg_pullback = jax.vjp(lambda q: solved_x(cg_implicit, q), p) - (dense_bar,) = dense_pullback(theta_bar) - (cg_bar,) = cg_pullback(theta_bar) - - assert jnp.allclose(cg_dot, dense_dot, rtol=1e-5, atol=1e-5) - assert jnp.allclose(cg_bar, dense_bar, rtol=1e-5, atol=1e-5) - - -def test_implicit_cg_sign_and_transpose_match_closed_form(): - matrix = jnp.array([[1.0, 2.0, -0.5, 0.3], [0.2, -1.0, 1.5, 2.0]]) - target_matrix = jnp.array([[1.0, -0.5, 0.7], [0.3, 1.2, -1.0]]) - metric_weights = jnp.array([2.0, 0.5, 1.5, 3.0]) - metric_inverse = jnp.diag(1.0 / metric_weights) - - def residual(theta, _, p): - return matrix @ theta - target_matrix @ p - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=30, - ad_solver="gram_cg", - ad_solver_tol=1e-7, - metric=metric_from_diagonal(metric_weights), - geodesic_acceleration=False, - ) - theta0 = jnp.zeros(matrix.shape[1]) - - def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - p = jnp.array([0.7, -1.0, 0.4]) - p_dot = jnp.array([0.2, -0.1, 0.3]) - theta_bar = jnp.array([0.4, -0.2, 0.7, 0.1]) - gram = matrix @ metric_inverse @ matrix.T - expected_dot = metric_inverse @ matrix.T @ _solve_2x2(gram, target_matrix @ p_dot) - expected_bar = target_matrix.T @ _solve_2x2( - gram, matrix @ metric_inverse @ theta_bar - ) - - _, theta_dot = jax.jvp(solved_x, (p,), (p_dot,)) - _, pullback = jax.vjp(solved_x, p) - (p_bar,) = pullback(theta_bar) - - assert jnp.allclose(theta_dot, expected_dot, rtol=1e-5, atol=1e-5) - assert jnp.allclose(p_bar, expected_bar, rtol=1e-5, atol=1e-5) - assert jnp.allclose(theta_dot @ theta_bar, p_dot @ p_bar, atol=1e-5) - - -def test_implicit_cg_jvp_and_vjp_jit(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ad_solver="auto", - ad_solver_tol=1e-7, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - @jax.jit - def jitted_jvp(p, p_dot): - return jax.jvp(solved_x, (p,), (p_dot,))[1] - - @jax.jit - def jitted_vjp(p, theta_bar): - _, pullback = jax.vjp(solved_x, p) - return pullback(theta_bar)[0] - - p = jnp.asarray(3.0) - assert jnp.allclose( - jitted_jvp(p, jnp.asarray(0.7)), - jnp.array([0.7 / 5.0, 1.4 / 5.0]), - atol=1e-6, - ) - assert jnp.allclose( - jitted_vjp(p, jnp.array([3.0, 4.0])), - (3.0 + 2.0 * 4.0) / 5.0, - atol=1e-6, - ) - - -def test_implicit_cg_jaxpr_does_not_materialize_dense_jacobian_transpose(): - n = 257 - grid = jnp.linspace(0.0, 1.0, n) - row0 = jnp.sin(2.0 * jnp.pi * grid) + 1.5 - row1 = jnp.cos(3.0 * jnp.pi * grid) - 0.25 - row2 = grid + 0.1 - - def residual(theta, _, p): - return jnp.stack( - ( - jnp.vdot(row0, theta) - p[0], - jnp.vdot(row1, theta) - p[1], - jnp.vdot(row2, theta) - p[2], - ) - ) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-6, - iterative_maxiter=5, - ad_solver="auto", - ad_solver_tol=1e-6, - ad_solver_maxiter=5, - geodesic_acceleration=False, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(n), p=p, max_steps=1, atol=0.0).x - - jaxpr = str( - jax.make_jaxpr(lambda p, p_dot: jax.jvp(solved_x, (p,), (p_dot,))[1])( - jnp.array([1.0, -0.5, 0.25]), - jnp.array([0.2, -0.1, 0.3]), - ) - ) - - assert f"f32[{n},3]" not in jaxpr - assert f"f32[3,{n}]" not in jaxpr - - -def test_vmap_over_solve_matches_loop_and_implicit_ad(): - matrix = jnp.array([[1.0, 0.5, -0.2, 0.1], [0.3, -0.7, 0.4, 1.0]]) - gram = matrix @ matrix.T - right_inverse = matrix.T @ jnp.linalg.inv(gram) - - def residual(theta, _, p): - return matrix @ theta - p - - solver = LevenbergMarquardt( - residual, init_damping=1e-2, geodesic_acceleration=False - ) - ps = jnp.array([[1.0, -0.5], [0.25, 0.75], [-1.2, 0.2], [0.1, -1.4]]) - x0s = jnp.zeros((ps.shape[0], matrix.shape[1])) - - def solve_one(x0, p): - return solver.solve(x0, p=p, max_steps=80, atol=1e-5) - - batched = jax.vmap(solve_one)(x0s, ps) - loop = jax.tree.map( - lambda *xs: jnp.stack(xs), - *[solve_one(x0s[i], ps[i]) for i in range(ps.shape[0])], - ) - expected_x = jax.vmap(lambda p: right_inverse @ p)(ps) - - assert jnp.array_equal(batched.status, loop.status) - assert jnp.array_equal(batched.steps, loop.steps) - assert jnp.allclose(batched.x, loop.x, atol=1e-6) - assert jnp.allclose(batched.x, expected_x, atol=1e-4) - - p_dot = jnp.array([[0.2, -0.1], [0.0, 0.3], [0.7, -0.4], [-0.2, 0.5]]) - - def vmapped_x(p_batch): - return jax.vmap(lambda p: solve_one(jnp.zeros(matrix.shape[1]), p).x)(p_batch) - - _, x_dot = jax.jvp(vmapped_x, (ps,), (p_dot,)) - expected_x_dot = jax.vmap(lambda dp: right_inverse @ dp)(p_dot) - assert jnp.allclose(x_dot, expected_x_dot, atol=1e-5) - - cotangent = jnp.array( - [ - [0.1, -0.2, 0.3, 0.0], - [0.0, 0.4, -0.1, 0.2], - [-0.3, 0.2, 0.1, 0.5], - [0.7, -0.1, 0.0, -0.4], - ] - ) - _, pullback = jax.vjp(vmapped_x, ps) - (p_bar,) = pullback(cotangent) - expected_p_bar = jax.vmap(lambda c: jnp.linalg.solve(gram, matrix @ c))(cotangent) - assert jnp.allclose(p_bar, expected_p_bar, atol=1e-5) - - -@pytest.mark.parametrize("linear_solver", ["gram_cholesky", "qr", "augmented_qr"]) -def test_solve_implicit_jvp_wrt_p_uses_metric(linear_solver): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - metric_matrix = jnp.array([[4.0, 0.0], [0.0, 1.0]]) - metric_inverse = jnp.linalg.inv(metric_matrix) - jacobian = jnp.array([[1.0, 2.0]]) - full_metric = metric_from_cholesky(jnp.linalg.cholesky(metric_matrix)) - metric = ( - full_metric - if linear_solver == "gram_cholesky" - else GramMetric( - inv_sqrt=full_metric.inv_sqrt, - inv_sqrt_transpose=full_metric.inv_sqrt_transpose, - ) - ) - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver=linear_solver, - metric=metric, - # The QR cases deliberately supply a square-root-only metric (no - # norm), which the geodesic default would reject at construction. - geodesic_acceleration=False, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - p_dot = jnp.asarray(0.7) - _, x_dot = jax.jvp(solved_x, (jnp.asarray(3.0),), (p_dot,)) - expected_x_dot = ( - metric_inverse - @ jacobian.T - @ jnp.linalg.solve(jacobian @ metric_inverse @ jacobian.T, jnp.array([p_dot])) - ).ravel() - - assert jnp.allclose(x_dot, expected_x_dot, atol=1e-6) - - -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "gram_cg", "qr", "augmented_qr", "lsmr"] -) -def test_grad_norm_and_step_norm_match_closed_form(linear_solver): - def residual(theta, args, p): - matrix, target = args - return matrix @ theta - target - - matrix = jnp.array([[1.0, 2.0, 0.5, -1.0], [0.0, 1.0, 3.0, 2.0]]) - target = jnp.array([1.0, -2.0]) - theta0 = jnp.zeros(matrix.shape[1]) - init_damping = 0.1 - solver_kwargs = {} - if linear_solver == "gram_cg": - solver_kwargs = { - "iterative_tol": 1e-7, - "iterative_maxiter": 30, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - elif linear_solver == "lsmr": - solver_kwargs = {"iterative_tol": 1e-10, "iterative_maxiter": 50} - - solver = LevenbergMarquardt( - residual, - init_damping=init_damping, - linear_solver=linear_solver, - **solver_kwargs, - ) - _, _, info = solver.update( - theta0, solver.init(theta0, (matrix, target)), (matrix, target) - ) - - expected_grad = matrix.T @ (matrix @ theta0 - target) - expected_step = jnp.linalg.solve( - matrix.T @ matrix + init_damping * jnp.eye(matrix.shape[1]), - matrix.T @ target, - ) - - assert jnp.allclose( - info.grad_norm, jnp.linalg.norm(expected_grad), rtol=1e-5, atol=1e-5 - ) - assert jnp.allclose( - info.step_norm, jnp.linalg.norm(expected_step), rtol=1e-5, atol=1e-5 - ) - - -def test_rejected_step_still_reports_step_norm(): - # The candidate step leaves theta = 0, producing a NaN residual, so every - # step is rejected; the attempted step norm must still be reported. - def residual(theta, _, __): - return jnp.where(theta[0] == 0.0, theta + 1.0, jnp.full_like(theta, jnp.nan)) - - solver = LevenbergMarquardt(residual, init_damping=1.0) - _, _, info = solver.update(jnp.zeros(1), solver.init(jnp.zeros(1))) - - assert not bool(info.accepted) - assert float(info.step_norm) == pytest.approx(0.5) - assert float(info.grad_norm) == pytest.approx(1.0) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_gtol_reports_converged(jit): - def residual(theta, args, p): - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), jnp.array([1.0]), max_steps=50, gtol=1e-6, jit=jit - ) - - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.grad_norm) < 1e-6 - assert int(result.steps) < 50 - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_xtol_reports_converged_on_accepted_step(jit): - def residual(theta, args, p): - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), jnp.array([1.0]), max_steps=50, xtol=1e-6, jit=jit - ) - - assert int(result.status) == LMStatus.CONVERGED - assert bool(result.info.accepted) - assert float(result.info.step_norm) < 1e-6 - assert int(result.steps) < 50 - - -def test_solve_xtol_ignores_rejected_steps(): - def residual(theta, _, __): - return jnp.where(theta[0] == 0.0, theta + 1.0, jnp.full_like(theta, jnp.nan)) - - solver = LevenbergMarquardt(residual, init_damping=1.0, max_damping=1e6) - result = solver.solve(jnp.zeros(1), max_steps=30, xtol=10.0) - - assert int(result.status) == LMStatus.MAX_STEPS - assert int(result.steps) == 30 - assert not bool(result.info.accepted) - - -def test_max_damping_caps_growth_under_repeated_rejection(): - def residual(theta, _, __): - return jnp.where(theta[0] == 0.0, theta + 1.0, jnp.full_like(theta, jnp.nan)) - - capped = LevenbergMarquardt(residual, init_damping=1e-3, max_damping=1e4) - result = capped.solve(jnp.zeros(1), max_steps=100) - assert int(result.status) == LMStatus.MAX_STEPS - assert float(result.lm_state.damping) == pytest.approx(1e4) - - uncapped = LevenbergMarquardt(residual, init_damping=1e-3) - result = uncapped.solve(jnp.zeros(1), max_steps=100) - assert not jnp.isfinite(result.lm_state.damping) - - -def test_solve_does_not_retrace_on_loop_control_changes(): - traces = {"count": 0} - - def residual(theta, args, p): - traces["count"] += 1 - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2, cache_jacobian=False) - solver.solve(jnp.array([0.0]), jnp.array([1.0]), max_steps=10, atol=1e-6) - count_after_first = traces["count"] - solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=25, - atol=1e-8, - gtol=1e-9, - xtol=1e-9, - ) - - assert traces["count"] == count_after_first - - -def test_equal_settings_solvers_share_the_compiled_solve_loop(): - traces = {"count": 0} - - def residual(theta, args, p): - traces["count"] += 1 - return theta - args - - def build(**overrides): - settings = dict(init_damping=1e-2, cache_jacobian=False) - settings.update(overrides) - return LevenbergMarquardt(residual, **settings) - - a, b = build(), build() - assert a == b - assert hash(a) == hash(b) - - a.solve(jnp.array([0.0]), jnp.array([1.0]), max_steps=10, atol=1e-6) - count_after_first = traces["count"] - b.solve(jnp.array([0.0]), jnp.array([1.0]), max_steps=10, atol=1e-6) - assert traces["count"] == count_after_first - - # Any static-setting change (or a different residual function) is a - # different solver, so it cannot silently reuse the wrong compiled loop. - assert a != build(init_damping=2e-2) - assert a != build(min_damping=1e-8) - assert a != build(geodesic_acceleration=False) - assert a != LevenbergMarquardt( - lambda theta, args, p: theta - args, init_damping=1e-2, cache_jacobian=False - ) - # The knobs added by the reconciliation phase must also key the compiled - # loop -- a collision here would silently reuse a loop with the wrong AD - # or assembly behavior, the exact failure this package guards against. - assert a != build(jacobian_mode="rev") - assert a != build(ad_solver="augmented_qr", ad_solver_penalty=1e-6) - assert a != build(ad_solver="svd") - - -@pytest.mark.parametrize("cache_jacobian", [False, True]) -def test_solve_callback_epoch_boundary_resamples_args_and_resets_damping( - cache_jacobian, -): - def residual(theta, args, _): - return theta - args - - steps_per_epoch = 3 - - def callback(ctx): - boundary = ctx.step % steps_per_epoch == 0 - new_args = jnp.where(boundary, ctx.args + 1.0, ctx.args) - new_lm_state = dataclasses.replace( - ctx.lm_state, - damping=jnp.where( - boundary, ctx.initial_lm_state.damping, ctx.lm_state.damping - ), - ) - epochs = ctx.user_state + jnp.where(boundary, 1, 0) - return LMSolveAction(args=new_args, lm_state=new_lm_state, user_state=epochs) - - solver = LevenbergMarquardt( - residual, init_damping=1e-2, cache_jacobian=cache_jacobian - ) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=7, - callback=callback, - user_state=jnp.asarray(0), - ) - - assert int(result.status) == LMStatus.MAX_STEPS - assert int(result.user_state) == 2 - assert jnp.allclose(result.args, jnp.array([3.0])) - # Step 6 reset damping to init; the accepted step 7 halved it once. - assert float(result.lm_state.damping) == pytest.approx(5e-3) - - -def test_callback_returning_args_invalidates_jacobian_cache(): - # theta stays at 0 (every candidate is NaN, so every step is rejected) and - # the cache is therefore valid; when the callback swaps args at step 2, - # step 3 must recompute the residual with the new args. A stale cache - # would report loss_old = 1 (old args) instead of 4 (new args). - def residual(theta, args, _): - return jnp.where(theta[0] == 0.0, theta + args, jnp.full_like(theta, jnp.nan)) - - def callback(ctx): - new_args = jnp.where(ctx.step == 2, jnp.asarray([2.0]), ctx.args) - return LMSolveAction(args=new_args) - - solver = LevenbergMarquardt(residual, init_damping=1.0, cache_jacobian=True) - result = solver.solve( - jnp.zeros(1), jnp.asarray([1.0]), max_steps=3, callback=callback - ) - - assert int(result.status) == LMStatus.MAX_STEPS - assert float(result.info.loss_old) == pytest.approx(4.0) - - -def test_callback_returning_unchanged_args_keeps_jacobian_cache(): - # Every candidate is NaN, so every step is rejected and the cache stays - # valid; a jit-style callback returning args with unchanged values must - # not invalidate it. - def residual(theta, args, _): - return jnp.where(theta[0] == 0.0, theta + args, jnp.full_like(theta, jnp.nan)) - - def callback(ctx): - return LMSolveAction(args=ctx.args) - - solver = LevenbergMarquardt(residual, init_damping=1.0, cache_jacobian=True) - result = solver.solve( - jnp.zeros(1), jnp.asarray([1.0]), max_steps=3, callback=callback - ) - - assert int(result.status) == LMStatus.MAX_STEPS - assert bool(result.lm_state.jacobian_valid) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_callback_changing_args_defers_stale_convergence(jit): - # A callback that swaps args exactly when the old problem meets atol must - # not let solve report CONVERGED for the swapped (x, args) pair; the - # tolerances wait for a fresh update against the new args. - def residual(theta, args, p): - return theta - args - - def callback(ctx): - swap = (jnp.sqrt(ctx.info.loss) < 1e-3) & (ctx.args[0] < 50.0) - return LMSolveAction(args=jnp.where(swap, jnp.asarray([100.0]), ctx.args)) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.zeros(1), - jnp.ones(1), - max_steps=400, - atol=1e-3, - callback=callback, - jit=jit, - ) - - assert int(result.status) == LMStatus.CONVERGED - assert float(result.args[0]) == pytest.approx(100.0) - assert jnp.allclose(result.x, result.args, atol=1e-2) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_callback_echoing_nan_args_still_converges(jit): - # An unchanged NaN sentinel in echoed args is not a change (equal_nan - # comparison) and must not defer the tolerance checks. - def residual(theta, _, __): - return theta - 1.0 - - def callback(ctx): - return LMSolveAction(args=ctx.args) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.zeros(1), - jnp.asarray([jnp.nan]), - max_steps=100, - atol=1e-3, - callback=callback, - jit=jit, - ) - - assert int(result.status) == LMStatus.CONVERGED - assert jnp.allclose(result.x, 1.0, atol=1e-2) - - -def test_callback_bare_lm_state_with_cache_raises_clear_error(): - def residual(theta, args, _): - return theta - args - - def callback(ctx): - return LMSolveAction(lm_state=LMState(ctx.lm_state.damping)) - - solver = LevenbergMarquardt(residual, init_damping=1e-2, cache_jacobian=True) - with pytest.raises(ValueError, match="Jacobian cache"): - solver.solve(jnp.zeros(1), jnp.ones(1), max_steps=3, callback=callback) - - -def test_hyperparams_typing_and_solve_population(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - - # init() stays lean for manual update() loops; solve() populates hyper. - assert solver.init({"a": 1.0, "b": 0.0}, (ts, ys)).hyper is None - hyper = solver.hyperparams(jnp.float32) - assert hyper.damping_decrease.dtype == jnp.float32 - assert hyper.min_damping.dtype == jnp.float32 - assert hyper.min_damping == jnp.finfo(jnp.float32).tiny - assert hyper.iterative_maxiter.dtype == jnp.int32 - assert hyper.max_damping is None - result = solver.solve({"a": 1.0, "b": 0.0}, (ts, ys), max_steps=2) - assert result.lm_state.hyper.damping_decrease.dtype == jnp.float32 - - -def test_bare_lm_state_matches_hyper_lm_state_update(): - # hyper=None falls back to the constructor values, so both states must - # produce the same step. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2, cache_jacobian=False) - - x_hyper, _, info_hyper = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - x_bare, _, info_bare = solver.update( - x, LMState(jnp.asarray(1e-2, dtype=jnp.float32)), (ts, ys) - ) - - assert jnp.allclose(x_hyper["a"], x_bare["a"]) - assert jnp.allclose(x_hyper["b"], x_bare["b"]) - assert jnp.allclose(info_hyper.loss, info_bare.loss) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_callback_grows_cg_budget_when_loss_small(jit): - # The cookbook schedule: cheap CG steps far from the solution, accurate - # ones near it, inside a single solve call. - matrix = jnp.diag(jnp.logspace(0.0, 1.5, 8)) - target = jnp.linspace(1.0, 2.0, 8) - - def residual(theta, _, __): - return matrix @ theta - target - - def grow_budget(ctx): - grown = jnp.asarray(40, dtype=jnp.int32) - new_maxiter = jnp.where( - ctx.info.loss < 1.0, grown, ctx.lm_state.hyper.iterative_maxiter - ) - new_hyper = dataclasses.replace( - ctx.lm_state.hyper, iterative_maxiter=new_maxiter - ) - return LMSolveAction( - lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper) - ) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-1, - linear_solver="gram_cg", - iterative_maxiter=2, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - ) - theta0 = jnp.zeros(8) - fixed = solver.solve(theta0, max_steps=60, jit=jit) - scheduled = solver.solve(theta0, max_steps=60, callback=grow_budget, jit=jit) - - assert int(scheduled.lm_state.hyper.iterative_maxiter) == 40 - assert float(scheduled.info.loss) < 1e-2 * float(fixed.info.loss) - - -def test_callback_resets_max_damping_cap(): - # Every step rejects (NaN candidates), so damping grows; the callback - # tightens the traced cap mid-solve. - def residual(theta, args, _): - return jnp.where(theta[0] == 0.0, theta + args, jnp.full_like(theta, jnp.nan)) - - def cap_damping(ctx): - new_hyper = dataclasses.replace( - ctx.lm_state.hyper, max_damping=jnp.asarray(10.0, dtype=jnp.float32) - ) - return LMSolveAction( - lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper) - ) - - solver = LevenbergMarquardt(residual, init_damping=1.0, max_damping=1e6) - result = solver.solve( - jnp.zeros(1), jnp.asarray([1.0]), max_steps=20, callback=cap_damping - ) - - assert int(result.status) == LMStatus.MAX_STEPS - assert float(result.lm_state.damping) <= 10.0 - - -@pytest.mark.parametrize("jit", [True, False]) -def test_callback_enabling_none_hyper_knob_raises_clear_error(jit): - # max_damping=None is compiled out; flipping it on mid-solve must fail - # identically with and without jit. - def residual(theta, args, p): - return theta - args - - def enable_cap(ctx): - new_hyper = dataclasses.replace( - ctx.lm_state.hyper, max_damping=jnp.asarray(10.0, dtype=jnp.float32) - ) - return LMSolveAction( - lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper) - ) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - with pytest.raises(ValueError, match="enabled mid-solve"): - solver.solve( - jnp.zeros(1), jnp.ones(1), max_steps=3, callback=enable_cap, jit=jit - ) - - -def test_solve_callback_history_buffer_matches_update_loop(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - max_steps = 5 - - def callback(ctx): - history = { - "loss": jax.lax.dynamic_update_slice( - ctx.user_state["loss"], ctx.info.loss[None], (ctx.step - 1,) - ), - "damping": jax.lax.dynamic_update_slice( - ctx.user_state["damping"], ctx.info.damping[None], (ctx.step - 1,) - ), - } - return LMSolveAction(user_state=history) - - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - result = solver.solve( - x, - (ts, ys), - max_steps=max_steps, - callback=callback, - user_state={ - "loss": jnp.zeros(max_steps), - "damping": jnp.zeros(max_steps), - }, - ) - - loop_x, loop_lm_state = x, solver.init(x, (ts, ys)) - for i in range(max_steps): - loop_x, loop_lm_state, info = solver.update(loop_x, loop_lm_state, (ts, ys)) - assert float(result.user_state["loss"][i]) == pytest.approx( - float(info.loss), rel=1e-3, abs=1e-6 - ) - assert float(result.user_state["damping"][i]) == pytest.approx( - float(loop_lm_state.damping), rel=1e-6 - ) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_callback_returning_none_leaves_loop_untouched(jit): - # The cookbook logging pattern: observe the context, return None. - def residual(theta, args, p): - return theta - args - - def logging_callback(ctx): - def log(_): - jax.debug.print( - "step {step}: loss={loss:.3e}", step=ctx.step, loss=ctx.info.loss - ) - - jax.lax.cond(ctx.step % 10 == 0, log, lambda _: None, operand=None) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=40, - atol=1e-6, - callback=logging_callback, - jit=jit, - ) - - assert int(result.status) == LMStatus.CONVERGED - - -def test_one_arg_residual_closes_over_data(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - - def residual(x): - return x["a"] * jnp.exp(x["b"] * ts) - ys - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve({"a": 1.0, "b": 0.0}, max_steps=50, atol=1e-6) - - assert solver.residual_arity == 1 - assert int(result.status) == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], 2.0, atol=1e-4) - - -def test_two_arg_residual_takes_args(): - def residual(x, args): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt(residual, init_damping=1e-2) - x0 = {"a": 1.0, "b": 0.0} - x, lm_state, info = solver.update(x0, solver.init(x0, (ts, ys)), (ts, ys)) - - assert solver.residual_arity == 2 - assert bool(info.accepted) - - -def test_residual_arity_matches_three_arg_solver(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - def one_arg(theta): - return residual_fn(theta, (ts, ys), None) - - one_solver = LevenbergMarquardt(one_arg, init_damping=1e-2) - three_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - one_x, one_state, one_info = one_solver.update(x, one_solver.init(x)) - three_x, three_state, three_info = three_solver.update( - x, three_solver.init(x, (ts, ys)), (ts, ys) - ) - - assert jnp.allclose(one_x["a"], three_x["a"]) - assert jnp.allclose(one_x["b"], three_x["b"]) - assert jnp.allclose(one_info.loss, three_info.loss) - assert jnp.allclose(one_state.damping, three_state.damping) - - -def test_args_and_p_require_matching_residual_arity(): - def one_arg(theta): - return theta - - def two_arg(theta, args): - return theta - args - - one_solver = LevenbergMarquardt(one_arg) - two_solver = LevenbergMarquardt(two_arg) - theta0 = jnp.zeros(1) - - with pytest.raises(ValueError, match="takes only .x."): - one_solver.update(theta0, one_solver.init(theta0), jnp.ones(1)) - with pytest.raises(ValueError, match="takes only .x."): - one_solver.solve(theta0, jnp.ones(1)) - with pytest.raises(ValueError, match="takes no p argument"): - two_solver.update( - theta0, two_solver.init(theta0, jnp.ones(1)), jnp.ones(1), jnp.ones(1) - ) - with pytest.raises(ValueError, match="takes no p argument"): - two_solver.solve(theta0, jnp.ones(1), p=jnp.ones(1)) - - -def test_zero_or_many_arg_residual_rejected_at_construction(): - with pytest.raises(ValueError, match="1 to 3 positional arguments"): - LevenbergMarquardt(lambda: jnp.zeros(1)) - with pytest.raises(ValueError, match="1 to 3 positional arguments"): - LevenbergMarquardt(lambda a, b, c, d: a) - - -def test_residual_with_default_args_counts_as_three_arg(): - def residual(theta, _=None, __=None): - return theta - 1.0 - - solver = LevenbergMarquardt(residual) - assert solver.residual_arity == 3 - result = solver.solve(jnp.zeros(1), max_steps=30, atol=1e-6) - assert int(result.status) == LMStatus.CONVERGED - - -def test_cache_jacobian_single_step_matches_fresh_solver_after_rejection(): - # After a rejection the cached solver reuses (resid, Jt); its next step - # must match a fresh no-cache solver started at the identical (theta, - # damping) up to float noise. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - args = (ts, ys) - kw = {"init_damping": 1e-8, "damping_decrease": 0.01, "damping_increase": 100.0} - kw["geodesic_acceleration"] = False # float noise can flip its gate - cached = LevenbergMarquardt(residual_fn, cache_jacobian=True, **kw) - plain = LevenbergMarquardt(residual_fn, cache_jacobian=False, **kw) - - x = {"a": 1.0, "b": 3.0} - lm_state = cached.init(x0=x, args=args) - reuse_steps = 0 - for _ in range(12): - x_prev, state_prev = x, lm_state - x, lm_state, info = cached.update(x, lm_state, args) - if bool(state_prev.jacobian_valid): - reuse_steps += 1 - ref_x, _, ref_info = plain.update(x_prev, LMState(state_prev.damping), args) - assert bool(ref_info.accepted) == bool(info.accepted) - assert jnp.allclose(ref_x["a"], x["a"], rtol=1e-3, atol=1e-5) - assert jnp.allclose(ref_x["b"], x["b"], rtol=1e-3, atol=1e-5) - assert reuse_steps > 0 - - -def test_cache_jacobian_solve_converges_and_matches_plain(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - cached = LevenbergMarquardt(residual_fn, init_damping=1e-2, cache_jacobian=True) - plain = LevenbergMarquardt(residual_fn, init_damping=1e-2) - - cached_result = cached.solve( - {"a": 1.0, "b": 0.0}, (ts, ys), max_steps=50, atol=1e-6 - ) - plain_result = plain.solve({"a": 1.0, "b": 0.0}, (ts, ys), max_steps=50, atol=1e-6) - - assert int(cached_result.status) == LMStatus.CONVERGED - assert int(plain_result.status) == LMStatus.CONVERGED - assert jnp.allclose(cached_result.x["a"], 2.0, atol=1e-4) - assert jnp.allclose(cached_result.x["b"], -1.0, atol=1e-4) - - -def test_cache_jacobian_requires_sized_lm_state(): - solver = LevenbergMarquardt(residual_fn, cache_jacobian=True) - with pytest.raises(ValueError, match="no Jacobian cache"): - solver.update( - {"a": 1.0, "b": 0.0}, - LMState(jnp.asarray(1e-3)), - (jnp.ones(3), jnp.ones(3)), - ) - - -@pytest.mark.parametrize("linear_solver", ["gram_cg", "lsmr"]) -def test_cache_jacobian_is_inert_for_non_cholesky_solvers(linear_solver): - solver_kwargs = {"iterative_tol": 1e-7, "iterative_maxiter": 20} - if linear_solver == "gram_cg": - solver_kwargs |= { - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - solver = LevenbergMarquardt( - residual_fn, - linear_solver=linear_solver, - cache_jacobian=True, - **solver_kwargs, - ) - assert not solver.cache_jacobian - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - lm_state = solver.init(x, (ts, ys)) - assert lm_state.jacobian_valid is None - _, _, info = solver.update(x, lm_state, (ts, ys)) - assert bool(info.accepted) - - -def test_init_infers_dtype_from_residual(): - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - lm_state = solver.init(x0={"a": 1.0, "b": 0.0}, args=(ts, ys)) - assert lm_state.damping.dtype == jnp.float32 - - -def test_cache_jacobian_off_leaves_no_trace_in_the_jaxpr(): - # With caching (and geodesic) off there is no lax.cond in update at all, - # so the disabled flag provably adds zero compiled overhead. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - - plain = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - cache_jacobian=False, - geodesic_acceleration=False, - ) - cached = LevenbergMarquardt(residual_fn, init_damping=1e-2, cache_jacobian=True) - plain_jaxpr = str( - jax.make_jaxpr(lambda p, s: plain.update(p, s, (ts, ys)))( - x, plain.init(x, (ts, ys)) - ) - ) - cached_jaxpr = str( - jax.make_jaxpr(lambda p, s: cached.update(p, s, (ts, ys)))( - x, cached.init(x0=x, args=(ts, ys)) - ) - ) - - assert "cond" not in plain_jaxpr - assert "cond" in cached_jaxpr - - -def aux_residual_fn(x, args): - ts, ys = args - r = x["a"] * jnp.exp(x["b"] * ts) - ys - return r, {"mean_abs": jnp.mean(jnp.abs(r)), "max_abs": jnp.max(jnp.abs(r))} - - -@pytest.mark.parametrize( - "linear_solver", ["gram_cholesky", "gram_cg", "qr", "augmented_qr", "lsmr"] -) -def test_has_aux_reports_aux_at_pre_step_x(linear_solver): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver_kwargs = {} - if linear_solver == "gram_cg": - solver_kwargs = { - "iterative_tol": 1e-7, - "iterative_maxiter": 20, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - elif linear_solver == "lsmr": - solver_kwargs = {"iterative_tol": 1e-8, "iterative_maxiter": 20} - - solver = LevenbergMarquardt( - aux_residual_fn, - init_damping=1e-2, - has_aux=True, - linear_solver=linear_solver, - **solver_kwargs, - ) - lm_state = solver.init(x, (ts, ys)) - _, _, info = solver.update(x, lm_state, (ts, ys)) - - r, expected = aux_residual_fn(x, (ts, ys)) - assert float(info.aux["mean_abs"]) == pytest.approx( - float(expected["mean_abs"]), rel=1e-6 - ) - assert float(info.aux["max_abs"]) == pytest.approx( - float(expected["max_abs"]), rel=1e-6 - ) - assert float(info.loss) < float(info.loss_old) - - -def test_has_aux_flows_to_solve_callback_and_result(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - - def callback(ctx): - return LMSolveAction(stop=ctx.info.aux["max_abs"] < 1e-4) - - solver = LevenbergMarquardt( - aux_residual_fn, init_damping=1e-2, has_aux=True, geodesic_acceleration=True - ) - result = solver.solve( - {"a": 1.0, "b": 0.0}, (ts, ys), max_steps=50, callback=callback - ) - - assert int(result.status) == LMStatus.CALLBACK_STOP - assert float(result.info.aux["max_abs"]) < 1e-4 - - -def test_has_aux_works_with_jacobian_cache(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - solver = LevenbergMarquardt( - aux_residual_fn, init_damping=1e-2, has_aux=True, cache_jacobian=True - ) - result = solver.solve(x, (ts, ys), max_steps=50, atol=1e-6) - - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.aux["mean_abs"]) < 1e-4 - - -def test_has_aux_off_keeps_info_aux_none(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - _, _, info = solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - assert info.aux is None - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_returns_final_aux_at_returned_x(jit): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt(aux_residual_fn, init_damping=1e-2, has_aux=True) - result = solver.solve( - {"a": 1.0, "b": 0.0}, (ts, ys), max_steps=50, atol=1e-6, jit=jit - ) - - assert int(result.status) == LMStatus.CONVERGED - _, expected = aux_residual_fn(result.x, (ts, ys)) - assert float(result.aux["max_abs"]) == pytest.approx( - float(expected["max_abs"]), rel=1e-3, abs=1e-7 - ) - # the final aux is at the solution, tighter than the pre-step info.aux - assert float(result.aux["max_abs"]) <= float(result.info.aux["max_abs"]) - - -def test_solve_returns_final_aux_without_convergence(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt(aux_residual_fn, init_damping=1e-2, has_aux=True) - result = solver.solve({"a": 1.0, "b": 0.0}, (ts, ys), max_steps=3) - - assert int(result.status) == LMStatus.MAX_STEPS - _, expected = aux_residual_fn(result.x, (ts, ys)) - assert float(result.aux["max_abs"]) == pytest.approx( - float(expected["max_abs"]), rel=1e-3, abs=1e-7 - ) - - -def test_solve_result_aux_none_without_has_aux(): - def residual(theta, args): - return theta - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve(jnp.zeros(1), jnp.ones(1), max_steps=20, atol=1e-6) - assert result.aux is None - - -def test_aux_non_numeric_leaf_raises(): - def residual(theta): - r = theta**2 - 2.0 - return r, {"note": "not an array", "val": jnp.max(jnp.abs(r))} - - solver = LevenbergMarquardt(residual, has_aux=True) - x0 = jnp.array([1.0]) - with pytest.raises(TypeError, match="aux leaves"): - solver.solve(x0, atol=1e-5) - with pytest.raises(TypeError, match="aux leaves"): - solver.init(x0) - - -def test_solve_implicit_jvp_works_with_has_aux(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]), {"level": theta[0]} - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - - def solved(p): - result = solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6) - return result.x, result.aux["level"] - - (x, level), (x_dot, level_dot) = jax.jvp( - solved, (jnp.asarray(3.0),), (jnp.asarray(0.7),) - ) - assert jnp.allclose(x_dot, jnp.array([0.7 / 5.0, 1.4 / 5.0]), atol=1e-6) - # aux level = theta*[0] = p/5, so its tangent is p_dot/5. - assert jnp.allclose(level_dot, 0.7 / 5.0, atol=1e-6) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_solve_implicit_jvp_of_aux_wrt_p(jit): - # theta* = (p/5, 2p/5), so aux m = theta0*theta1 + p^2 has - # dm/dp = theta1/5 + 2*theta0/5 + 2p = 4p/25 + 2p through both the - # solution path and the direct p path. The int32 aux leaf must not - # break the rule. - def residual(theta, _, p): - aux = { - "m": theta[0] * theta[1] + p**2, - "count": jnp.asarray(1, dtype=jnp.int32), - } - return jnp.array([theta[0] + 2.0 * theta[1] - p]), aux - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - - def solved_aux_m(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6, jit=jit).aux[ - "m" - ] - - p, p_dot = jnp.asarray(3.0), jnp.asarray(0.7) - _, m_dot = jax.jvp(solved_aux_m, (p,), (p_dot,)) - expected = (4.0 * p / 25.0 + 2.0 * p) * p_dot - assert jnp.allclose(m_dot, expected, atol=1e-6) - - h = 1e-3 - fd = (solved_aux_m(p + h) - solved_aux_m(p - h)) / (2.0 * h) - assert jnp.allclose(m_dot, fd * p_dot, atol=1e-3) - - # The int32 aux leaf gets a float0 tangent, not a zero float. - def solved_aux(q): - return solver.solve(jnp.zeros(2), p=q, max_steps=80, atol=1e-6, jit=jit).aux - - _, aux_dot = jax.jvp(solved_aux, (p,), (p_dot,)) - assert aux_dot["count"].dtype == jax.dtypes.float0 - assert jnp.allclose(aux_dot["m"], expected, atol=1e-6) - - -def test_solve_implicit_jvp_of_aux_with_pytree_p(): - # theta* = (s/5, 2s/5) with s = p["scale"]; aux vec = (theta0*s, theta1) - # has d/ds = (theta0 + s/5, 2/5) = (2s/5, 2/5). The int32 p leaf takes a - # float0 tangent and the int32 aux leaf produces one. - def residual(theta, _, p): - aux = { - "vec": jnp.array([theta[0] * p["scale"], theta[1]]), - "count": jnp.asarray(1, dtype=jnp.int32), - } - return jnp.array([theta[0] + 2.0 * theta[1] - p["scale"]]), aux - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - p = {"scale": jnp.asarray(3.0), "flag": jnp.asarray(2, dtype=jnp.int32)} - p_dot = { - "scale": jnp.asarray(1.0), - "flag": jnp.zeros((), dtype=jax.dtypes.float0), - } - - def solved(q): - result = solver.solve(jnp.zeros(2), p=q, max_steps=80, atol=1e-6) - return result.x, result.aux - - (x, aux), (x_dot, aux_dot) = jax.jvp(solved, (p,), (p_dot,)) - s = p["scale"] - assert jnp.allclose(x_dot, jnp.array([1.0 / 5.0, 2.0 / 5.0]), atol=1e-6) - assert jnp.allclose( - aux_dot["vec"], jnp.array([2.0 * s / 5.0, 2.0 / 5.0]), atol=1e-5 - ) - assert aux_dot["count"].dtype == jax.dtypes.float0 - - # VJP: pull back a cotangent on the vector aux leaf; the int32 p leaf - # receives a float0 cotangent. - def solved_aux_vec(q): - return solver.solve(jnp.zeros(2), p=q, max_steps=80, atol=1e-6).aux["vec"] - - _, pullback = jax.vjp(solved_aux_vec, p) - vec_bar = jnp.array([1.0, 10.0]) - (p_bar,) = pullback(vec_bar) - assert jnp.allclose(p_bar["scale"], 2.0 * s / 5.0 + 10.0 * 2.0 / 5.0, atol=1e-5) - assert p_bar["flag"].dtype == jax.dtypes.float0 - - -def test_implicit_cg_works_with_has_aux_and_pytree_x_p(): - def residual(x, _, p): - theta = jnp.array([x["left"], x["right"]["value"]]) - scale = p["scale"] - r = jnp.array([theta[0] + 2.0 * theta[1] - scale]) - aux = { - "m": theta[0] * theta[1] + scale**2, - "count": jnp.asarray(1, dtype=jnp.int32), - } - return r, aux - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ad_solver="auto", - ad_solver_tol=1e-7, - has_aux=True, - ) - x0 = {"left": jnp.asarray(0.0), "right": {"value": jnp.asarray(0.0)}} - p = {"scale": jnp.asarray(3.0), "flag": jnp.asarray(2, dtype=jnp.int32)} - p_dot = { - "scale": jnp.asarray(0.7), - "flag": jnp.zeros((), dtype=jax.dtypes.float0), - } - - def solved(q): - result = solver.solve(x0, p=q, max_steps=80, atol=1e-6) - return result.x, result.aux - - (x, aux), (x_dot, aux_dot) = jax.jvp(solved, (p,), (p_dot,)) - expected_m_dot = (4.0 * p["scale"] / 25.0 + 2.0 * p["scale"]) * p_dot["scale"] - assert jnp.allclose(x["left"], p["scale"] / 5.0, atol=1e-5) - assert jnp.allclose(x["right"]["value"], 2.0 * p["scale"] / 5.0, atol=1e-5) - assert aux["count"].dtype == jnp.int32 - assert jnp.allclose(x_dot["left"], 0.7 / 5.0, atol=1e-6) - assert jnp.allclose(x_dot["right"]["value"], 1.4 / 5.0, atol=1e-6) - assert jnp.allclose(aux_dot["m"], expected_m_dot, atol=1e-5) - assert aux_dot["count"].dtype == jax.dtypes.float0 - - def solved_aux_m(q): - return solver.solve(x0, p=q, max_steps=80, atol=1e-6).aux["m"] - - _, pullback = jax.vjp(solved_aux_m, p) - (p_bar,) = pullback(jnp.asarray(1.3)) - assert jnp.allclose( - p_bar["scale"], - jnp.asarray(1.3) * (4.0 * p["scale"] / 25.0 + 2.0 * p["scale"]), - atol=1e-5, - ) - assert p_bar["flag"].dtype == jax.dtypes.float0 - - -def test_solve_implicit_vjp_of_aux_wrt_p(): - def residual(theta, _, p): - aux = { - "m": theta[0] * theta[1] + p**2, - "count": jnp.asarray(1, dtype=jnp.int32), - } - return jnp.array([theta[0] + 2.0 * theta[1] - p]), aux - - solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - p = jnp.asarray(3.0) - dm_dp = 4.0 * p / 25.0 + 2.0 * p - - def solved_aux_m(q): - return solver.solve(jnp.zeros(2), p=q, max_steps=80, atol=1e-6).aux["m"] - - _, pullback = jax.vjp(solved_aux_m, p) - m_bar = jnp.asarray(1.3) - (p_bar,) = pullback(m_bar) - assert jnp.allclose(p_bar, m_bar * dm_dp, atol=1e-6) - - # Joint cotangents on x and aux["m"] pull back additively. - def solved_joint(q): - result = solver.solve(jnp.zeros(2), p=q, max_steps=80, atol=1e-6) - return result.x, result.aux["m"] - - _, joint_pullback = jax.vjp(solved_joint, p) - x_bar = jnp.array([3.0, 4.0]) - (p_bar_joint,) = joint_pullback((x_bar, m_bar)) - expected_x_pullback = (x_bar[0] + 2.0 * x_bar[1]) / 5.0 - assert jnp.allclose(p_bar_joint, expected_x_pullback + m_bar * dm_dp, atol=1e-6) - - # grad-under-jit exercises the transposed rule inside an outer trace. - jitted_grad = jax.jit(jax.grad(solved_aux_m))(p) - assert jnp.allclose(jitted_grad, dm_dp, atol=1e-6) - - -def test_solve_callback_wall_clock_time_limit(): - # The cookbook recipe: read the host clock via io_callback with the start - # time and budget carried in user_state. - import time - - import numpy as np - from jax.experimental import io_callback - - time_limit_status = 100 - - def over_time_budget(start_and_budget, _step): - start, budget = start_and_budget - return np.bool_(time.perf_counter() - float(start) > float(budget)) - - def time_limit_callback(ctx): - timed_out = io_callback( - over_time_budget, - jax.ShapeDtypeStruct((), jnp.bool_), - ctx.user_state, - ctx.step, - ) - return LMSolveAction(stop=timed_out, status=time_limit_status) - - def residual(x, args): - return jnp.sin(x) - args - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - x0 = jnp.zeros(64) - target = jnp.full(64, 0.5) - - # exhausted budget: stops immediately with the custom status - result = solver.solve( - x0, - target, - max_steps=50, - callback=time_limit_callback, - user_state=jnp.asarray([time.perf_counter(), 0.0]), - ) - assert int(result.status) == time_limit_status - assert int(result.steps) == 1 - - # generous budget: runs to a normal stopping rule - result = solver.solve( - x0, - target, - max_steps=50, - atol=1e-6, - callback=time_limit_callback, - user_state=jnp.asarray([time.perf_counter(), 1e9]), - ) - assert int(result.status) == LMStatus.CONVERGED - - -def test_solve_implicit_ad_unaffected_by_cache_init_inside_trace(): - # With cache_jacobian=True, solve(lm_state=None) calls init() — one - # residual evaluation outside the custom_jvp boundary. Its outputs are - # shape-derived constants, so the implicit JVP/VJP wrt p must be - # identical to the uncached solver's. - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - cached = LevenbergMarquardt(residual, init_damping=1e-2, cache_jacobian=True) - plain = LevenbergMarquardt(residual, init_damping=1e-2) - - def solved_x(solver, p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - p, p_dot = jnp.asarray(3.0), jnp.asarray(0.7) - _, cached_dot = jax.jvp(lambda q: solved_x(cached, q), (p,), (p_dot,)) - _, plain_dot = jax.jvp(lambda q: solved_x(plain, q), (p,), (p_dot,)) - assert jnp.allclose(cached_dot, jnp.array([0.7 / 5.0, 1.4 / 5.0]), atol=1e-6) - assert jnp.allclose(cached_dot, plain_dot, atol=1e-7) - - _, pullback = jax.vjp(lambda q: solved_x(cached, q), p) - (p_bar,) = pullback(jnp.array([3.0, 4.0])) - assert jnp.allclose(p_bar, (3.0 + 2.0 * 4.0) / 5.0, atol=1e-6) - - -def test_solve_derivative_wrt_x0_is_zero_by_contract(): - # The implicit rule differentiates only wrt p; the initial guess is - # treated as fixed, so tangents on x0 are zero rather than an error. - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - - def solved_x(x0): - return solver.solve(x0, p=jnp.asarray(3.0), max_steps=80, atol=1e-6).x - - _, x0_dot = jax.jvp(solved_x, (jnp.zeros(2),), (jnp.ones(2),)) - assert jnp.allclose(x0_dot, jnp.zeros(2)) - - -def test_dual_preconditioner_requires_cg(): - with pytest.raises(ValueError, match="dual_preconditioner"): - LevenbergMarquardt(residual_fn, dual_preconditioner=lambda v, damping: v) - with pytest.raises(ValueError, match="dual_preconditioner"): - LevenbergMarquardt( - residual_fn, - linear_solver="qr", - dual_preconditioner=lambda v, damping: v, - ) - - -def test_cg_requires_dual_preconditioner(): - with pytest.raises(ValueError, match="identity_preconditioner"): - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - ) - with pytest.raises(ValueError, match="dual_preconditioner or"): - LevenbergMarquardt(residual_fn, linear_solver="gram_cg") - - -def test_implicit_cg_requires_preconditioner(): - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - LevenbergMarquardt(residual_fn, ad_solver="gram_cg") - - # Auto resolves to gram_cg only after a non-square shape is traced. - def residual(theta, _, p): - return jnp.array([theta[0] - p, 2.0 * theta[0] - 2.0 * p]) - - auto = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ) - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - jax.jvp( - lambda p: auto.solve(jnp.zeros(1), p=p, max_steps=20).x, - (jnp.asarray(1.0),), - (jnp.asarray(1.0),), - ) - # An explicit factorized method is the other escape hatch. - LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver="svd", - ) - - -def test_implicit_cg_exact_preconditioner_matches_closed_form_with_tiny_budget(): - matrix = jnp.array([[1.0, 0.5, -0.2, 0.1], [0.3, -0.7, 0.4, 1.0]]) - target_matrix = jnp.array([[1.0, -0.5], [0.25, 0.75]]) - gram = matrix @ matrix.T - - def residual(theta, _, p): - return matrix @ theta - target_matrix @ p - - def exact_ad_solver_preconditioner(v): - return _solve_2x2(gram, v) - - preconditioned = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ad_solver="gram_cg", - ad_solver_tol=0.0, - ad_solver_maxiter=1, - ad_solver_preconditioner=exact_ad_solver_preconditioner, - geodesic_acceleration=False, - ) - theta0 = jnp.zeros(matrix.shape[1]) - - def solved_x(solver, p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - p = jnp.array([0.2, -0.8]) - p_dot = jnp.array([0.7, -0.4]) - _, preconditioned_dot = jax.jvp( - lambda q: solved_x(preconditioned, q), (p,), (p_dot,) - ) - - _, preconditioned_pullback = jax.vjp(lambda q: solved_x(preconditioned, q), p) - theta_bar = jnp.array([0.1, -0.2, 0.3, 0.4]) - (preconditioned_bar,) = preconditioned_pullback(theta_bar) - expected_dot = matrix.T @ _solve_2x2(gram, target_matrix @ p_dot) - expected_bar = target_matrix.T @ _solve_2x2(gram, matrix @ theta_bar) - - assert jnp.allclose(preconditioned_dot, expected_dot, atol=1e-6) - assert jnp.allclose(preconditioned_bar, expected_bar, atol=1e-6) - - -def test_implicit_cg_does_not_reuse_forward_dual_preconditioner(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - # This callback is valid for the damped forward system, but would be - # singular if the implicit rule silently called it with zero damping; - # the implicit solve must use the separately supplied identity instead. - def dual_preconditioner(v, damping): - return v / damping - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - dual_preconditioner=dual_preconditioner, - ad_solver="auto", - ad_solver_tol=1e-7, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - _, x_dot = jax.jvp(solved_x, (jnp.asarray(3.0),), (jnp.asarray(0.7),)) - - assert jnp.all(jnp.isfinite(x_dot)) - assert jnp.allclose(x_dot, jnp.array([0.7 / 5.0, 1.4 / 5.0]), atol=1e-6) - - -def test_implicit_cg_can_explicitly_reuse_zero_damping_dual_preconditioner(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - def dual_preconditioner(v, damping): - return v / (5.0 + damping) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-7, - iterative_maxiter=20, - dual_preconditioner=dual_preconditioner, - ad_solver="auto", - ad_solver_tol=0.0, - ad_solver_maxiter=1, - ad_solver_preconditioner=lambda v: dual_preconditioner( - v, jnp.asarray(0.0, v.dtype) - ), - ) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - _, x_dot = jax.jvp(solved_x, (jnp.asarray(3.0),), (jnp.asarray(0.7),)) - _, pullback = jax.vjp(solved_x, jnp.asarray(3.0)) - (p_bar,) = pullback(jnp.array([3.0, 4.0])) - - assert jnp.allclose(x_dot, jnp.array([0.7 / 5.0, 1.4 / 5.0]), atol=1e-6) - assert jnp.allclose(p_bar, (3.0 + 2.0 * 4.0) / 5.0, atol=1e-6) - - -def test_ad_solver_preconditioner_accepts_dual_signature(): - # A callable REQUIRING (v, damping) serves the implicit hook directly: - # the solver calls it with an explicit ZERO damping. The dual here is - # diag(1, 25), so v / (diag + damping) at a one-iteration budget is - # exact only at damping == 0 — any other value (e.g. a leaked live - # damping) misses the analytic tangent by ~1e-3, far outside the - # tolerance. - def residual(theta, _, p): - return jnp.array([theta[0] - p, 5.0 * theta[1] - p]) - - dual_eigenvalues = jnp.array([1.0, 25.0]) - - def dual_preconditioner(v, damping): - return v / (dual_eigenvalues + damping) - - common = dict( - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-7, - iterative_maxiter=20, - dual_preconditioner=dual_preconditioner, - ad_solver="auto", - ad_solver_tol=0.0, - ad_solver_maxiter=1, - geodesic_acceleration=False, - ) - direct = LevenbergMarquardt( - residual, ad_solver_preconditioner=dual_preconditioner, **common - ) - wrapped = LevenbergMarquardt( - residual, - ad_solver_preconditioner=lambda v: dual_preconditioner( - v, jnp.asarray(0.0, v.dtype) - ), - **common, - ) - - def solved_x(solver, p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - p, p_dot = jnp.asarray(3.0), jnp.asarray(0.7) - expected_dot = jnp.array([0.7, 0.7 / 5.0]) - _, direct_dot = jax.jvp(lambda q: solved_x(direct, q), (p,), (p_dot,)) - _, wrapped_dot = jax.jvp(lambda q: solved_x(wrapped, q), (p,), (p_dot,)) - _, pullback = jax.vjp(lambda q: solved_x(direct, q), p) - (p_bar,) = pullback(jnp.array([3.0, 4.0])) - - assert jnp.allclose(direct_dot, expected_dot, atol=1e-6) - assert jnp.allclose(direct_dot, wrapped_dot, atol=1e-7) - assert jnp.allclose(p_bar, 3.0 + 4.0 / 5.0, atol=1e-6) - - -def test_ad_solver_preconditioner_arity_edge_cases(): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - common = dict( - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-7, - iterative_maxiter=20, - dual_preconditioner=identity_preconditioner(), - ad_solver_tol=1e-7, - ) - - # A 1-arg-callable with a defaulted EXTRA argument passes through - # unchanged: were it wrongly called with a zero second argument, the - # preconditioner would return the zero vector and the tangent would be - # garbage. - def one_arg_with_default(v, scale=1.0): - return v * scale - - def solved_x(solver, p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - solver = LevenbergMarquardt( - residual, ad_solver_preconditioner=one_arg_with_default, **common - ) - _, x_dot = jax.jvp( - lambda q: solved_x(solver, q), (jnp.asarray(3.0),), (jnp.asarray(0.7),) - ) - assert jnp.allclose(x_dot, jnp.array([0.7 / 5.0, 1.4 / 5.0]), atol=1e-6) - - # A jit-wrapped 1-arg callable is accepted unchanged. - LevenbergMarquardt( - residual, ad_solver_preconditioner=jax.jit(lambda v: v), **common - ) - - # Zero-argument callables are rejected at construction. - with pytest.raises(ValueError, match="callable as .v."): - LevenbergMarquardt(residual, ad_solver_preconditioner=lambda: 0, **common) - - # pad_dual_preconditioner divides by the live damping; the zero-damping - # implicit hook rejects it at construction instead of dividing by zero. - with pytest.raises(ValueError, match="undamped"): - LevenbergMarquardt( - residual, - ad_solver_preconditioner=pad_dual_preconditioner( - identity_preconditioner(), 1 - ), - **common, - ) - - -def test_cg_preconditioned_step_matches_cholesky_identity_step(): - # A valid SPD preconditioner changes only the inner Krylov iteration, not - # the step the inner solve converges to. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - weights = 1.0 + jnp.arange(20, dtype=jnp.float32) / 10.0 - - cholesky_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - cg_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=40, - dual_preconditioner=lambda v, damping: v / weights, - ) - - cholesky_x, cholesky_state, cholesky_info = cholesky_solver.update( - x, cholesky_solver.init(x, (ts, ys)), (ts, ys) - ) - cg_x, cg_state, cg_info = cg_solver.update(x, cg_solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(cg_info.accepted) == bool(cholesky_info.accepted) - # float32 across BLAS/SIMD variants: CI runners land ~2e-5 off macOS. - assert jnp.allclose(cg_x["a"], cholesky_x["a"], rtol=1e-4, atol=1e-4) - assert jnp.allclose(cg_x["b"], cholesky_x["b"], rtol=1e-4, atol=1e-4) - assert jnp.allclose(cg_state.damping, cholesky_state.damping) - assert jnp.allclose( - cg_info.loss, - cholesky_info.loss, - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - - -def test_cg_preconditioned_update_jits(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - weights = 1.0 + jnp.arange(20, dtype=jnp.float32) / 10.0 - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=40, - dual_preconditioner=lambda v, damping: v / weights, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(lm_state.damping) - - -def test_cg_preconditioned_geodesic_matches_cholesky(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - cg_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=10, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - dual_preconditioner=lambda v, damping: v / (1.0 + damping), - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, target), target - ) - cg_theta, _, cg_info = cg_solver.update( - theta0, cg_solver.init(theta0, target), target - ) - - assert bool(cg_info.accepted) - assert bool(cg_info.used_geodesic) - assert jnp.allclose(cg_theta, cholesky_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose( - cg_info.acceleration_ratio, - cholesky_info.acceleration_ratio, - rtol=1e-6, - atol=1e-6, - ) - - -def test_cg_dual_preconditioner_enables_ill_conditioned_convergence(): - # Kernel-collocation miniature: affine residual K x - b with metric M = K, - # so the dual operator is K K^{-1} K = K itself -- as ill-conditioned as - # the kernel (cond ~ 1e4 here). At a tight inner-iteration budget plain CG - # stalls, while the exact preconditioner (a K-solve) recovers - # Gauss-Newton-quality steps and converges immediately. - n = 40 - rho = 0.98 - idx = jnp.arange(n) - K = rho ** jnp.abs(idx[:, None] - idx[None, :]) - L = jnp.linalg.cholesky(K) - x_true = jnp.sin(idx / 3.0) - b = K @ x_true - - def residual(x): - return K @ x - b - - def preconditioner(v, damping): - y = jsp_linalg.solve_triangular(L, v, lower=True) - return jsp_linalg.solve_triangular(L.T, y, lower=False) - - common = dict( - init_damping=1e-6, - linear_solver="gram_cg", - iterative_maxiter=3, - ad_solver_preconditioner=identity_preconditioner(), - metric=metric_from_cholesky(L), - ) - plain = LevenbergMarquardt( - residual, dual_preconditioner=identity_preconditioner(), **common - ) - preconditioned = LevenbergMarquardt( - residual, dual_preconditioner=preconditioner, **common - ) - x0 = jnp.zeros(n) - - plain_result = plain.solve(x0, max_steps=20, atol=1e-3) - preconditioned_result = preconditioned.solve(x0, max_steps=20, atol=1e-3) - - assert int(preconditioned_result.status) == LMStatus.CONVERGED - assert int(plain_result.status) != LMStatus.CONVERGED - - -def repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon): - n = K.shape[0] - blocks = [K + epsilon * jnp.eye(n)] * repeats - if zero_pad_size: - blocks.append(epsilon * jnp.eye(zero_pad_size)) - return jsp_linalg.block_diag(*blocks) - - -def dense_matern_gram(t, sigma, ell, nu): - tau = jnp.abs(t[:, None] - t[None, :]) - ft = jnp.sqrt(2.0 * nu) * tau / ell - if nu == 0.5: - corr = jnp.exp(-ft) - elif nu == 1.5: - corr = (1.0 + ft) * jnp.exp(-ft) - else: - corr = (1.0 + ft + ft**2 / 3.0) * jnp.exp(-ft) - return sigma**2 * corr - - -def assert_metric_matches_dense(metric, M, key): - total = M.shape[0] - key_x, key_X = jax.random.split(key) - x = jax.random.normal(key_x, (total,)) - X = jax.random.normal(key_X, (total, 3)) - - with jax.default_matmul_precision("highest"): - assert jnp.allclose( - jax.jit(metric.solve)(x), jnp.linalg.solve(M, x), rtol=3e-4, atol=3e-4 - ) - assert jnp.allclose( - jax.jit(metric.solve)(X), jnp.linalg.solve(M, X), rtol=3e-4, atol=3e-4 - ) - assert jnp.allclose(metric.norm(x), jnp.sqrt(x @ M @ x), rtol=3e-4, atol=3e-4) - S = jax.jit(metric.inv_sqrt)(jnp.eye(total)) - ST = jax.jit(metric.inv_sqrt_transpose)(jnp.eye(total)) - assert jnp.allclose(S @ S.T, jnp.linalg.inv(M), rtol=5e-4, atol=5e-4) - assert jnp.allclose(ST, S.T, rtol=3e-4, atol=3e-4) - - -@pytest.mark.parametrize("zero_pad_size", [0, 2]) -def test_repeated_shifted_dense_metric_matches_explicit_matrix(zero_pad_size): - K = jnp.array( - [ - [2.0, 0.2, 0.1, 0.0], - [0.2, 1.8, 0.0, 0.1], - [0.1, 0.0, 1.5, 0.2], - [0.0, 0.1, 0.2, 1.2], - ] - ) - repeats, epsilon = 3, 0.2 - metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - assert_metric_matches_dense(metric, M, jax.random.PRNGKey(zero_pad_size)) - - -def test_repeated_shifted_metrics_promote_integer_inputs(): - integer_K = jnp.array([[2, 1], [1, 2]]) - epsilon = 0.2 - dense_metric = repeated_shifted_dense_metric( - integer_K, - repeats=2, - zero_pad_size=1, - epsilon=epsilon, - ) - dense_M = repeated_shifted_matrix(integer_K, 2, 1, epsilon) - assert_metric_matches_dense(dense_metric, dense_M, jax.random.PRNGKey(17)) - - t = jnp.arange(5) - state_metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(1, 2, 0.5), - repeats=2, - zero_pad_size=1, - epsilon=epsilon, - parallel=False, - ) - state_K = dense_matern_gram(t, 1.0, 2.0, 0.5) - state_M = repeated_shifted_matrix(state_K, 2, 1, epsilon) - assert_metric_matches_dense(state_metric, state_M, jax.random.PRNGKey(18)) - - -@pytest.mark.parametrize("nu", [0.5, 1.5, 2.5]) -@pytest.mark.parametrize("parallel", [False, True]) -@pytest.mark.parametrize("zero_pad_size", [0, 2]) -def test_repeated_shifted_state_space_metric_matches_explicit_matrix( - nu, parallel, zero_pad_size -): - n, repeats = 18, 3 - t = jnp.cumsum( - jax.random.uniform(jax.random.PRNGKey(2), (n,), minval=0.6, maxval=1.4) - ) - sigma, ell, epsilon = 1.3, 0.8, 0.05 - K = dense_matern_gram(t, sigma, ell, nu) - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma, ell, nu), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - parallel=parallel, - ) - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - assert_metric_matches_dense(metric, M, jax.random.PRNGKey(3)) - - -def test_repeated_shifted_metric_validation_and_callback_shapes(): - K = jnp.eye(3) - for repeats in (0, -1, True): - with pytest.raises(ValueError, match="repeats"): - repeated_shifted_dense_metric( - K, repeats=repeats, zero_pad_size=0, epsilon=0.1 - ) - for zero_pad_size in (-1, True): - with pytest.raises(ValueError, match="zero_pad_size"): - repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=zero_pad_size, epsilon=0.1 - ) - with pytest.raises(ValueError, match="nonempty square"): - repeated_shifted_dense_metric( - jnp.zeros((0, 0)), repeats=1, zero_pad_size=0, epsilon=0.1 - ) - with pytest.raises(ValueError, match="nonempty square"): - repeated_shifted_dense_metric( - jnp.zeros((2, 3)), repeats=1, zero_pad_size=0, epsilon=0.1 - ) - with pytest.raises(ValueError, match="scalar"): - repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=0, epsilon=jnp.ones(2) - ) - with pytest.raises(ValueError, match="positive"): - repeated_shifted_dense_metric(K, repeats=1, zero_pad_size=0, epsilon=0.0) - with pytest.raises(ValueError, match="nonempty 1-D"): - repeated_shifted_state_space_metric( - jnp.zeros((2, 2)), - *matern_state_space(1.0, 1.0, 1.5), - repeats=1, - zero_pad_size=0, - epsilon=0.1, - ) - with pytest.raises(ValueError, match="positive"): - repeated_shifted_state_space_metric( - jnp.arange(3.0), - *matern_state_space(1.0, 1.0, 1.5), - repeats=1, - zero_pad_size=0, - epsilon=0.0, - ) - with pytest.raises(ValueError, match="scalars"): - matern_state_space(jnp.ones(2), 1.0, 1.5) - unordered_metric = repeated_shifted_state_space_metric( - jnp.array([0.0, 2.0, 1.0]), - *matern_state_space(1.0, 1.0, 1.5), - repeats=1, - zero_pad_size=0, - epsilon=0.1, - ) - assert bool(jnp.all(jnp.isnan(unordered_metric.solve(jnp.ones(3))))) - - metric = repeated_shifted_dense_metric(K, repeats=2, zero_pad_size=1, epsilon=0.1) - with pytest.raises(ValueError, match="leading size"): - metric.solve(jnp.ones(3)) - with pytest.raises(ValueError, match="vector or matrix"): - metric.solve(jnp.ones((7, 1, 1))) - with pytest.raises(ValueError, match="requires a vector"): - metric.norm(jnp.ones((7, 1))) - - -def test_repeated_shifted_dense_metric_supports_traced_epsilon(): - K = jnp.array([[1.5, 0.2], [0.2, 1.0]]) - repeats, zero_pad_size = 2, 1 - v = jnp.arange(1.0, repeats * K.shape[0] + zero_pad_size + 1.0) - - def structured_loss(epsilon): - metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - return v @ metric.solve(v) + metric.norm(v) - - def dense_loss(epsilon): - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - return v @ jnp.linalg.solve(M, v) + jnp.sqrt(v @ M @ v) - - epsilon = jnp.asarray(0.2) - assert jnp.allclose(jax.jit(structured_loss)(epsilon), dense_loss(epsilon)) - assert jnp.allclose( - jax.jit(jax.grad(structured_loss))(epsilon), - jax.grad(dense_loss)(epsilon), - rtol=2e-4, - atol=2e-4, - ) - - @jax.jit - def invalid_solve(invalid_epsilon): - invalid_metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=invalid_epsilon, - ) - return invalid_metric.solve(v) - - assert bool(jnp.all(jnp.isnan(invalid_solve(jnp.asarray(-0.1))))) - - -def test_repeated_shifted_state_space_hyperparameter_grad_matches_dense(): - n, repeats, zero_pad_size = 16, 2, 1 - t = jnp.cumsum( - jax.random.uniform(jax.random.PRNGKey(4), (n,), minval=0.6, maxval=1.4) - ) - v = jax.random.normal(jax.random.PRNGKey(5), (repeats * n + zero_pad_size,)) - - def structured_loss(params): - sigma, ell, epsilon = params - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma, ell, 1.5), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - return v @ metric.solve(v) + metric.norm(v) - - def dense_loss(params): - sigma, ell, epsilon = params - K = dense_matern_gram(t, sigma, ell, 1.5) - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - return v @ jnp.linalg.solve(M, v) + jnp.sqrt(v @ M @ v) - - params = jnp.array([1.3, 0.8, 0.05]) - with jax.default_matmul_precision("highest"): - structured_grad = jax.jit(jax.grad(structured_loss))(params) - dense_grad = jax.grad(dense_loss)(params) - assert jnp.allclose(structured_grad, dense_grad, rtol=3e-3, atol=3e-3) - assert bool(jnp.isnan(jax.jit(structured_loss)(params.at[2].set(-params[2])))) - - -def test_repeated_shifted_state_space_float32_default_is_stable(): - n, repeats = 1000, 2 - t = jnp.linspace(0.0, 5.0, n, dtype=jnp.float32) - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(1.0, 1.0, 2.5), - repeats=repeats, - zero_pad_size=1, - epsilon=1e-4, - ) - x = jnp.ones(repeats * n + 1, dtype=jnp.float32) - assert bool(jnp.all(jnp.isfinite(metric.inv_sqrt(x)))) - assert bool(jnp.all(jnp.isfinite(metric.solve(x)))) - - -def shifted_solver_kwargs(linear_solver): - if linear_solver == "gram_cg": - return { - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - if linear_solver == "normal_cg": - return { - "normal_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - return {} - - -@pytest.mark.parametrize("metric_kind", ["dense", "state_space"]) -@pytest.mark.parametrize( - "linear_solver", - [ - "auto", - "gram_cholesky", - "normal_cholesky", - "qr", - "augmented_qr", - "gram_cg", - "normal_cg", - "lsmr", - ], -) -def test_repeated_shifted_metric_step_matches_closed_form(metric_kind, linear_solver): - n, repeats, zero_pad_size, epsilon = 4, 2, 1, 0.2 - t = jnp.arange(n, dtype=jnp.float32) - K = dense_matern_gram(t, 1.2, 0.9, 1.5) - if metric_kind == "dense": - metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - else: - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(1.2, 0.9, 1.5), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - total = M.shape[0] - A = jax.random.normal(jax.random.PRNGKey(6), (3, total)) - b = jnp.array([1.0, -0.5, 2.0]) - - def residual(theta): - return A @ theta - b - - damping = 0.1 - solver = LevenbergMarquardt( - residual, - init_damping=damping, - linear_solver=linear_solver, - metric=metric, - geodesic_acceleration=False, - iterative_tol=1e-7, - iterative_maxiter=500, - **shifted_solver_kwargs(linear_solver), - ) - x0 = jnp.zeros(total) - x1, _, info = solver.update(x0, solver.init(x0)) - expected = jnp.linalg.solve(A.T @ A + damping * M, A.T @ b) - assert bool(info.accepted) - assert jnp.allclose(x1, expected, rtol=3e-3, atol=3e-3) - - -def test_repeated_shifted_metric_geodesic_matches_explicit_dense_metric(): - K = jnp.array([[1.5, 0.2], [0.2, 1.0]]) - repeats, zero_pad_size, epsilon = 2, 1, 0.2 - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - structured = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - dense = metric_from_cholesky(jnp.linalg.cholesky(M)) - - def residual(theta): - return jnp.array([theta[0] ** 2 - 4.0, theta[1] ** 2 - 1.0, jnp.sum(theta[2:])]) - - def update(metric): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - metric=metric, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - x0 = jnp.array([1.9, 0.9, 0.1, -0.1, 0.2]) - return solver.update(x0, solver.init(x0)) - - x_structured, _, info_structured = update(structured) - x_dense, _, info_dense = update(dense) - assert jnp.allclose(x_structured, x_dense, atol=1e-5) - assert jnp.allclose( - info_structured.acceleration_ratio, - info_dense.acceleration_ratio, - atol=1e-5, - ) - - -@pytest.mark.parametrize("metric_kind", ["dense", "state_space"]) -@pytest.mark.parametrize("linear_solver", ["gram_cholesky", "qr"]) -def test_repeated_shifted_metric_implicit_jvp_and_vjp_match_dense( - metric_kind, linear_solver -): - n, repeats, zero_pad_size, epsilon = 4, 2, 1, 0.2 - t = jnp.arange(n, dtype=jnp.float32) - K = dense_matern_gram(t, 1.2, 0.9, 1.5) - M = repeated_shifted_matrix(K, repeats, zero_pad_size, epsilon) - if metric_kind == "dense": - metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - else: - metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(1.2, 0.9, 1.5), - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=epsilon, - ) - dense = metric_from_cholesky(jnp.linalg.cholesky(M)) - total = M.shape[0] - A = jax.random.normal(jax.random.PRNGKey(7), (3, total)) - - def residual(theta, _, p): - return A @ theta - p * jnp.array([1.0, 0.5, -1.0]) - - def solved_x(chosen_metric, p): - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver=linear_solver, - metric=chosen_metric, - ) - return solver.solve(jnp.zeros(total), p=p, max_steps=60, atol=1e-6).x - - p, p_dot = jnp.asarray(2.0), jnp.asarray(1.0) - x_value, x_dot = jax.jvp(lambda q: solved_x(metric, q), (p,), (p_dot,)) - dense_value, dense_dot = jax.jvp(lambda q: solved_x(dense, q), (p,), (p_dot,)) - assert jnp.allclose(x_value, dense_value, atol=2e-4) - assert jnp.allclose(x_dot, dense_dot, atol=2e-4) - - x_bar = jnp.linspace(-1.0, 1.0, total) - _, pullback = jax.vjp(lambda q: solved_x(metric, q), p) - _, dense_pullback = jax.vjp(lambda q: solved_x(dense, q), p) - assert jnp.allclose(pullback(x_bar)[0], dense_pullback(x_bar)[0], atol=2e-4) - - -def test_sherman_morrison_preconditioner_matches_dense_inverse(): - n = 12 - idx = jnp.arange(n) - A = 0.6 ** jnp.abs(idx[:, None] - idx[None, :]) - L = jnp.linalg.cholesky(A) - u = jnp.ones(n) - weight = 50.0 - - preconditioner = sherman_morrison_preconditioner( - metric_from_cholesky(L).solve, u, weight - ) - P = A + weight * jnp.outer(u, u) - v = jax.random.normal(jax.random.PRNGKey(8), (n,)) - - assert jnp.allclose( - preconditioner(v, 0.0), jnp.linalg.solve(P, v), rtol=1e-3, atol=1e-3 - ) - - -def test_woodbury_preconditioner_matches_dense_inverse(): - n, k = 12, 2 - idx = jnp.arange(n) - A = 0.6 ** jnp.abs(idx[:, None] - idx[None, :]) - solve = metric_from_cholesky(jnp.linalg.cholesky(A)).solve - U = jax.random.normal(jax.random.PRNGKey(28), (n, k)) - weights = jnp.array([50.0, 20.0]) - - preconditioner = woodbury_preconditioner(solve, U, weights) - B = A + U @ jnp.diag(weights) @ U.T - v = jax.random.normal(jax.random.PRNGKey(29), (n,)) - assert jnp.allclose( - preconditioner(v, 0.0), jnp.linalg.solve(B, v), rtol=1e-3, atol=1e-3 - ) - - rank1 = woodbury_preconditioner(solve, U[:, :1], weights[:1]) - sherman = sherman_morrison_preconditioner(solve, U[:, 0], weights[0]) - assert jnp.allclose(rank1(v, 0.0), sherman(v, 0.0), rtol=1e-5, atol=1e-6) - - with pytest.raises(ValueError, match="U must"): - woodbury_preconditioner(solve, U[:, 0], weights) - - -def test_cg_with_woodbury_spike_preconditioner_matches_cholesky_step(): - n, k, eps = 16, 2, 1e-3 - t = jnp.arange(n) * 1.0 - K = dense_matern_gram(t, 1.3, 0.8, 1.5) - K_shifted = K + eps * jnp.eye(n) - metric = repeated_shifted_dense_metric(K, repeats=1, zero_pad_size=k, epsilon=eps) - - m = 8 - J_alpha = jax.random.normal(jax.random.PRNGKey(30), (m, n)) - J_beta = jax.random.normal(jax.random.PRNGKey(31), (m, k)) - A = jnp.concatenate([J_alpha, J_beta], axis=1) - b = jax.random.normal(jax.random.PRNGKey(32), (m,)) - - def residual(theta, _, p): - return A @ theta - b - - base = J_alpha @ jnp.linalg.solve(K_shifted, J_alpha.T) - base_solve = metric_from_cholesky(jnp.linalg.cholesky(base)).solve - dual_preconditioner = woodbury_preconditioner( - base_solve, J_beta, (1.0 / eps) * jnp.ones(k) - ) - - common = dict(init_damping=1e-2, geodesic_acceleration=False, metric=metric) - cg_solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-8, - iterative_maxiter=200, - dual_preconditioner=dual_preconditioner, - **common, - ) - cholesky_solver = LevenbergMarquardt( - residual, linear_solver="gram_cholesky", **common - ) - - x0 = jnp.zeros(n + k) - x_cg, _, info_cg = cg_solver.update(x0, cg_solver.init(x0, None)) - x_ch, _, info_ch = cholesky_solver.update(x0, cholesky_solver.init(x0, None)) - assert bool(info_cg.accepted) and bool(info_ch.accepted) - assert jnp.allclose(x_cg, x_ch, rtol=1e-2, atol=1e-3) - - -def test_nystrom_preconditioner_full_rank_matches_dense_solve(): - n = 12 - G = jax.random.normal(jax.random.PRNGKey(37), (n, n)) - A = G @ G.T + 0.5 * jnp.eye(n) - preconditioner = nystrom_preconditioner( - lambda X: A @ X, n, n, jax.random.PRNGKey(38) - ) - v = jax.random.normal(jax.random.PRNGKey(39), (n,)) - - # rank = n makes the Nystrom approximation exact, so the apply is the - # exact damped inverse; damping=0 is valid because A is positive definite. - for damping in (0.0, 0.5): - expected = jnp.linalg.solve(A + damping * jnp.eye(n), v) - assert jnp.allclose(preconditioner(v, damping), expected, rtol=1e-3, atol=1e-4) - - -def test_nystrom_preconditioner_exact_for_low_rank_operator(): - # A rank-r PSD operator sketched at rank >= r is recovered exactly, so - # the apply matches the dense damped inverse. - n, r = 14, 4 - W = jax.random.normal(jax.random.PRNGKey(40), (n, r)) - A = W @ W.T - preconditioner = nystrom_preconditioner( - lambda X: A @ X, n, 6, jax.random.PRNGKey(41) - ) - v = jax.random.normal(jax.random.PRNGKey(42), (n,)) - damping = 0.3 - - expected = jnp.linalg.solve(A + damping * jnp.eye(n), v) - assert jnp.allclose(preconditioner(v, damping), expected, rtol=1e-3, atol=1e-4) - - -def test_nystrom_preconditioner_matches_ftu_formula(): - # Replicate the construction with the same key and assemble the FTU - # apply densely: the unresolved complement must be balanced at - # rho + damping (rho the smallest retained eigenvalue), not at the - # bare damping. - n, rank = 16, 6 - G = jax.random.normal(jax.random.PRNGKey(43), (n, n)) - A = G @ G.T / n + jnp.eye(n) - key = jax.random.PRNGKey(44) - preconditioner = nystrom_preconditioner(lambda X: A @ X, n, rank, key) - - Omega = jnp.linalg.qr(jax.random.normal(key, (n, rank)))[0] - Y = A @ Omega - finfo = jnp.finfo(Y.dtype) - nu = jnp.maximum(finfo.eps * jnp.linalg.norm(Y), finfo.tiny / finfo.eps) - Y_nu = Y + nu * Omega - core = Omega.T @ Y_nu - L = jnp.linalg.cholesky(0.5 * (core + core.T)) - B = jsp_linalg.solve_triangular(L, Y_nu.T, lower=True).T - U, sigma, _ = jnp.linalg.svd(B, full_matrices=False) - lam = jnp.maximum(sigma**2 - nu, 0.0) - rho = lam[-1] - damping = 0.25 - v = jax.random.normal(jax.random.PRNGKey(45), (n,)) - - ftu = U @ ((U.T @ v) / (lam + damping)) + (v - U @ (U.T @ v)) / (rho + damping) - assert jnp.allclose(preconditioner(v, damping), ftu, rtol=1e-5, atol=1e-6) - # rho sits strictly inside the spectrum here (A is positive definite), - # so the FTU complement genuinely differs from a sketch-and-solve - # inverse that would divide the complement by the bare damping. - assert float(rho) > damping - naive = U @ ((U.T @ v) / (lam + damping)) + (v - U @ (U.T @ v)) / damping - assert not jnp.allclose(preconditioner(v, damping), naive, rtol=1e-3) - - -def test_nystrom_preconditioner_symmetry_definiteness_and_key_determinism(): - n, rank = 10, 4 - G = jax.random.normal(jax.random.PRNGKey(46), (n, n)) - A = G @ G.T / n + 0.5 * jnp.eye(n) - key = jax.random.PRNGKey(47) - preconditioner = nystrom_preconditioner(lambda X: A @ X, n, rank, key) - x = jax.random.normal(jax.random.PRNGKey(48), (n,)) - y = jax.random.normal(jax.random.PRNGKey(49), (n,)) - damping = 0.1 - - assert jnp.allclose( - x @ preconditioner(y, damping), - y @ preconditioner(x, damping), - rtol=1e-4, - atol=1e-5, - ) - assert float(x @ preconditioner(x, damping)) > 0.0 - same = nystrom_preconditioner(lambda X: A @ X, n, rank, key) - assert jnp.allclose(preconditioner(x, damping), same(x, damping)) - different = nystrom_preconditioner(lambda X: A @ X, n, rank, jax.random.PRNGKey(50)) - assert not jnp.allclose(preconditioner(x, damping), different(x, damping)) - - -def test_nystrom_preconditioner_validation_and_zero_operator(): - def matvec(X): - return X - - key = jax.random.PRNGKey(51) - with pytest.raises(ValueError, match="rank must"): - nystrom_preconditioner(matvec, 4, 0, key) - with pytest.raises(ValueError, match="rank must"): - nystrom_preconditioner(matvec, 4, 5, key) - with pytest.raises(ValueError, match="rank must"): - nystrom_preconditioner(matvec, 4, 2.0, key) - with pytest.raises(ValueError, match="n must"): - nystrom_preconditioner(matvec, 0, 1, key) - - # The tiny floor on the stabilization shift keeps a zero operator's - # build and apply finite. - zero = nystrom_preconditioner(lambda X: 0.0 * X, 4, 2, key) - assert bool(jnp.all(jnp.isfinite(zero(jnp.ones(4), 1.0)))) - - -def test_cg_nystrom_preconditioner_enables_ill_conditioned_convergence(): - # Identity-metric mirror of the kernel-preconditioner test above: the - # residual K x - b makes the dual operator K^2 + damping I, - # ill-conditioned like cond(K)^2. At a tight inner budget - # identity-preconditioned CG stalls; the Nystrom preconditioner built - # from the K^2 matvec recovers Gauss-Newton-quality steps and converges. - n = 40 - rho = 0.9 - idx = jnp.arange(n) - K = rho ** jnp.abs(idx[:, None] - idx[None, :]) - x_true = jnp.sin(idx / 3.0) - b = K @ x_true - - def residual(x): - return K @ x - b - - # rank 16 of 40: the sketch resolves only the decaying head of the K^2 - # spectrum (the advertised low-rank regime), and the FTU complement - # balance carries the rest. - nystrom = nystrom_preconditioner( - lambda V: K @ (K @ V), n, 16, jax.random.PRNGKey(52) - ) - common = dict( - init_damping=1e-6, - linear_solver="gram_cg", - iterative_maxiter=3, - ad_solver_preconditioner=identity_preconditioner(), - ) - plain = LevenbergMarquardt( - residual, dual_preconditioner=identity_preconditioner(), **common - ) - preconditioned = LevenbergMarquardt(residual, dual_preconditioner=nystrom, **common) - x0 = jnp.zeros(n) - - plain_result = plain.solve(x0, max_steps=20, atol=1e-3) - preconditioned_result = preconditioned.solve(x0, max_steps=20, atol=1e-3) - - assert int(preconditioned_result.status) == LMStatus.CONVERGED - assert int(plain_result.status) != LMStatus.CONVERGED - - -def test_cg_nystrom_mlp_ntk_example(): - # Copyable example: pure-jax MLP least squares under the identity - # metric (n_params >> m collocation residuals), with the CG dual - # preconditioner built by sketching the m x m empirical NTK Gram J J' - # at the initial parameters via jax.linearize / jax.linear_transpose. - m, width = 10, 16 - ts = jnp.linspace(-1.0, 1.0, m) - targets = jnp.sin(jnp.pi * ts) - - keys = jax.random.split(jax.random.PRNGKey(53), 3) - x0 = { - "w1": jax.random.normal(keys[0], (1, width)), - "b1": jnp.zeros(width), - "w2": jax.random.normal(keys[1], (width, width)) / jnp.sqrt(width), - "b2": jnp.zeros(width), - "w3": jax.random.normal(keys[2], (width, 1)) / jnp.sqrt(width), - "b3": jnp.zeros(1), - } - - def mlp(params, t): - h = jnp.tanh(t[:, None] @ params["w1"] + params["b1"]) - h = jnp.tanh(h @ params["w2"] + params["b2"]) - return (h @ params["w3"] + params["b3"]).ravel() - - def residual(params): - return mlp(params, ts) - targets - - theta0, unravel = ravel_pytree(x0) - _, jvp_fn = jax.linearize(lambda th: residual(unravel(th)), theta0) - transpose_fn = jax.linear_transpose(jvp_fn, theta0) - - def ntk_matvec(V): - # V is (m, k); apply J (J' v) column by column, frozen at x0. - return jax.vmap( - lambda col: jvp_fn(transpose_fn(col)[0]), in_axes=1, out_axes=1 - )(V) - - cg_solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - iterative_tol=1e-6, - iterative_maxiter=20, - # rank 6 of m=10: the NTK spectrum decays fast enough that a low-rank - # sketch of its head preconditions the whole solve. - dual_preconditioner=nystrom_preconditioner( - ntk_matvec, m, 6, jax.random.PRNGKey(54) - ), - ad_solver_preconditioner=identity_preconditioner(), - ) - cholesky_solver = LevenbergMarquardt(residual, init_damping=1e-2) - - cg_result = cg_solver.solve(x0, max_steps=100, atol=1e-3) - cholesky_result = cholesky_solver.solve(x0, max_steps=100, atol=1e-3) - - assert int(cg_result.status) == LMStatus.CONVERGED - assert int(cholesky_result.status) == LMStatus.CONVERGED - # Compare model outputs, not raw parameters: an underdetermined network - # has many interpolating parameter roots. - assert jnp.allclose(mlp(cg_result.x, ts), targets, atol=2e-3) - assert jnp.allclose(mlp(cg_result.x, ts), mlp(cholesky_result.x, ts), atol=2e-3) - - -def test_padded_zero_residual_cholesky_matches_unpadded(): - # Fixed-residual-shape pattern: appending exact-zero residual entries - # (zero Jacobian rows) adds a decoupled damping*I block to the dual, so - # the cholesky step is unchanged. - m, n, pad = 12, 30, 4 - A = jax.random.normal(jax.random.PRNGKey(55), (m, n)) - b = jax.random.normal(jax.random.PRNGKey(56), (m,)) - init_damping = 1e-6 - - def residual(theta): - return A @ theta - b - - def residual_padded(theta): - return jnp.concatenate((A @ theta - b, jnp.zeros(pad))) - - plain = LevenbergMarquardt( - residual, init_damping=init_damping, geodesic_acceleration=False - ) - padded = LevenbergMarquardt( - residual_padded, init_damping=init_damping, geodesic_acceleration=False - ) - theta0 = jnp.zeros(n) - x_plain, _, info_plain = plain.update(theta0, plain.init(theta0)) - x_padded, _, info_padded = padded.update(theta0, padded.init(theta0)) - - # Dual (residual-space) form of the damped step: well-conditioned in - # float32, unlike the equivalent n x n primal solve. - expected_step = A.T @ jnp.linalg.solve(A @ A.T + init_damping * jnp.eye(m), b) - assert bool(info_plain.accepted) and bool(info_padded.accepted) - assert jnp.allclose(x_padded, x_plain, rtol=1e-5, atol=1e-6) - assert jnp.allclose(x_padded, expected_step, rtol=1e-4, atol=1e-4) - assert jnp.allclose( - info_padded.loss_candidate, info_plain.loss_candidate, rtol=1e-5 - ) - assert jnp.allclose(info_padded.grad_norm, info_plain.grad_norm, rtol=1e-5) - - -def test_padded_zero_residual_geodesic_matches_unpadded(): - # Nonlinear endgame with geodesic acceleration: the second-order solve - # reuses the same factorization, so padding must not change the - # accelerated step either. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.9, "b": -0.95} - pad = 3 - - def residual_padded(x, args, p): - return jnp.concatenate((residual_fn(x, args, p), jnp.zeros(pad))) - - kwargs = dict( - init_damping=1e-4, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - plain = LevenbergMarquardt(residual_fn, **kwargs) - padded = LevenbergMarquardt(residual_padded, **kwargs) - - x_plain, _, info_plain = plain.update(x, plain.init(x, (ts, ys)), (ts, ys)) - x_padded, _, info_padded = padded.update(x, padded.init(x, (ts, ys)), (ts, ys)) - - # The two dual factorizations have different sizes (m vs m + pad), so - # float32 agreement is to solver noise, not bitwise. - assert bool(info_plain.accepted) and bool(info_padded.accepted) - assert bool(info_padded.used_geodesic) == bool(info_plain.used_geodesic) - assert jnp.allclose(x_padded["a"], x_plain["a"], rtol=1e-4, atol=1e-5) - assert jnp.allclose(x_padded["b"], x_plain["b"], rtol=1e-4, atol=1e-5) - assert jnp.allclose( - info_padded.acceleration_ratio, - info_plain.acceleration_ratio, - rtol=1e-3, - atol=1e-4, - ) - - -def test_padded_zero_residual_cg_with_padded_preconditioner(): - # The dual operator of a padded problem is blockdiag(J J' + damping I, - # damping I); pad_dual_preconditioner extends an exact base inverse with - # the exact 1/damping pad block, so a one-iteration CG budget reproduces - # the cholesky step. - m, n, pad = 10, 24, 3 - A = jax.random.normal(jax.random.PRNGKey(57), (m, n)) - b = jax.random.normal(jax.random.PRNGKey(58), (m,)) - gram = A @ A.T - init_damping = 1e-2 - - def residual_padded(theta): - return jnp.concatenate((A @ theta - b, jnp.zeros(pad))) - - def base_preconditioner(v, damping): - return jnp.linalg.solve(gram + damping * jnp.eye(m), v) - - cg_solver = LevenbergMarquardt( - residual_padded, - init_damping=init_damping, - linear_solver="gram_cg", - iterative_tol=0.0, - iterative_maxiter=1, - dual_preconditioner=pad_dual_preconditioner(base_preconditioner, m), - ad_solver_preconditioner=identity_preconditioner(), - geodesic_acceleration=False, - ) - cholesky_solver = LevenbergMarquardt( - residual_padded, init_damping=init_damping, geodesic_acceleration=False - ) - theta0 = jnp.zeros(n) - - x_cg, _, info_cg = cg_solver.update(theta0, cg_solver.init(theta0)) - x_ch, _, info_ch = cholesky_solver.update(theta0, cholesky_solver.init(theta0)) - - assert bool(info_cg.accepted) and bool(info_ch.accepted) - assert jnp.allclose(x_cg, x_ch, rtol=1e-4, atol=1e-5) - - # A shape-fixed base preconditioner used unwrapped is invalid on the - # padded residual space and fails at trace time. - mismatched = LevenbergMarquardt( - residual_padded, - init_damping=init_damping, - linear_solver="gram_cg", - iterative_tol=0.0, - iterative_maxiter=1, - dual_preconditioner=base_preconditioner, - ad_solver_preconditioner=identity_preconditioner(), - geodesic_acceleration=False, - ) - with pytest.raises(ValueError, match="inconsistent size"): - mismatched.update(theta0, mismatched.init(theta0)) - - -def test_pad_dual_preconditioner_validation(): - with pytest.raises(ValueError, match="n_real must"): - pad_dual_preconditioner(lambda v, damping: v, 0) - with pytest.raises(ValueError, match="n_real must"): - pad_dual_preconditioner(lambda v, damping: v, 2.0) - # A vector shorter than n_real would silently clip through a - # shape-generic base; the callback rejects it at trace time instead. - padded = pad_dual_preconditioner(identity_preconditioner(), 4) - with pytest.raises(ValueError, match="at least"): - padded(jnp.ones(3), 0.1) - assert jnp.allclose(padded(jnp.ones(6), 0.5), jnp.array([1.0] * 4 + [2.0] * 2)) - - -def test_padded_zero_residual_qr_is_rank_deficient(): - # Padded zero rows make the Jacobian rank-deficient, which the qr - # path's triangular solves cannot handle: the padded step is - # non-finite where the unpadded one is fine. - m, n, pad = 12, 30, 4 - A = jax.random.normal(jax.random.PRNGKey(60), (m, n)) - b = jax.random.normal(jax.random.PRNGKey(61), (m,)) - - def residual_padded(theta): - return jnp.concatenate((A @ theta - b, jnp.zeros(pad))) - - solver = LevenbergMarquardt( - residual_padded, - init_damping=1e-4, - linear_solver="qr", - geodesic_acceleration=False, - ) - theta0 = jnp.zeros(n) - x_padded, _, info = solver.update(theta0, solver.init(theta0)) - assert not bool(jnp.all(jnp.isfinite(x_padded))) or not bool( - jnp.isfinite(info.loss_candidate) - ) - - -def test_padded_zero_residual_implicit_ad_is_singular_by_design(): - # Padded rows are zero Jacobian rows, so the UNDAMPED implicit dual - # J P J' is singular. QR keeps the loud unregularized contract - # (non-finite tangent); SVD resolves the padding to the - # minimum-metric-norm tangent of the unpadded formulation, with no - # padding-aware special casing. - A = jax.random.normal(jax.random.PRNGKey(59), (3, 8)) - - def residual(theta, _, p): - return A @ theta - p - - def residual_padded(theta, _, p): - return jnp.concatenate((A @ theta - p, jnp.zeros(2))) - - plain = LevenbergMarquardt(residual, init_damping=1e-2, geodesic_acceleration=False) - padded_loud = LevenbergMarquardt( - residual_padded, - init_damping=1e-2, - geodesic_acceleration=False, - ad_solver="qr", - ) - padded_default = LevenbergMarquardt( - residual_padded, - init_damping=1e-2, - geodesic_acceleration=False, - ad_solver="svd", - ) - - def solved_x(solver, p): - return solver.solve(jnp.zeros(8), p=p, max_steps=40, atol=1e-5).x - - p0 = jnp.array([1.0, -0.5, 0.25]) - p_dot = jnp.ones(3) - x_plain, x_plain_dot = jax.jvp(lambda p: solved_x(plain, p), (p0,), (p_dot,)) - x_padded, x_dot = jax.jvp(lambda p: solved_x(padded_loud, p), (p0,), (p_dot,)) - # The forward padded solve is healthy and matches the unpadded solution; - # only the unregularized implicit tangent is non-finite. - assert bool(jnp.all(jnp.isfinite(x_padded))) - assert jnp.allclose(x_padded, x_plain, atol=1e-4) - assert not bool(jnp.all(jnp.isfinite(x_dot))) - # The SVD pseudoinverse recovers the unpadded implicit tangent. - _, x_dot_default = jax.jvp(lambda p: solved_x(padded_default, p), (p0,), (p_dot,)) - assert bool(jnp.all(jnp.isfinite(x_dot_default))) - assert jnp.allclose(x_dot_default, x_plain_dot, atol=1e-4) - - -def test_implicit_cg_with_repeated_shifted_dense_metric_matches_dense(): - # The CG implicit rule applies the repeated metric solve to - # tangent-dependent data through its self-adjoint declaration. - n, k, eps = 10, 2, 1e-2 - t = jnp.arange(n) * 1.0 - K = dense_matern_gram(t, 1.3, 0.8, 2.5) - composite = repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=k, epsilon=eps - ) - M = repeated_shifted_matrix(K, 1, k, eps) - dense = metric_from_cholesky(jnp.linalg.cholesky(M)) - - A = jax.random.normal(jax.random.PRNGKey(33), (3, n + k)) - - def residual(theta, _, p): - return A @ theta - jnp.array([p, 0.5 * p, -p]) - - def solved_x(metric, linear_solver, ad_solver, p): - preconditioner_kwargs = {} - if linear_solver == "gram_cg": - preconditioner_kwargs["dual_preconditioner"] = identity_preconditioner() - if ad_solver == "gram_cg": - preconditioner_kwargs["ad_solver_preconditioner"] = ( - identity_preconditioner() - ) - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver=linear_solver, - ad_solver=ad_solver, - ad_solver_tol=1e-8, - metric=metric, - iterative_tol=1e-8, - iterative_maxiter=500, - **preconditioner_kwargs, - ) - return solver.solve(jnp.zeros(n + k), p=p, max_steps=80, atol=1e-6).x - - p, p_dot = jnp.asarray(2.0), jnp.asarray(1.0) - x_bar = jnp.linspace(-1.0, 1.0, n + k) - _, dense_dot = jax.jvp( - lambda q: solved_x(dense, "gram_cholesky", "svd", q), (p,), (p_dot,) - ) - _, dense_pull = jax.vjp(lambda q: solved_x(dense, "gram_cholesky", "svd", q), p) - - # Exercise the CG implicit rule under both dense and CG forward solves. - for linear_solver in ("gram_cholesky", "gram_cg"): - _, cg_dot = jax.jvp( - lambda q, ls=linear_solver: solved_x(composite, ls, "gram_cg", q), - (p,), - (p_dot,), - ) - _, cg_pull = jax.vjp( - lambda q, ls=linear_solver: solved_x(composite, ls, "gram_cg", q), p - ) - assert jnp.allclose(cg_dot, dense_dot, atol=1e-4) - assert jnp.allclose(cg_pull(x_bar)[0], dense_pull(x_bar)[0], atol=1e-4) - - -def test_implicit_cg_woodbury_preconditioner_with_shifted_metric(): - # Under the unified shifted metric, the scalar block injects the rank-k - # spike (1/eps) J_beta J_beta' into the UNDAMPED implicit dual operator - # too. An exact Woodbury preconditioner (passed directly; the implicit - # hook calls it with zero damping) makes a - # one-iteration implicit CG budget reproduce the dense-rule derivative. - n, k, eps = 12, 2, 1e-3 - t = jnp.arange(n) * 1.0 - K = dense_matern_gram(t, 1.3, 0.8, 1.5) - K_shifted = K + eps * jnp.eye(n) - metric = repeated_shifted_dense_metric(K, repeats=1, zero_pad_size=k, epsilon=eps) - - m = 6 - J_alpha = jax.random.normal(jax.random.PRNGKey(34), (m, n)) - J_beta = jax.random.normal(jax.random.PRNGKey(35), (m, k)) - A = jnp.concatenate([J_alpha, J_beta], axis=1) - - def residual(theta, _, p): - return A @ theta - p * jnp.linspace(1.0, 2.0, m) - - base = J_alpha @ jnp.linalg.solve(K_shifted, J_alpha.T) - base_solve = metric_from_cholesky(jnp.linalg.cholesky(base)).solve - spike_preconditioner = woodbury_preconditioner( - base_solve, J_beta, (1.0 / eps) * jnp.ones(k) - ) - - def solved_x(ad_kwargs_value, p): - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - iterative_tol=1e-8, - iterative_maxiter=200, - metric=metric, - geodesic_acceleration=False, - **ad_kwargs_value, - ) - return solver.solve(jnp.zeros(n + k), p=p, max_steps=80, atol=1e-6).x - - p, p_dot = jnp.asarray(1.0), jnp.asarray(1.0) - _, dense_dot = jax.jvp( - lambda q: solved_x({"ad_solver": "qr"}, q), - (p,), - (p_dot,), - ) - _, spike_dot = jax.jvp( - lambda q: solved_x( - { - "ad_solver": "gram_cg", - "ad_solver_tol": 0.0, - "ad_solver_maxiter": 1, - # A (v, damping) helper passes directly; the implicit hook - # calls it with zero damping. - "ad_solver_preconditioner": spike_preconditioner, - }, - q, - ), - (p,), - (p_dot,), - ) - assert jnp.allclose(spike_dot, dense_dot, rtol=1e-3, atol=1e-4) - - -def test_implicit_cg_vmap_and_hessian_match_dense(): - # jax.vmap over differentiated solves and vmap-based second derivatives - # (jax.hessian) must compose with the cg implicit rule -- the - # self-adjoint metric-inverse declaration is built on - # custom_linear_solve, which has a batching rule (linear_call does not). - n, k, eps = 8, 2, 1e-2 - t = jnp.arange(n) * 1.0 - K = dense_matern_gram(t, 1.3, 0.8, 2.5) - composite = repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=k, epsilon=eps - ) - M = repeated_shifted_matrix(K, 1, k, eps) - dense = metric_from_cholesky(jnp.linalg.cholesky(M)) - - A = jax.random.normal(jax.random.PRNGKey(36), (3, n + k)) - - def residual(theta, _, p): - return A @ theta - jnp.array([p, 0.5 * p, -p]) - - def solved_x(metric, ad_solver, p): - preconditioner_kwargs = ( - {"ad_solver_preconditioner": identity_preconditioner()} - if ad_solver == "gram_cg" - else {} - ) - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver=ad_solver, - ad_solver_tol=1e-8, - metric=metric, - iterative_tol=1e-8, - iterative_maxiter=300, - **preconditioner_kwargs, - ) - return solver.solve(jnp.zeros(n + k), p=p, max_steps=60, atol=1e-6).x - - ps = jnp.array([1.0, 2.0, 3.0]) - one = jnp.asarray(1.0) - _, dots_cg = jax.vmap( - lambda q: jax.jvp(lambda r: solved_x(composite, "gram_cg", r), (q,), (one,)) - )(ps) - _, dots_dense = jax.vmap( - lambda q: jax.jvp(lambda r: solved_x(dense, "svd", r), (q,), (one,)) - )(ps) - assert jnp.allclose(dots_cg, dots_dense, atol=1e-4) - - def loss_cg(q): - return jnp.sum(solved_x(composite, "gram_cg", q) ** 2) - - def loss_dense(q): - return jnp.sum(solved_x(dense, "svd", q) ** 2) - - assert jnp.allclose( - jax.vmap(jax.grad(loss_cg))(ps), jax.vmap(jax.grad(loss_dense))(ps), atol=1e-3 - ) - assert jnp.allclose( - jax.hessian(loss_cg)(jnp.asarray(2.0)), - jax.hessian(loss_dense)(jnp.asarray(2.0)), - rtol=1e-3, - ) - - -def test_implicit_cg_rank_deficient_dual_fails_loudly_by_default(): - # J P J' singular with an INCONSISTENT tangent right-hand side: the - # unregularized QR hits the rank guard, - # and the cg rule's run-to-tolerance default diverges to non-finite as - # well. Only a small bounded ad_solver_maxiter (the exact-preconditioner - # budget mode) returns a finite -- and wrong -- derivative, which is why - # that mode is reserved for exact preconditioners. (No ridge can make an - # inconsistent dual meaningful; an explicitly regularized method would - # return a finite, penalty-inflated tangent here.) - A = jnp.array( - [ - [1.0, 0.0, 0.0, 0.0, 0.0], - [0.0, 1.0, 0.0, 0.0, 0.0], - [1.0, 1.0, 0.0, 0.0, 0.0], - ] - ) - - def residual(theta, _, p): - return A @ theta - p - - def x_dot(ad_solver, ad_solver_maxiter): - preconditioner_kwargs = ( - {"ad_solver_preconditioner": identity_preconditioner()} - if ad_solver == "gram_cg" - else {} - ) - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver=ad_solver, - ad_solver_tol=1e-8, - ad_solver_maxiter=ad_solver_maxiter, - iterative_tol=1e-8, - iterative_maxiter=100, - geodesic_acceleration=False, - **preconditioner_kwargs, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(5), p=p, max_steps=40, atol=1e-5).x - - p0 = jnp.array([1.0, 2.0, 3.0]) - p_dot = jnp.array([1.0, 0.0, 0.0]) - return jax.jvp(solved_x, (p0,), (p_dot,))[1] - - assert not bool(jnp.all(jnp.isfinite(x_dot("qr", None)))) - assert not bool(jnp.all(jnp.isfinite(x_dot("gram_cg", None)))) - assert bool(jnp.all(jnp.isfinite(x_dot("gram_cg", 1)))) - - -@pytest.mark.parametrize("jit", [True, False]) -def test_callback_returns_bare_lmstatus_members_without_casts(jit): - # The spooky-shaped epoch callback: a lax.cond whose branches return bare - # LMStatus members / weak values -- no .astype or dtype= casts. The solver - # canonicalizes stop to bool and status to int32 at the boundary. - def residual(theta, args, p): - return theta - args - - def epoch_callback(ctx): - def check(_): - stop = ctx.info.loss < 1e-8 - status = jnp.where(stop, LMStatus.CONVERGED, LMStatus.RUNNING) - return stop, status - - def keep_running(_): - return jnp.asarray(False), jnp.asarray(LMStatus.RUNNING) - - stop, status = jax.lax.cond(ctx.step % 2 == 0, check, keep_running, None) - return LMSolveAction(stop=stop, status=status) - - solver = LevenbergMarquardt(residual, init_damping=1e-2) - result = solver.solve( - jnp.array([0.0]), - jnp.array([1.0]), - max_steps=50, - callback=epoch_callback, - jit=jit, - ) - assert result.status.dtype == jnp.int32 - assert int(result.status) == LMStatus.CONVERGED - - -def test_lmstatus_intenum_semantics(): - assert int(LMStatus.CONVERGED) == 1 - assert LMStatus(2) is LMStatus.MAX_STEPS - assert LMStatus.MAX_STEPS.name == "MAX_STEPS" - labels = {LMStatus.CONVERGED: "early_stopping_met"} - assert labels.get(LMStatus(int(jnp.asarray(1)))) == "early_stopping_met" - assert bool(jnp.asarray(1, dtype=jnp.int32) == LMStatus.CONVERGED) diff --git a/tests/test_implicit_geometry.py b/tests/test_implicit_geometry.py deleted file mode 100644 index 8f9668f..0000000 --- a/tests/test_implicit_geometry.py +++ /dev/null @@ -1,440 +0,0 @@ -# The factorized AD rules on tall systems (issue #22) and the jacobian_mode -# assembly geometry it relies on (issue #23). The workhorse is a -# tall (m > n) linear least-squares residual A x - (b + p) with a nonzero -# residual at the solution, where the Gauss-Newton implicit tangent has the -# closed form x_dot = (A'A)^{-1} A' p_dot. - -import jax -import jax.numpy as jnp -import numpy as np - -from nlls_gram import ( - LevenbergMarquardt, - LMStatus, - identity_preconditioner, - metric_from_diagonal, -) - -M, N = 7, 3 -_rng = np.random.default_rng(1234) -A_TALL = jnp.asarray(_rng.normal(size=(M, N)), dtype=jnp.float32) -B_TALL = jnp.asarray(_rng.normal(size=(M,)), dtype=jnp.float32) -P0 = jnp.asarray(_rng.normal(size=(M,)), dtype=jnp.float32) -P_DOT = jnp.asarray(_rng.normal(size=(M,)), dtype=jnp.float32) -X_BAR = jnp.asarray(_rng.normal(size=(N,)), dtype=jnp.float32) -X0 = jnp.zeros(N, dtype=jnp.float32) - - -def tall_residual(x, args, p): - return A_TALL @ x - (B_TALL + p) - - -def analytic_tangent(A, p_dot): - # x*(p) = argmin ||A x - (b + p)||^2 = (A'A)^{-1} A'(b + p), so - # dx*/dp p_dot = (A'A)^{-1} A' p_dot -- metric-independent for a - # full-column-rank tall system. - return jnp.linalg.solve(A.T @ A, A.T @ p_dot) - - -def tall_solver(**overrides): - settings = dict( - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ) - settings.update(overrides) - return LevenbergMarquardt(tall_residual, **settings) - - -def solved_x_fn(solver): - def solved_x(p): - return solver.solve(X0, p=p, max_steps=100, gtol=1e-5).x - - return solved_x - - -def test_tall_augmented_qr_jvp_matches_analytic_and_finite_differences(): - solver = tall_solver() - result = solver.solve(X0, p=P0, max_steps=100, gtol=1e-5) - assert int(result.status) == LMStatus.CONVERGED - # The system is inconsistent: the residual at the solution is nonzero, so - # this exercises the nonzero-residual Gauss-Newton implicit contract. - assert float(result.info.loss) > 1e-2 - - solved_x = solved_x_fn(solver) - x, x_dot = jax.jvp(solved_x, (P0,), (P_DOT,)) - # Measured 1.8e-7 (x) and 2.2e-7 (x_dot) float32 under the SVD/QR rule. - assert jnp.allclose(x, analytic_tangent(A_TALL, B_TALL + P0), atol=1e-4) - assert jnp.allclose(x_dot, analytic_tangent(A_TALL, P_DOT), atol=2e-6) - - # Central finite differences: the problem is linear in p, so a large step - # has zero truncation error and only solver noise divided by 2 * eps. - eps = 0.5 - finite_difference = (solved_x(P0 + eps * P_DOT) - solved_x(P0 - eps * P_DOT)) / ( - 2.0 * eps - ) - assert jnp.allclose(x_dot, finite_difference, atol=1e-3) - - -def test_tall_vjp_jvp_dot_product_transpose_identity(): - solver = tall_solver() - solved_x = solved_x_fn(solver) - _, x_dot = jax.jvp(solved_x, (P0,), (P_DOT,)) - _, pullback = jax.vjp(solved_x, P0) - (p_bar,) = pullback(X_BAR) - # Measured 3.7e-6 relative float32. - assert jnp.allclose( - jnp.vdot(X_BAR, x_dot), jnp.vdot(p_bar, P_DOT), rtol=5e-5, atol=1e-6 - ) - - -def test_metric_whitened_tall_tangent_is_metric_independent(): - # A nonidentity diagonal metric changes the whitened B = J S the normal - # form factors, but for a full-column-rank tall system the tangent is the - # unique (J'J)^{-1} J' p_dot regardless of the metric. - metric = metric_from_diagonal(jnp.asarray([0.5, 2.0, 4.0], dtype=jnp.float32)) - solver = tall_solver(metric=metric) - assert solver._ad_solver_at(X0, None, P0) == "svd" - _, x_dot = jax.jvp(solved_x_fn(solver), (P0,), (P_DOT,)) - # Measured 6e-8 float32. - assert jnp.allclose(x_dot, analytic_tangent(A_TALL, P_DOT), atol=1e-6) - - -# Rank-deficient tall system: parameter column 2 duplicates column 1, so -# B = J is column-rank-deficient. The disjoint one-hot columns are exact in -# float arithmetic, so the undamped normal matrix is exactly singular and the -# unregularized QR rank guard poisons the tangent to NaN. -_A_RANK_DEFICIENT = jnp.zeros((M, N), dtype=jnp.float32) -_A_RANK_DEFICIENT = _A_RANK_DEFICIENT.at[0, 0].set(2.0) -_A_RANK_DEFICIENT = _A_RANK_DEFICIENT.at[1, 1].set(3.0) -_A_RANK_DEFICIENT = _A_RANK_DEFICIENT.at[1, 2].set(3.0) - - -def rank_deficient_residual(x, args, p): - return _A_RANK_DEFICIENT @ x - (B_TALL + p) - - -def test_rank_deficient_tall_algorithms_have_explicit_rank_contracts(): - def tangent(ad_solver, penalty=None): - solver = LevenbergMarquardt( - rank_deficient_residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver=ad_solver, - ad_solver_penalty=penalty, - ) - - def solved_x(p): - return solver.solve(X0, p=p, max_steps=100, gtol=1e-5).x - - return jax.jvp(solved_x, (P0,), (P_DOT,))[1] - - # Default None: the spectral-filter pseudoinverse returns the exact - # minimum-norm tangent, which splits evenly across the duplicated - # parameters -- no ridge, no bias. - filtered = tangent("svd") - assert bool(jnp.all(jnp.isfinite(filtered))) - assert jnp.allclose(filtered[1], filtered[2], atol=1e-5) - - # The opt-in ridge solves the augmented QR [B; sqrt(penalty * trace) I]; - # check it against the float64 analytic ridged solution. Resolving an - # EXACTLY duplicated column pair against the ridge pivot is a cancellation - # at eps32 * sigma_max^2 / (penalty * trace) regardless of factorization - # (measured: 5.6e-5 relative at penalty 1e-4, 1.3e-3 at 1e-5, 4.8e-2 at - # 1e-6), so this fixture floors near penalty 1e-5 in float32; the - # cond(B)-not-cond(B)^2 accuracy of the path itself is pinned on a - # generic fixture by test_ridged_dense_tangent_accuracy_scales_with_cond_b. - A64 = np.asarray(_A_RANK_DEFICIENT, np.float64) - G64 = A64.T @ A64 - p_dot64 = np.asarray(P_DOT, np.float64) - - def analytic_ridged(penalty): - return np.linalg.solve( - G64 + penalty * np.trace(G64) * np.eye(N), A64.T @ p_dot64 - ) - - for penalty, tolerance in ((1e-4, 3e-4), (1e-5, 5e-3)): - regularized = tangent("augmented_qr", penalty) - assert bool(jnp.all(jnp.isfinite(regularized))) - reference = analytic_ridged(penalty) - relative = np.linalg.norm( - np.asarray(regularized, np.float64) - reference - ) / np.linalg.norm(reference) - assert relative < tolerance, (penalty, relative) - - unregularized = tangent("qr") - assert not bool(jnp.all(jnp.isfinite(unregularized))) - - -def test_qr_success_path_on_full_rank_tall_and_square(): - # The m >= n QR SUCCESS path: on a full-column-rank - # system the plain small-side QR is nonsingular and returns the exact - # Gauss-Newton tangent, rather than the rank-guard NaN the singular case - # produces. (Previously only the FAT branch had value coverage at 0.0.) - def qr_tangent(p_dot, **overrides): - solver = LevenbergMarquardt( - tall_residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="qr", - **overrides, - ) - return jax.jvp(solved_x_fn(solver), (P0,), (p_dot,))[1] - - x_dot = qr_tangent(P_DOT) - assert bool(jnp.all(jnp.isfinite(x_dot))) - assert jnp.allclose(x_dot, analytic_tangent(A_TALL, P_DOT), atol=2e-6) - - # A non-identity metric leaves the full-column-rank tangent unchanged but - # exercises the inv_sqrt composition inside the 0.0 branch. - metric = metric_from_diagonal(jnp.array([1.0, 4.0, 0.25], dtype=jnp.float32)) - x_dot_metric = qr_tangent(P_DOT, metric=metric) - assert jnp.allclose(x_dot_metric, analytic_tangent(A_TALL, P_DOT), atol=2e-6) - - # jvp/vjp dot-product identity on the linear tangent map T(p_dot) = x_dot. - solver = LevenbergMarquardt( - tall_residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="qr", - ) - solved_x = solved_x_fn(solver) - _, vjp_fn = jax.vjp(solved_x, P0) - lhs = jnp.vdot(X_BAR, jax.jvp(solved_x, (P0,), (P_DOT,))[1]) - rhs = jnp.vdot(vjp_fn(X_BAR)[0], P_DOT) - assert jnp.allclose(lhs, rhs, atol=2e-5) - - # Square nonsingular: the same 0.0 path gives dx/dp = A^{-1} p_dot. - sq_rng = np.random.default_rng(7) - A_sq = jnp.asarray(sq_rng.normal(size=(N, N)), dtype=jnp.float32) - b_sq = jnp.asarray(sq_rng.normal(size=(N,)), dtype=jnp.float32) - - def square_residual(x, args, p): - return A_sq @ x - (b_sq + p) - - square_solver = LevenbergMarquardt( - square_residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="qr", - ) - p0 = jnp.asarray(sq_rng.normal(size=(N,)), dtype=jnp.float32) - p_dot = jnp.asarray(sq_rng.normal(size=(N,)), dtype=jnp.float32) - sq_tangent = jax.jvp( - lambda p: square_solver.solve(X0, p=p, max_steps=100, gtol=1e-6).x, - (p0,), - (p_dot,), - )[1] - assert jnp.allclose(sq_tangent, jnp.linalg.solve(A_sq, p_dot), atol=2e-5) - - -def test_augmented_qr_tangent_accuracy_scales_with_cond_b(): - # Regression for the cond(B)-not-cond(B)^2 contract of augmented QR: - # rule: at cond(B) ~ 1e3 and penalty 1e-6 a normal-equations Cholesky - # loses eps32 * cond^2 ~ 0.1 of the tangent, while the small-side - # augmented QR [B; sqrt(penalty * trace) I] keeps the float32 error at - # the eps32 * cond level -- measured 2.2e-6 relative against the float64 - # analytic ridge. - m, n, penalty = 12, 4, 1e-6 - U, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (m, n))) - V, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(1), (n, n))) - A = ((U * jnp.logspace(0.0, -3.0, n)) @ V.T).astype(jnp.float32) - b = jax.random.normal(jax.random.key(2), (m,), dtype=jnp.float32) - p_dot = jax.random.normal(jax.random.key(3), (m,), dtype=jnp.float32) - - def residual(x, args, p): - return A @ x - (b + p) - - solver = LevenbergMarquardt( - residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="augmented_qr", - ad_solver_penalty=penalty, - ) - x_dot = jax.jvp( - lambda p: ( - solver.solve(jnp.zeros(n, jnp.float32), p=p, max_steps=100, gtol=1e-5).x - ), - (jnp.zeros(m, jnp.float32),), - (p_dot,), - )[1] - - A64 = np.asarray(A, np.float64) - G64 = A64.T @ A64 - expected = np.linalg.solve( - G64 + penalty * np.trace(G64) * np.eye(n), - A64.T @ np.asarray(p_dot, np.float64), - ) - relative = np.linalg.norm( - np.asarray(x_dot, np.float64) - expected - ) / np.linalg.norm(expected) - assert relative < 2e-5, relative - - -def test_auto_ad_solver_dispatch(): - auto_solver = LevenbergMarquardt(tall_residual) - assert auto_solver._ad_solver_at(X0, None, P0) == "svd" - - cg_solver = LevenbergMarquardt( - tall_residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - ) - assert cg_solver._ad_solver_at(X0, None, P0) == "gram_cg" - - # Every non-cg forward uses SVD on this non-square problem. - for linear_solver in ("qr", "augmented_qr", "lsmr"): - whitened = LevenbergMarquardt(tall_residual, linear_solver=linear_solver) - assert whitened._ad_solver_at(X0, None, P0) == "svd" - - for form, resolved in ( - ("gram_cholesky", "svd"), - ("normal_cholesky", "svd"), - ("normal_cg", "normal_cg"), - ): - kwargs = ( - {"normal_preconditioner": identity_preconditioner()} - if form == "normal_cg" - else {} - ) - follows = LevenbergMarquardt(tall_residual, linear_solver=form, **kwargs) - assert follows._ad_solver_at(X0, None, P0) == resolved - - -def test_svd_ad_tangent_is_invariant_across_jacobian_mode(): - # The SVD AD rule assembles B via _assemble_jt, which picks fwd/rev by - # shape; a forced mode must change only cost, never the tangent (guards a - # transposed-axis / (m, n) arg-order flip that a green suite would miss). - def tangent(jacobian_mode): - solver = LevenbergMarquardt( - tall_residual, - linear_solver="augmented_qr", - jacobian_mode=jacobian_mode, - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="svd", - ) - return jax.jvp(solved_x_fn(solver), (P0,), (P_DOT,))[1] - - reference = analytic_tangent(A_TALL, P_DOT) - for jacobian_mode in ("auto", "fwd", "rev"): - assert jnp.allclose(tangent(jacobian_mode), reference, atol=2e-6) - - -def _iter_jaxprs(jaxpr): - yield jaxpr - for eqn in jaxpr.eqns: - for value in eqn.params.values(): - yield from _iter_jaxprs_in_param(value) - - -def _iter_jaxprs_in_param(value): - if hasattr(value, "jaxpr"): # ClosedJaxpr - yield from _iter_jaxprs(value.jaxpr) - elif hasattr(value, "eqns"): # raw Jaxpr - yield from _iter_jaxprs(value) - elif isinstance(value, (list, tuple)): - for item in value: - yield from _iter_jaxprs_in_param(item) - - -def test_tall_jvp_jaxpr_materializes_no_m_by_m_array(): - # Issue #23's memory contract: differentiating the tall solve must never - # build an (m, m) residual-space array -- neither the dense-assembly - # identity basis nor a dual Gram matrix -- anywhere in the program. - solver = tall_solver() - solved_x = solved_x_fn(solver) - closed = jax.make_jaxpr(lambda p: jax.jvp(solved_x, (p,), (P_DOT,)))(P0) - offenders = [] - for jaxpr in _iter_jaxprs(closed.jaxpr): - variables = list(jaxpr.invars) + list(jaxpr.constvars) + list(jaxpr.outvars) - for eqn in jaxpr.eqns: - variables.extend(eqn.invars) - variables.extend(eqn.outvars) - for var in variables: - aval = getattr(var, "aval", None) - if aval is not None and tuple(getattr(aval, "shape", ())) == (M, M): - offenders.append(str(var)) - assert not offenders, f"(m, m) arrays found in the jvp jaxpr: {offenders}" - - -# Consistent tall system: a full-rank square system stacked twice, so m = 2n -# but the residual at the solution is ~0 and the dual J J' is rank n. -A_SQUARE = jnp.asarray(np.eye(3) + 0.3 * _rng.normal(size=(3, 3)), dtype=jnp.float32) -X_TRUE = jnp.asarray(_rng.normal(size=(3,)), dtype=jnp.float32) -P_STACKED = jnp.concatenate([A_SQUARE @ X_TRUE, A_SQUARE @ X_TRUE]) -P_STACKED_DOT = jnp.asarray(_rng.normal(size=(6,)), dtype=jnp.float32) - - -def stacked_residual(x, args, p): - top = A_SQUARE @ x - return jnp.concatenate([top, top]) - p - - -def test_stacked_residual_augmented_qr_tangent_matches_analytic(): - # An explicit ad_solver_penalty is the trace-scaled ridge on B'B - # (trace(J P J') = trace(B'B), so the ridge means the same thing in - # either push-through composition of the augmented-QR rule); the O(penalty * m) - # bias stays below the analytic tolerance. - solver = LevenbergMarquardt( - stacked_residual, - linear_solver="augmented_qr", - geodesic_acceleration=False, - cache_jacobian=False, - ad_solver="augmented_qr", - ad_solver_penalty=1e-4, - ) - - def solved_x(p): - return solver.solve( - jnp.zeros(3, dtype=jnp.float32), p=p, max_steps=100, atol=1e-5 - ).x - - ridged = jax.jvp(solved_x, (P_STACKED,), (P_STACKED_DOT,))[1] - assert bool(jnp.all(jnp.isfinite(ridged))) - # Agrees with the analytic minimum-norm tangent of the stacked system, - # x_dot = pinv([A; A]) p_dot = (2 A'A)^{-1} A'(p_dot_top + p_dot_bottom), - # up to the O(penalty * m) ridge bias. - expected = jnp.linalg.solve( - 2.0 * A_SQUARE.T @ A_SQUARE, - A_SQUARE.T @ (P_STACKED_DOT[:3] + P_STACKED_DOT[3:]), - ) - assert jnp.allclose(ridged, expected, atol=5e-3) - - -def test_svd_tangent_on_inconsistent_tall_matches_analytic(): - # -S (B'B)^+ B' (r_p p_dot) = -S B^+ (r_p p_dot): the default - # spectral-filter pseudoinverse computes the Gauss-Newton tangent even - # when the residual at the solution is nonzero (the rhs B'(r_p p_dot) - # always lies in range(B'B), so the filtered solve is exact). - solver = tall_solver(ad_solver="svd") - svd_tangent = jax.jvp(solved_x_fn(solver), (P0,), (P_DOT,))[1] - # Measured 2.2e-7 float32. - assert jnp.allclose(svd_tangent, analytic_tangent(A_TALL, P_DOT), atol=2e-6) - - -def test_lsmr_forward_with_auto_implicit_matches_analytic_tangent(): - solver = LevenbergMarquardt( - tall_residual, - linear_solver="lsmr", - iterative_maxiter=200, - iterative_tol=1e-8, - geodesic_acceleration=False, - cache_jacobian=False, - ) - assert solver._ad_solver_at(X0, None, P0) == "svd" - - def solved_x(p): - return solver.solve(X0, p=p, max_steps=100, gtol=1e-5).x - - x, x_dot = jax.jvp(solved_x, (P0,), (P_DOT,)) - # Measured 3e-7 (x) and 2.2e-7 (x_dot) float32. - assert jnp.allclose(x, analytic_tangent(A_TALL, B_TALL + P0), atol=1e-4) - assert jnp.allclose(x_dot, analytic_tangent(A_TALL, P_DOT), atol=2e-6) diff --git a/tests/test_jacobian_mode.py b/tests/test_jacobian_mode.py deleted file mode 100644 index f69f38a..0000000 --- a/tests/test_jacobian_mode.py +++ /dev/null @@ -1,225 +0,0 @@ -# Issue #23: jacobian_mode ("auto"/"fwd"/"rev") dense Jacobian assembly. - -import jax -import jax.numpy as jnp -import pytest - -from nlls_gram import LevenbergMarquardt, LMStatus, identity_preconditioner - -TALL_M, TALL_N = 10, 3 -FAT_M, FAT_N = 3, 10 - - -def _linear_problem(m, n, seed): - key_a, key_b = jax.random.split(jax.random.key(seed)) - A = jax.random.normal(key_a, (m, n)) + 0.1 - b = jax.random.normal(key_b, (m,)) - return A, b - - -def _pinv_solution(A, b): - return jnp.linalg.pinv(A) @ b - - -# "auto" resolves to normal_cholesky on the tall shape and gram_cholesky on -# the fat one, so the shape parametrize covers both dense cholesky forms. -DENSE_CONFIGS = [ - ("qr", False), - ("augmented_qr", False), - ("auto", True), - ("auto", False), -] - - -@pytest.mark.parametrize("shape", [(TALL_M, TALL_N), (FAT_M, FAT_N)]) -@pytest.mark.parametrize("linear_solver,cache_jacobian", DENSE_CONFIGS) -def test_fwd_rev_auto_agree_and_match_closed_form(shape, linear_solver, cache_jacobian): - m, n = shape - A, b = _linear_problem(m, n, seed=7) - expected = _pinv_solution(A, b) - - def residual(x, args, p): - return A @ x - b - - def build(mode): - return LevenbergMarquardt( - residual, - linear_solver=linear_solver, - jacobian_mode=mode, - cache_jacobian=cache_jacobian, - geodesic_acceleration=False, - ) - - # The core of issue #23: fwd and rev assemble the SAME Jacobian two ways, - # so a single deterministic update from x0 must agree tightly. This is the - # platform-robust invariant -- unlike a full float32 LM solve, whose - # accept/reject trajectory near the solution is rounding-sensitive and can - # stop at slightly different points on different CPUs. - steps = {} - for mode in ("auto", "fwd", "rev"): - solver = build(mode) - x_next, _, _ = solver.update(jnp.zeros(n), solver.init(jnp.zeros(n))) - steps[mode] = x_next - assert jnp.allclose(steps["fwd"], steps["rev"], atol=1e-5) - assert jnp.allclose(steps["auto"], steps["fwd"], atol=1e-5) - assert jnp.allclose(steps["auto"], steps["rev"], atol=1e-5) - - # End to end each mode reaches the minimum-norm (pseudoinverse) solution; - # from x0 = 0 every dense step stays in range(A'). The tolerance is loose - # because a float32 LM solve stops at a platform-dependent point near the - # solution -- the tight invariant is the per-update agreement above. - for mode in ("auto", "fwd", "rev"): - result = build(mode).solve(jnp.zeros(n), max_steps=200, gtol=1e-6) - assert jnp.allclose(result.x, expected, atol=1e-3), ( - f"{linear_solver} mode={mode} missed the closed form" - ) - - -def _collect_shapes_from_jaxpr(jaxpr, shapes): - for eqn in jaxpr.eqns: - for var in list(eqn.invars) + list(eqn.outvars): - aval = getattr(var, "aval", None) - if aval is not None and hasattr(aval, "shape"): - shapes.add(tuple(aval.shape)) - for value in eqn.params.values(): - _collect_shapes_from_param(value, shapes) - - -def _collect_shapes_from_param(value, shapes): - if hasattr(value, "jaxpr") and hasattr(value.jaxpr, "eqns"): - _collect_shapes_from_jaxpr(value.jaxpr, shapes) - elif hasattr(value, "eqns"): - _collect_shapes_from_jaxpr(value, shapes) - elif isinstance(value, (list, tuple)): - for item in value: - _collect_shapes_from_param(item, shapes) - - -def _update_shapes(jacobian_mode, m, n): - A, b = _linear_problem(m, n, seed=11) - - def residual(x, args, p): - return A @ x - b - - solver = LevenbergMarquardt( - residual, - linear_solver="augmented_qr", - jacobian_mode=jacobian_mode, - cache_jacobian=False, - geodesic_acceleration=False, - ) - x0 = jnp.zeros(n) - lm_state = solver.init(x0) - closed = jax.make_jaxpr(lambda x, s: solver.update(x, s))(x0, lm_state) - shapes = set() - _collect_shapes_from_jaxpr(closed.jaxpr, shapes) - return shapes - - -def test_auto_never_materializes_m_by_m_for_tall_systems(): - m, n = 13, 3 - for mode in ("auto", "fwd"): - shapes = _update_shapes(mode, m, n) - assert (m, m) not in shapes, ( - f"jacobian_mode={mode} materialized an (m, m) array on a tall system" - ) - # Sanity check that the structural probe can see the blowup at all: the - # forced reverse mode vmaps over an m x m residual identity basis. - rev_shapes = _update_shapes("rev", m, n) - assert (m, m) in rev_shapes - - -def test_auto_resolution_breaks_square_tie_to_fwd(): - # At n == m the pass counts are equal, so the tie goes to the cheaper - # forward-mode JVP columns; reverse rows are kept only for strictly fat - # systems (a shape probe cannot distinguish the modes at n == m, so the - # resolution itself is asserted). - solver = LevenbergMarquardt(lambda x, args, p: x - p) - assert solver._resolve_jacobian_mode(5, 5) == "fwd" - assert solver._resolve_jacobian_mode(6, 5) == "fwd" - assert solver._resolve_jacobian_mode(5, 6) == "rev" - - -def test_has_aux_under_fwd_mode(): - A, b = _linear_problem(TALL_M, TALL_N, seed=3) - - def residual(x, args, p): - r = A @ x - b - return r, {"first_param": x[0], "sum_sq": jnp.sum(r**2)} - - solver = LevenbergMarquardt( - residual, - jacobian_mode="fwd", - has_aux=True, - geodesic_acceleration=False, - ) - result = solver.solve(jnp.zeros(TALL_N), max_steps=100, gtol=1e-6) - - expected_x = _pinv_solution(A, b) - expected_r = A @ result.x - b - assert jnp.allclose(result.x, expected_x, atol=1e-4) - # result.aux is the aux evaluated at the returned solution. - assert jnp.allclose(result.aux["first_param"], result.x[0], atol=1e-6) - assert jnp.allclose(result.aux["sum_sq"], jnp.sum(expected_r**2), atol=1e-4) - # The per-step info aux has the same pytree structure. - assert set(result.info.aux.keys()) == {"first_param", "sum_sq"} - - -def test_unknown_jacobian_mode_raises(): - with pytest.raises(ValueError, match="jacobian_mode"): - LevenbergMarquardt(lambda x: x, jacobian_mode="bogus") - - -def test_fwd_mode_with_explicit_cg_ad_solver_raises(): - with pytest.raises(ValueError, match="jacobian_mode"): - LevenbergMarquardt( - lambda x: x, - linear_solver="gram_cg", - jacobian_mode="fwd", - dual_preconditioner=identity_preconditioner(), - ad_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - ) - - -def test_fwd_mode_with_lsmr_and_svd_implicit_is_accepted(): - # The lsmr forward path is matrix-free, but the SVD implicit method - # consumes the jacobian_mode setting, so this is valid. - solver = LevenbergMarquardt( - lambda x: x, - linear_solver="lsmr", - jacobian_mode="fwd", - ad_solver="svd", - ) - assert solver.jacobian_mode == "fwd" - - -def test_fwd_mode_with_lsmr_and_assembled_ad_is_accepted(): - # This square system resolves auto to direct, so jacobian_mode has a - # consumer even though the forward LSMR path is matrix-free. - solver = LevenbergMarquardt( - lambda x: x, - linear_solver="lsmr", - jacobian_mode="fwd", - ) - assert solver.jacobian_mode == "fwd" - - -def test_geodesic_acceleration_under_fwd_mode(): - a_true, b_true = 2.0, -1.0 - ts = jnp.linspace(0.0, 2.0, 12) - ys = a_true * jnp.exp(b_true * ts) - - def residual(x, args, p): - return x["a"] * jnp.exp(x["b"] * ts) - ys - - # Default solver settings: auto (normal_cholesky on this tall problem, - # m=12 > n=2), cache_jacobian=True, geodesic_acceleration=True, forced fwd. - solver = LevenbergMarquardt(residual, jacobian_mode="fwd") - assert solver.geodesic_acceleration - - result = solver.solve({"a": 1.0, "b": 0.0}, max_steps=100, atol=1e-5) - - assert int(result.status) == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], a_true, atol=1e-4) - assert jnp.allclose(result.x["b"], b_true, atol=1e-4) diff --git a/tests/test_lsmr.py b/tests/test_lsmr.py deleted file mode 100644 index 1941d47..0000000 --- a/tests/test_lsmr.py +++ /dev/null @@ -1,716 +0,0 @@ -import dataclasses -import subprocess -import sys -import textwrap - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import pytest - -from nlls_gram import ( - GramMetric, - LevenbergMarquardt, - LMSolveAction, - LMStatus, - MultiStart, - RecycleConfig, - WhitenedPreconditioner, - identity_preconditioner, - metric_from_cholesky, -) -from nlls_gram.lsmr import lsmr - - -def _right_preconditioner(G, lam): - # Parameter-space right-preconditioner R = chol(G'G + lam I)': A_r = G R^{-1} - # has a clustered spectrum (a Schur-style factor). Returns the hook and R. - R = jnp.linalg.cholesky(G.T @ G + lam * jnp.eye(G.shape[1])).T - - def solve(v, damping): - return jsp_linalg.solve_triangular(R, v, lower=False) - - def solve_transpose(w, damping): - return jsp_linalg.solve_triangular(R.T, w, lower=True) - - return WhitenedPreconditioner(solve, solve_transpose), R - - -# --- LSMR core correctness vs a dense reference ------------------------------ - - -@pytest.mark.parametrize("shape", [(20, 8), (8, 20), (12, 12)]) -@pytest.mark.parametrize("lam", [1.0, 1e-2]) -def test_lsmr_core_matches_dense(shape, lam): - # Well-conditioned so the float32 dense normal-equations reference is itself - # trustworthy; LSMR solves min ||A x - b||^2 + lam ||x||^2. - m, n = shape - A = jax.random.normal(jax.random.key(0), (m, n)) - b = jax.random.normal(jax.random.key(1), (m,)) - x, state = lsmr( - lambda z: A @ z, - lambda y: A.T @ y, - b, - damp=jnp.sqrt(jnp.asarray(lam)), - atol=1e-8, - btol=0.0, - maxiter=200, - ) - xref = jnp.linalg.solve(A.T @ A + lam * jnp.eye(n), A.T @ b) - assert jnp.allclose(x, xref, rtol=1e-3, atol=1e-4) - assert int(state.iterations) >= 1 - assert float(state.normal_residual) < 1e-3 - - -def test_lsmr_core_jits(): - m, n = 15, 6 - A = jax.random.normal(jax.random.key(0), (m, n)) - b = jax.random.normal(jax.random.key(1), (m,)) - - @jax.jit - def solve(b): - return lsmr(lambda z: A @ z, lambda y: A.T @ y, b, atol=1e-8, maxiter=100)[0] - - xref = jnp.linalg.lstsq(A, b)[0] - assert jnp.allclose(solve(b), xref, rtol=1e-3, atol=1e-4) - - -# --- step parity with the dense whitened / dual paths ------------------------ - - -def residual_fn(x, args, p): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -def test_lsmr_step_matches_augmented_qr_and_cholesky(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - common = dict(init_damping=1e-2, geodesic_acceleration=False) - cholesky = LevenbergMarquardt(residual_fn, **common) - aug_qr = LevenbergMarquardt(residual_fn, linear_solver="augmented_qr", **common) - lsmr_solver = LevenbergMarquardt( - residual_fn, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=50, - **common, - ) - xc, _, ic = cholesky.update(x, cholesky.init(x, (ts, ys)), (ts, ys)) - xa, _, _ = aug_qr.update(x, aug_qr.init(x, (ts, ys)), (ts, ys)) - xl, _, il = lsmr_solver.update(x, lsmr_solver.init(x, (ts, ys)), (ts, ys)) - assert bool(il.accepted) == bool(ic.accepted) - for key in ("a", "b"): - assert jnp.allclose(xl[key], xc[key], rtol=1e-4, atol=1e-4) - assert jnp.allclose(xl[key], xa[key], rtol=1e-4, atol=1e-4) - - -def _ill_conditioned_linear(m=12, n=12, cond=1e3): - U, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (m, m))) - V, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(1), (n, n))) - k = min(m, n) - sv = jnp.logspace(0.0, -jnp.log10(cond), k) - G = (U[:, :k] * sv) @ V[:k, :] - b = jax.random.normal(jax.random.key(2), (m,)) - - def residual(x): - return G @ x - b - - return residual, jnp.zeros(n), G, b - - -def test_lsmr_beats_cg_dual_step_on_ill_conditioned_operator(): - # THE motivating case: the cg dual operator J M^{-1} J' + lambda I has - # condition ~ cond(G)^2, so at tiny lambda its float32 step bottoms out at - # eps * cond and here degrades enough to be rejected; the whitened operator - # (augmented_qr and lsmr) works at cond(G) and produces an accurate step. - residual, x0, G, b = _ill_conditioned_linear(cond=1e3) - lam = 1e-8 - common = dict(init_damping=lam, geodesic_acceleration=False) - reference = LevenbergMarquardt(residual, linear_solver="augmented_qr", **common) - cg = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=200, - **common, - ) - lsmr_solver = LevenbergMarquardt( - residual, - linear_solver="lsmr", - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=200, - **common, - ) - xr, _, _ = reference.update(x0, reference.init(x0)) - xc, _, _ = cg.update(x0, cg.init(x0)) - xl, _, _ = lsmr_solver.update(x0, lsmr_solver.init(x0)) - scale = float(jnp.linalg.norm(xr)) - err_cg = float(jnp.linalg.norm(xc - xr)) / scale - err_lsmr = float(jnp.linalg.norm(xl - xr)) / scale - # lsmr tracks the whitened reference; the squared cg step is far off. - assert err_lsmr < 1e-3 - assert err_cg > 0.1 - assert err_lsmr < 0.01 * err_cg - - -# --- solve / jit / callbacks ------------------------------------------------- - - -def test_lsmr_solve_converges(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=50, - ) - result = solver.solve({"a": 1.0, "b": 0.0}, (ts, ys), max_steps=60, atol=1e-6) - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.loss) < 1e-6 - - -def test_lsmr_update_jits(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="lsmr", - iterative_tol=1e-9, - iterative_maxiter=40, - ) - - @jax.jit - def step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = step(x, solver.init(x, (ts, ys))) - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - - -def test_lsmr_callback_maxiter_schedule_composes(): - # A callback that grows iterative_maxiter mid-solve reschedules the traced - # LSMR cap; the loop retraces nothing (maxiter rides hyper) and still converges. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="lsmr", - geodesic_acceleration=False, - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=2, - ) - - def schedule(ctx): - grown = dataclasses.replace( - ctx.lm_state, - hyper=dataclasses.replace( - ctx.lm_state.hyper, - iterative_maxiter=jnp.where( - ctx.info.loss < 1e-1, jnp.int32(40), jnp.int32(2) - ), - ), - ) - return LMSolveAction(lm_state=grown) - - result = solver.solve( - {"a": 1.0, "b": 0.0}, (ts, ys), max_steps=80, atol=1e-6, callback=schedule - ) - assert int(result.status) == LMStatus.CONVERGED - - -def test_lsmr_multi_start_vmap(): - residual, x0, _, _ = _ill_conditioned_linear(cond=1e2) - solver = LevenbergMarquardt( - residual, - init_damping=1e-4, - linear_solver="lsmr", - geodesic_acceleration=False, - iterative_tol=1e-9, - iterative_maxiter=40, - ) - - def draw(key, x, args): - return x + 0.01 * jax.random.normal(key, x.shape), args - - for parallel in (False, True): - ms = MultiStart( - key=jax.random.key(0), num_starts=3, draw=draw, parallel=parallel - ) - result = solver.solve(x0, max_steps=80, atol=1e-6, multi_start=ms) - assert int(result.status) == LMStatus.CONVERGED - - -# --- custom metric ----------------------------------------------------------- - - -def test_lsmr_with_custom_metric_matches_cholesky(): - # A dense-cholesky metric supplies inv_sqrt / inv_sqrt_transpose; the whitened - # operator B = J S uses them and the step matches the cholesky dual solve. - n = 6 - W = jax.random.normal(jax.random.key(0), (n, n)) - Mmat = W @ W.T + n * jnp.eye(n) - L = jnp.linalg.cholesky(Mmat) - metric = metric_from_cholesky(L) - G = jax.random.normal(jax.random.key(3), (10, n)) - b = jax.random.normal(jax.random.key(4), (10,)) - - def residual(x): - return G @ x - b - - common = dict(init_damping=1e-3, metric=metric, geodesic_acceleration=False) - cholesky = LevenbergMarquardt(residual, **common) - lsmr_solver = LevenbergMarquardt( - residual, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=80, - **common, - ) - x0 = jnp.zeros(n) - xc, _, _ = cholesky.update(x0, cholesky.init(x0)) - xl, _, _ = lsmr_solver.update(x0, lsmr_solver.init(x0)) - assert jnp.allclose(xl, xc, rtol=1e-3, atol=1e-4) - - -# --- differentiation --------------------------------------------------------- - - -def test_lsmr_update_reverse_ad_matches_cholesky(): - ts = jnp.linspace(0.0, 2.0, 20) - - def residual_data(x, args, p): - return x["a"] * jnp.exp(x["b"] * ts) - args - - x = {"a": 1.0, "b": 0.0} - cholesky = LevenbergMarquardt( - residual_data, init_damping=1e-2, geodesic_acceleration=False - ) - lsmr_solver = LevenbergMarquardt( - residual_data, - init_damping=1e-2, - linear_solver="lsmr", - geodesic_acceleration=False, - iterative_tol=1e-10, - iterative_maxiter=80, - ) - - def loss_of(solver): - def loss(ys): - new_x, _, _ = solver.update(x, solver.init(x, ys), ys) - return jnp.sum(new_x["a"] ** 2 + new_x["b"] ** 2) - - return loss - - ys = 2.0 * jnp.exp(-1.0 * ts) - g_lsmr = jax.grad(loss_of(lsmr_solver))(ys) - g_cholesky = jax.grad(loss_of(cholesky))(ys) - assert jnp.allclose(g_lsmr, g_cholesky, rtol=1e-3, atol=1e-4) - - -def test_lsmr_geodesic_matches_cholesky(): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - cholesky = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - lsmr_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=20, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - ct, _, ci = cholesky.update(theta0, cholesky.init(theta0, target), target) - lt, _, li = lsmr_solver.update(theta0, lsmr_solver.init(theta0, target), target) - assert bool(li.used_geodesic) - assert jnp.allclose(lt, ct, rtol=1e-5, atol=1e-5) - assert jnp.allclose( - li.acceleration_ratio, ci.acceleration_ratio, rtol=1e-4, atol=1e-5 - ) - - -def test_lsmr_implicit_p_derivative_matches_analytic(): - # auto + lsmr defers the implicit form to trace-time shapes; this system - # is tall (m=12 > n=1), so shape_auto resolves to normal_cholesky and the - # p-derivative matches the analytic least-squares sensitivity - # sum(ts)/sum(ts^2) exactly. The gram_cholesky forward's default filter - # computes the same tangent through the rank-1 12x12 dual. - ts = jnp.linspace(0.0, 2.0, 12) - - def residual_p(x, args, p): - return x * ts - p - - cholesky = LevenbergMarquardt( - residual_p, init_damping=1e-3, linear_solver="gram_cholesky" - ) - lsmr_solver = LevenbergMarquardt( - residual_p, - init_damping=1e-3, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=60, - ) - p = jnp.asarray(1.7) - assert lsmr_solver._resolved_ad_solver == "auto" - assert lsmr_solver._ad_solver_at(jnp.zeros(()), None, p) == "svd" - j_analytic = jnp.sum(ts) / jnp.sum(ts**2) - - def solved(solver, q): - return solver.solve(jnp.zeros(()), p=q, max_steps=60, atol=1e-9).x - - j_cholesky = jax.jacobian(lambda q: solved(cholesky, q))(p) - j_lsmr = jax.jacobian(lambda q: solved(lsmr_solver, q))(p) - assert jnp.allclose(j_lsmr, j_analytic, rtol=1e-4, atol=1e-5) - assert jnp.allclose(j_cholesky, j_analytic, rtol=1e-4, atol=1e-5) - - -# --- validation -------------------------------------------------------------- - - -def test_lsmr_rejects_recycle_and_preconditioner_hooks(): - residual, x0, _, _ = _ill_conditioned_linear() - with pytest.raises(ValueError, match="recycle requires"): - LevenbergMarquardt( - residual, linear_solver="lsmr", recycle=RecycleConfig(rank=2) - ) - from nlls_gram import PreconditionerFactory - - with pytest.raises(ValueError, match="preconditioner_factory requires"): - LevenbergMarquardt( - residual, - linear_solver="lsmr", - preconditioner_factory=PreconditionerFactory( - lambda *a: jnp.zeros(()), lambda *a: a[1] - ), - ) - with pytest.raises(ValueError, match="dual_preconditioner requires"): - LevenbergMarquardt( - residual, - linear_solver="lsmr", - dual_preconditioner=identity_preconditioner(), - ) - - -def test_lsmr_custom_metric_requires_inv_sqrt(): - with pytest.raises(ValueError, match="inv_sqrt"): - LevenbergMarquardt( - lambda x: x, - linear_solver="lsmr", - geodesic_acceleration=False, - metric=GramMetric(solve=lambda x: x), - ) - - -def test_unknown_linear_solver_rejected(): - with pytest.raises(ValueError, match="unknown linear_solver"): - LevenbergMarquardt(lambda x: x, linear_solver="lsqr") - - -# --- x64 in a clean subprocess ----------------------------------------------- - - -def test_lsmr_float64_subprocess(): - script = textwrap.dedent( - """ - import jax - jax.config.update("jax_enable_x64", True) - import jax.numpy as jnp - from nlls_gram import LevenbergMarquardt, LMStatus - - # Ill-conditioned whitened operator: the float64 dense normal-equations - # solve is limited by cond(G)^2 ~ 1e12 (~1e-4 relative), while lsmr works - # at cond(G) ~ 1e6 and matches the whitened augmented_qr reference tightly. - f64 = jnp.float64 - m, n = 12, 12 - U, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (m, m), dtype=f64)) - V, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(1), (n, n), dtype=f64)) - sv = jnp.logspace(0.0, -6.0, n, dtype=f64) - G = (U[:, :n] * sv) @ V[:n, :] - b = jax.random.normal(jax.random.key(2), (m,), dtype=f64) - - def residual(x): - return G @ x - b - - x0 = jnp.zeros(n, dtype=f64) - lam = 1e-10 - common = dict(init_damping=lam, geodesic_acceleration=False) - ref = LevenbergMarquardt(residual, linear_solver="augmented_qr", **common) - lsmr_solver = LevenbergMarquardt( - residual, linear_solver="lsmr", iterative_tol=0.0, - iterative_atol=0.0, iterative_maxiter=400, **common, - ) - xr, _, _ = ref.update(x0, ref.init(x0)) - xl, lm_state, info = lsmr_solver.update(x0, lsmr_solver.init(x0)) - assert xl.dtype == f64 - assert lm_state.damping.dtype == f64 - rel = float(jnp.linalg.norm(xl - xr) / jnp.linalg.norm(xr)) - assert rel < 1e-5, rel - upd = lambda x, s: lsmr_solver.update(x, s) - jaxpr = str(jax.make_jaxpr(upd)(x0, lsmr_solver.init(x0))) - assert "f32" not in jaxpr, jaxpr - print("OK", rel) - """ - ) - completed = subprocess.run( - [sys.executable, "-c", script], capture_output=True, text=True - ) - assert completed.returncode == 0, completed.stderr - assert "OK" in completed.stdout - - -# --- whitened_preconditioner (parameter-space right-preconditioner) ---------- - - -def test_whitened_preconditioner_reduces_lsmr_iterations(): - # A good right-preconditioner clusters the spectrum of B R^{-1}, so LSMR reaches - # the same relative tolerance in far fewer iterations than plain LSMR. - residual, x0, G, b = _ill_conditioned_linear(m=40, n=40, cond=1e3) - lam = 1e-6 - prec, R = _right_preconditioner(G, lam) - sq = jnp.sqrt(jnp.asarray(lam)) - _, plain = lsmr( - lambda z: G @ z, lambda y: G.T @ y, -b, damp=sq, atol=1e-8, maxiter=500 - ) - _, precond = lsmr( - lambda z: G @ prec.solve(z, lam), - lambda y: prec.solve_transpose(G.T @ y, lam), - -b, - damp=sq, - atol=1e-8, - maxiter=500, - ) - assert int(precond.iterations) < int(plain.iterations) // 10 - - -def test_whitened_preconditioner_converges_at_tight_budget(): - # THE motivating case: at a tight inner budget the right-preconditioner is what - # lets the LM solve converge; plain LSMR stalls. - residual, x0, G, b = _ill_conditioned_linear(m=40, n=40, cond=1e3) - lam = 1e-6 - prec, _ = _right_preconditioner(G, lam) - common = dict( - init_damping=lam, - linear_solver="lsmr", - geodesic_acceleration=False, - iterative_tol=1e-8, - iterative_atol=0.0, - iterative_maxiter=12, - ) - plain = LevenbergMarquardt(residual, **common) - preconditioned = LevenbergMarquardt( - residual, whitened_preconditioner=prec, **common - ) - plain_result = plain.solve(x0, max_steps=60, atol=1e-4) - precond_result = preconditioned.solve(x0, max_steps=60, atol=1e-4) - assert int(precond_result.status) == LMStatus.CONVERGED - assert float(precond_result.info.loss) < 1e-6 - assert int(plain_result.status) != LMStatus.CONVERGED - assert float(plain_result.info.loss) > 1e-2 - - -def test_whitened_preconditioner_converged_solution_invariant(): - # The R'R-metric damping reweights the per-step subproblem but not the converged - # selection: a generously-budgeted preconditioned solve reaches cholesky's x*. - residual, x0, G, b = _ill_conditioned_linear(m=30, n=30, cond=1e2) - lam = 1e-5 - prec, _ = _right_preconditioner(G, lam) - cholesky = LevenbergMarquardt( - residual, init_damping=lam, geodesic_acceleration=False - ) - preconditioned = LevenbergMarquardt( - residual, - init_damping=lam, - linear_solver="lsmr", - geodesic_acceleration=False, - whitened_preconditioner=prec, - iterative_tol=1e-10, - iterative_maxiter=200, - ) - rc = cholesky.solve(x0, max_steps=80, atol=1e-6) - rp = preconditioned.solve(x0, max_steps=80, atol=1e-6) - assert jnp.allclose(rp.x, rc.x, rtol=1e-3, atol=1e-4) - - -def test_whitened_preconditioner_forward_step_is_identity_damped(): - # The augmented damping row is sqrt(lam) R^{-1} z = sqrt(lam) u, so the - # preconditioned single-step update is EXACTLY the I-damped - # u = (G'G + lam I)^{-1} G' b at x0=0 (resid = -b) for any R -- and - # distinguishable from the old R'R-damped surrogate for this non-trivial R. - residual, x0, G, b = _ill_conditioned_linear(m=10, n=10, cond=1e2) - lam = 1e-2 - prec, R = _right_preconditioner(G, lam) - solver = LevenbergMarquardt( - residual, - init_damping=lam, - linear_solver="lsmr", - geodesic_acceleration=False, - whitened_preconditioner=prec, - iterative_tol=1e-12, - iterative_maxiter=200, - ) - xl, _, info = solver.update(x0, solver.init(x0)) - n = G.shape[1] - u_rtr = jnp.linalg.solve(G.T @ G + lam * (R.T @ R), G.T @ b) - u_identity = jnp.linalg.solve(G.T @ G + lam * jnp.eye(n), G.T @ b) - assert bool(info.accepted) - assert jnp.allclose(xl, u_identity, rtol=1e-3, atol=1e-4) - assert not jnp.allclose(xl, u_rtr, rtol=1e-2, atol=1e-3) - - -def test_whitened_preconditioner_reverse_ad_and_implicit_p(): - # Reverse-AD through a preconditioned update is finite (the custom_linear_solve - # on the preconditioned normal operator differentiates), and the converged - # p-derivative -- R-invariant, resolved by shape to the normal form on - # this tall system -- matches the analytic sensitivity, as does the - # gram_cholesky forward's default filter. - ts = jnp.linspace(0.0, 2.0, 12) - - def residual_p(x, args, p): - return x * ts - p - - # data-independent frozen R from a fixed matrix (J = diag(ts) here) - M = jax.random.normal(jax.random.key(0), (1, 1)) - R = jnp.linalg.cholesky(M @ M.T + jnp.eye(1)).T - - def solve(v, damping): - return jsp_linalg.solve_triangular(R, v, lower=False) - - def solve_transpose(w, damping): - return jsp_linalg.solve_triangular(R.T, w, lower=True) - - prec = WhitenedPreconditioner(solve, solve_transpose) - cholesky = LevenbergMarquardt( - residual_p, init_damping=1e-3, linear_solver="gram_cholesky" - ) - preconditioned = LevenbergMarquardt( - residual_p, - init_damping=1e-3, - linear_solver="lsmr", - whitened_preconditioner=prec, - iterative_tol=1e-10, - iterative_maxiter=60, - ) - - def update_loss(pp): - nx, _, _ = preconditioned.update( - jnp.zeros(()), preconditioned.init(jnp.zeros(()), p=pp), p=pp - ) - return jnp.sum(nx**2) - - g = jax.grad(update_loss)(jnp.asarray(1.3)) - assert bool(jnp.isfinite(g)) - - p = jnp.asarray(1.7) - j_analytic = jnp.sum(ts) / jnp.sum(ts**2) - - def solved(solver, q): - return solver.solve(jnp.zeros(()), p=q, max_steps=60, atol=1e-9).x - - j_cholesky = jax.jacobian(lambda q: solved(cholesky, q))(p) - j_preconditioned = jax.jacobian(lambda q: solved(preconditioned, q))(p) - assert jnp.allclose(j_preconditioned, j_analytic, rtol=1e-4, atol=1e-5) - assert jnp.allclose(j_cholesky, j_analytic, rtol=1e-4, atol=1e-5) - - -def test_whitened_preconditioner_requires_lsmr(): - residual, x0, G, b = _ill_conditioned_linear() - prec, _ = _right_preconditioner(G, 1e-6) - with pytest.raises(ValueError, match="whitened_preconditioner requires"): - LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - whitened_preconditioner=prec, - ) - - -def test_whitened_preconditioner_hashing_shares_compilation(): - residual, x0, G, b = _ill_conditioned_linear() - prec, _ = _right_preconditioner(G, 1e-6) - common = dict(linear_solver="lsmr", iterative_maxiter=8) - a = LevenbergMarquardt(residual, whitened_preconditioner=prec, **common) - b_solver = LevenbergMarquardt(residual, whitened_preconditioner=prec, **common) - c = LevenbergMarquardt(residual, **common) # plain - assert a == b_solver and hash(a) == hash(b_solver) - assert a != c - - -# --- chained two-phase AD contract ------------------------------------------- - - -def test_chained_solve_derivative_is_final_phase_implicit_rule(): - # The two-phase pattern (fast solver to a plateau, then a certifying lsmr - # solve warm-started from it) must differentiate as the implicit rule at - # the FINAL converged point only: solve()'s custom JVP consumes the p - # tangent alone, so warm-start (x0/lm_state) tangents from an unconverged - # phase 1 are dropped by construction. - n = 6 - A = jax.random.normal(jax.random.key(0), (n, n)) + 3.0 * jnp.eye(n) - p0 = jnp.exp(0.2 * jax.random.normal(jax.random.key(1), (n,))) - - def residual(x, args, p): - return A @ x + 0.1 * jnp.tanh(x) - p - - phase1 = LevenbergMarquardt(residual, init_damping=1e-2, ad_solver="svd") - phase2 = LevenbergMarquardt( - residual, - linear_solver="lsmr", - ad_solver="svd", - init_damping=1e-10, - iterative_tol=1e-13, - iterative_atol=1e-13, - iterative_maxiter=200, - geodesic_acceleration=False, - ) - reference = LevenbergMarquardt(residual, init_damping=1e-2, ad_solver="svd") - - def chained(p): - plateau = phase1.solve(jnp.zeros(n), p=p, max_steps=2, atol=0.0) - return phase2.solve(plateau.x, p=p, max_steps=20, atol=1e-12).x - - def direct(p): - return reference.solve(jnp.zeros(n), p=p, max_steps=60, atol=1e-12).x - - tangent = jnp.linspace(-1.0, 1.0, n) - x_chained, dx_chained = jax.jvp(chained, (p0,), (tangent,)) - x_direct, dx_direct = jax.jvp(direct, (p0,), (tangent,)) - # Well-determined system: unique root, so both paths converge to the same - # x* and the chained derivative must equal the single-solve implicit rule. - assert jnp.allclose(x_chained, x_direct, rtol=1e-5, atol=1e-6) - assert jnp.allclose(dx_chained, dx_direct, rtol=1e-4, atol=1e-5) - - # Reverse mode agrees with forward mode through the chain. - cotangent = jnp.cos(jnp.arange(n, dtype=p0.dtype)) - _, pullback = jax.vjp(chained, p0) - (p_bar,) = pullback(cotangent) - assert jnp.allclose(p_bar @ tangent, cotangent @ dx_chained, rtol=1e-4, atol=1e-5) - - # The phase boundary carries no derivative: perturbing the warm start - # leaves the chained solution's tangent at exactly zero. - def from_start(x0): - return phase2.solve(x0, p=p0, max_steps=20, atol=1e-12).x - - _, dx_start = jax.jvp(from_start, (0.1 * jnp.ones(n),), (jnp.ones(n),)) - assert jnp.allclose(dx_start, jnp.zeros(n), atol=1e-12) diff --git a/tests/test_metric_factory.py b/tests/test_metric_factory.py deleted file mode 100644 index 61096f4..0000000 --- a/tests/test_metric_factory.py +++ /dev/null @@ -1,546 +0,0 @@ -import dataclasses - -import jax -import jax.numpy as jnp -import pytest - -from nlls_gram import ( - GramMetric, - LevenbergMarquardt, - LMSolveAction, - LMStatus, - MetricFactory, - MultiStart, - identity_preconditioner, - metric_from_diagonal, - repeated_shifted_dense_metric, -) - -TS = jnp.linspace(0.0, 1.0, 5) - - -def exp_residual_aux(x, args, p): - r = x["a"] * jnp.exp(x["b"] * TS) - p["target"] - w = 1.0 + x["a"] ** 2 + jnp.arange(2.0) - return r, {"w": w} - - -def exp_residual_plain(x, args, p): - return x["a"] * jnp.exp(x["b"] * TS) - p["target"] - - -X0 = { - "a": jnp.asarray(0.8, dtype=jnp.float32), - "b": jnp.asarray(0.4, dtype=jnp.float32), -} -P = {"target": 1.3 * jnp.exp(0.9 * TS)} - -DIAG_FACTORY = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, -) - - -def solver_kwargs_for(linear_solver): - if linear_solver == "gram_cg": - return { - "iterative_tol": 1e-7, - "iterative_maxiter": 30, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - if linear_solver == "normal_cg": - return { - "iterative_tol": 1e-7, - "iterative_maxiter": 30, - "normal_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - if linear_solver == "lsmr": - return {"iterative_tol": 1e-10, "iterative_maxiter": 50} - return {} - - -@pytest.mark.parametrize( - "linear_solver", - [ - "gram_cholesky", - "gram_cg", - "normal_cholesky", - "normal_cg", - "qr", - "augmented_qr", - "lsmr", - ], -) -@pytest.mark.parametrize("geodesic_acceleration", [False, True]) -def test_factory_update_matches_static_metric_at_same_point( - linear_solver, geodesic_acceleration -): - # One update with the factory must equal one update with a fixed GramMetric - # built from the same values the factory prepares at the pre-step x -- - # exercising every solver family's call sites, and with geodesic - # acceleration both norm applications sharing the pre-step state. - w_at_x0 = 1.0 + X0["a"] ** 2 + jnp.arange(2.0) - dynamic = LevenbergMarquardt( - exp_residual_aux, - has_aux=True, - linear_solver=linear_solver, - metric_factory=DIAG_FACTORY, - geodesic_acceleration=geodesic_acceleration, - **solver_kwargs_for(linear_solver), - ) - static = LevenbergMarquardt( - exp_residual_plain, - linear_solver=linear_solver, - metric=metric_from_diagonal(w_at_x0), - geodesic_acceleration=geodesic_acceleration, - **solver_kwargs_for(linear_solver), - ) - - x_dyn, _, info_dyn = dynamic.update(X0, dynamic.init(X0, p=P), None, P) - x_st, _, info_st = static.update(X0, static.init(X0, p=P), None, P) - - assert jnp.allclose(x_dyn["a"], x_st["a"], rtol=1e-6, atol=1e-7) - assert jnp.allclose(x_dyn["b"], x_st["b"], rtol=1e-6, atol=1e-7) - assert jnp.allclose(info_dyn.loss, info_st.loss, rtol=1e-6) - assert jnp.allclose( - info_dyn.acceleration_ratio, info_st.acceleration_ratio, rtol=1e-5, atol=1e-7 - ) - - -def test_factory_cholesky_step_matches_closed_form_underdetermined(): - # One dual step: step = -P J' (J P J' + damping)^{-1} r with P read from - # the aux the residual just produced. - weights = jnp.array([4.0, 1.0]) - - def residual(theta, args, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]), {"w": weights} - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, - ) - init_damping = 1e-2 - solver = LevenbergMarquardt( - residual, - has_aux=True, - init_damping=init_damping, - metric_factory=factory, - geodesic_acceleration=False, - ) - theta0 = jnp.zeros(2) - p = jnp.asarray(3.0) - theta1, _, _ = solver.update(theta0, solver.init(theta0, p=p), None, p) - - jacobian = jnp.array([[1.0, 2.0]]) - P_inv = jnp.diag(1.0 / weights) - dual = jnp.linalg.solve( - jacobian @ P_inv @ jacobian.T + init_damping * jnp.eye(1), - jnp.array([theta0[0] + 2.0 * theta0[1] - p]), - ) - expected = theta0 - (P_inv @ jacobian.T @ dual).ravel() - assert jnp.allclose(theta1, expected, atol=1e-6) - - -@pytest.mark.parametrize( - "linear_solver", - [ - "gram_cholesky", - "gram_cg", - "normal_cholesky", - "normal_cg", - "qr", - "augmented_qr", - "lsmr", - ], -) -def test_factory_full_solve_converges(linear_solver): - solver = LevenbergMarquardt( - exp_residual_aux, - has_aux=True, - linear_solver=linear_solver, - metric_factory=DIAG_FACTORY, - **solver_kwargs_for(linear_solver), - ) - result = solver.solve(X0, p=P, atol=1e-5, max_steps=100) - assert result.status == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], 1.3, atol=1e-3) - assert jnp.allclose(result.x["b"], 0.9, atol=1e-3) - - -def test_factory_solve_python_matches_jit(): - solver = LevenbergMarquardt( - exp_residual_aux, has_aux=True, metric_factory=DIAG_FACTORY - ) - jitted = solver.solve(X0, p=P, atol=1e-5, max_steps=100) - python = solver.solve(X0, p=P, atol=1e-5, max_steps=100, jit=False) - assert jitted.status == python.status - assert jnp.allclose(jitted.x["a"], python.x["a"], rtol=1e-6) - assert jnp.allclose(jitted.x["b"], python.x["b"], rtol=1e-6) - - -def scalar_residual_aux(theta, args, p): - w = 1.0 + jnp.atleast_1d(theta[0]) ** 2 - return jnp.atleast_1d(theta[0] ** 2 - 1.0), {"w": w} - - -def make_scalar_solver(): - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, - ) - return LevenbergMarquardt( - scalar_residual_aux, - has_aux=True, - init_damping=1e-4, - metric_factory=factory, - geodesic_acceleration=False, - ) - - -def test_metric_valid_tracks_rejection_and_acceptance(): - solver = make_scalar_solver() - # theta = 0.1: the tiny-damping Gauss-Newton step overshoots wildly and - # the update is rejected, so the carried state stays valid. - theta_reject = jnp.array([0.1]) - _, state, info = solver.update( - theta_reject, solver.init(theta_reject, p=None), None, None - ) - assert not bool(info.accepted) - assert bool(state.metric_valid) - # theta = 2.0: the step improves the loss and is accepted, so the carried - # state is stale at the new x and marked for rebuild. - theta_accept = jnp.array([2.0]) - _, state, info = solver.update( - theta_accept, solver.init(theta_accept, p=None), None, None - ) - assert bool(info.accepted) - assert not bool(state.metric_valid) - - -def test_metric_state_reused_when_valid_and_rebuilt_when_invalid(): - solver = make_scalar_solver() - theta = jnp.array([2.0]) - fresh_state = solver.init(theta, p=None) - wrong = jax.tree.map(lambda v: 10.0 * v, fresh_state.metric_state) - x_fresh, _, _ = solver.update(theta, fresh_state, None, None) - # valid=True: the carried (wrong) state must be used, changing the step. - x_wrong, _, _ = solver.update( - theta, - dataclasses.replace(fresh_state, metric_state=wrong), - None, - None, - ) - assert not jnp.allclose(x_wrong, x_fresh) - # valid=False: prepare() runs at the current x, so the wrong carry is - # ignored and the step matches the fresh one. - x_rebuilt, _, _ = solver.update( - theta, - dataclasses.replace( - fresh_state, - metric_state=wrong, - metric_valid=jnp.asarray(False), - ), - None, - None, - ) - assert jnp.allclose(x_rebuilt, x_fresh) - - -def test_callback_x_replacement_invalidates_metric_state(): - solver = make_scalar_solver() - theta = jnp.array([2.0]) - lm_state = solver.init(theta, p=None) - action = LMSolveAction(x=theta + 0.5) - _, _, new_state, _, _, problem_changed = solver._apply_action( - action, theta, lm_state, None, None - ) - assert bool(problem_changed) - assert not bool(new_state.metric_valid) - # Returning the unchanged x is not a change and keeps the state valid. - _, _, same_state, _, _, problem_changed = solver._apply_action( - LMSolveAction(x=theta), theta, lm_state, None, None - ) - assert not bool(problem_changed) - assert bool(same_state.metric_valid) - - -def test_callback_lm_state_must_preserve_metric_state(): - solver = make_scalar_solver() - theta = jnp.array([2.0]) - lm_state = solver.init(theta, p=None) - action = LMSolveAction(lm_state=dataclasses.replace(lm_state, metric_state=None)) - with pytest.raises(ValueError, match="preserve the metric_state"): - solver._apply_action(action, theta, lm_state, None, None) - - -def test_update_requires_init_built_lm_state(): - from nlls_gram import LMState - - solver = make_scalar_solver() - with pytest.raises(ValueError, match="create the lm_state with init"): - solver.update(jnp.array([2.0]), LMState(jnp.asarray(1e-4)), None, None) - - -def test_jacobian_assembly_does_not_differentiate_aux(): - # The aux map has a non-finite derivative at the evaluation point - # (d sqrt at 0); linearize(has_aux=True) must keep aux primal, so the - # Jacobian, the step, and the solve stay finite. - def residual(x, args, p): - r = x["a"] * jnp.exp(x["b"] * TS) - p["target"] - spike = jnp.sqrt(jnp.sum(0.0 * x["a"] ** 2)) - w = 1.0 + x["a"] ** 2 + jnp.arange(2.0) + spike - return r, {"w": w} - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, - ) - solver = LevenbergMarquardt(residual, has_aux=True, metric_factory=factory) - result = solver.solve(X0, p=P, atol=1e-5, max_steps=100) - assert result.status == LMStatus.CONVERGED - assert bool(jnp.isfinite(result.x["a"])) - - -@pytest.mark.parametrize("ad_solver", ["svd", "gram_cg", "normal_cg"]) -def test_implicit_jvp_freezes_metric_at_solution(ad_solver): - # Underdetermined linear residual with a p-dependent metric read from aux: - # the solve returns the min-M(p)-norm solution, and the implicit tangent - # must use the FROZEN metric at the solution -- the min-norm formula with - # P* = P(w(p)) held constant, no dP/dp term. - def residual(theta, args, p): - w = jnp.array([1.0 + p**2, 1.0]) - return jnp.array([theta[0] + 2.0 * theta[1] - p]), {"w": w} - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, - ) - solver = LevenbergMarquardt( - residual, - has_aux=True, - init_damping=1e-2, - metric_factory=factory, - geodesic_acceleration=False, - ad_solver=ad_solver, - ad_solver_preconditioner=( - identity_preconditioner() if ad_solver in ("gram_cg", "normal_cg") else None - ), - ad_solver_maxiter=30 if ad_solver in ("gram_cg", "normal_cg") else None, - ) - - def solved_x(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x - - p0 = jnp.asarray(3.0) - p_dot = jnp.asarray(0.7) - x_star, x_dot = jax.jvp(solved_x, (p0,), (p_dot,)) - - jacobian = jnp.array([[1.0, 2.0]]) - P_frozen = jnp.diag(1.0 / jnp.array([1.0 + p0**2, 1.0])) - min_norm = ( - P_frozen - @ jacobian.T - @ jnp.linalg.solve(jacobian @ P_frozen @ jacobian.T, jnp.eye(1)) - ).ravel() - assert jnp.allclose(x_star, min_norm * p0, atol=1e-5) - frozen_tangent = min_norm * p_dot - assert jnp.allclose(x_dot, frozen_tangent, atol=1e-5) - - # The full derivative of p -> P(p) J' (J P(p) J')^{-1} p has a dP/dp term; - # the frozen contract must NOT include it. - def full_map(p): - P_of_p = jnp.diag(1.0 / jnp.array([1.0 + p**2, 1.0])) - return ( - P_of_p - @ jacobian.T - @ jnp.linalg.solve(jacobian @ P_of_p @ jacobian.T, jnp.array([p])) - ).ravel() - - _, full_tangent = jax.jvp(full_map, (p0,), (p_dot,)) - assert not jnp.allclose(x_dot, full_tangent, atol=1e-4) - - -def test_implicit_aux_dot_uses_frozen_metric_solution_path(): - # aux_dot composes the solution tangent; with a factory it must run at the - # frozen solution metric without error and stay finite. - def residual(theta, args, p): - w = jnp.array([1.0 + p**2, 1.0]) - return jnp.array([theta[0] + 2.0 * theta[1] - p]), {"w": w} - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=metric_from_diagonal, - ) - solver = LevenbergMarquardt( - residual, - has_aux=True, - metric_factory=factory, - geodesic_acceleration=False, - ) - - def solved_aux(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).aux["w"] - - _, aux_dot = jax.jvp(solved_aux, (jnp.asarray(3.0),), (jnp.asarray(1.0),)) - assert bool(jnp.all(jnp.isfinite(aux_dot))) - assert jnp.allclose(aux_dot, jnp.array([6.0, 0.0]), atol=1e-4) - - -def test_multi_start_parallel_does_not_leak_metric_state(): - def draw(key, x, args): - return jax.tree.map( - lambda v: v + 0.3 * jax.random.normal(key, jnp.shape(v)), x - ), args - - solver = LevenbergMarquardt( - exp_residual_aux, has_aux=True, metric_factory=DIAG_FACTORY - ) - result = solver.solve( - X0, - p=P, - atol=1e-5, - max_steps=100, - multi_start=MultiStart( - draw=draw, num_starts=3, key=jax.random.key(0), parallel=True - ), - ) - assert result.status == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], 1.3, atol=1e-3) - - -def test_factory_solves_do_not_retrace_on_new_aux_values(): - traces = {"count": 0} - - def counting_build(w): - traces["count"] += 1 - return metric_from_diagonal(w) - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=counting_build, - ) - solver = LevenbergMarquardt(exp_residual_aux, has_aux=True, metric_factory=factory) - solver.solve(X0, p=P, atol=1e-5, max_steps=50) - count_after_first = traces["count"] - other_p = {"target": 1.1 * jnp.exp(0.7 * TS)} - solver.solve(X0, p=other_p, atol=1e-5, max_steps=50) - assert traces["count"] == count_after_first - - # Equal-config solvers built around the same factory share the loop. - twin = LevenbergMarquardt(exp_residual_aux, has_aux=True, metric_factory=factory) - assert twin == solver - assert hash(twin) == hash(solver) - twin.solve(X0, p=P, atol=1e-5, max_steps=50) - assert traces["count"] == count_after_first - - -def test_factory_builds_repeated_shifted_dense_metric(): - def residual(x, args, p): - r = x["a"] * jnp.exp(x["b"] * TS) - p["target"] - K = jnp.diag(1.0 + x["a"] ** 2 + jnp.zeros(1)) - return r, {"K": K} - - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["K"], - build=lambda K: repeated_shifted_dense_metric( - K, repeats=1, zero_pad_size=1, epsilon=1.0 - ), - ) - solver = LevenbergMarquardt(residual, has_aux=True, metric_factory=factory) - result = solver.solve(X0, p=P, atol=1e-5, max_steps=100) - assert result.status == LMStatus.CONVERGED - assert jnp.allclose(result.x["a"], 1.3, atol=1e-3) - - -def test_factory_allows_has_aux_false_with_none_aux(): - seen = {} - - def prepare(x, args, p, aux): - seen["aux"] = aux - return 1.0 + x["a"] ** 2 + jnp.arange(2.0) - - factory = MetricFactory(prepare=prepare, build=metric_from_diagonal) - solver = LevenbergMarquardt(exp_residual_plain, metric_factory=factory) - result = solver.solve(X0, p=P, atol=1e-5, max_steps=100) - assert result.status == LMStatus.CONVERGED - assert seen["aux"] is None - - -def test_constructor_rejects_metric_and_factory_together(): - with pytest.raises(ValueError, match="at most one of metric or metric_factory"): - LevenbergMarquardt( - exp_residual_aux, - has_aux=True, - metric=GramMetric(solve=lambda v: v), - metric_factory=DIAG_FACTORY, - ) - - -def test_constructor_rejects_non_factory_and_non_callable_hooks(): - with pytest.raises(TypeError, match="MetricFactory or None"): - LevenbergMarquardt(exp_residual_plain, metric_factory=object()) - with pytest.raises(TypeError, match="prepare must be callable"): - MetricFactory(prepare=None, build=metric_from_diagonal) - with pytest.raises(TypeError, match="build must be callable"): - MetricFactory(prepare=lambda x, args, p, aux: aux, build=None) - - -@pytest.mark.parametrize( - "linear_solver,build,match", - [ - ( - "gram_cholesky", - lambda w: GramMetric(inv_sqrt=lambda v: v, inv_sqrt_transpose=lambda v: v), - "requires metric.solve", - ), - ( - "normal_cholesky", - lambda w: GramMetric(solve=lambda v: v / w), - "requires metric.inv_sqrt", - ), - ( - "lsmr", - lambda w: GramMetric(solve=lambda v: v / w), - "requires metric.inv_sqrt", - ), - ], -) -def test_build_output_validated_at_trace_time(linear_solver, build, match): - factory = MetricFactory(prepare=lambda x, args, p, aux: aux["w"], build=build) - solver = LevenbergMarquardt( - exp_residual_aux, - has_aux=True, - linear_solver=linear_solver, - metric_factory=factory, - geodesic_acceleration=False, - **solver_kwargs_for(linear_solver), - ) - with pytest.raises(ValueError, match=match): - solver.solve(X0, p=P, max_steps=2) - - -def test_build_requiring_norm_under_geodesic_and_non_metric_output(): - no_norm = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], - build=lambda w: GramMetric(solve=lambda v: v / w), - ) - solver = LevenbergMarquardt( - exp_residual_aux, - has_aux=True, - linear_solver="gram_cholesky", - metric_factory=no_norm, - geodesic_acceleration=True, - ) - with pytest.raises(ValueError, match="requires metric.norm"): - solver.solve(X0, p=P, max_steps=2) - - not_a_metric = MetricFactory( - prepare=lambda x, args, p, aux: aux["w"], build=lambda w: w - ) - solver = LevenbergMarquardt( - exp_residual_aux, has_aux=True, metric_factory=not_a_metric - ) - with pytest.raises(TypeError, match="must return a GramMetric"): - solver.solve(X0, p=P, max_steps=2) diff --git a/tests/test_metric_lm.py b/tests/test_metric_lm.py new file mode 100644 index 0000000..e70139e --- /dev/null +++ b/tests/test_metric_lm.py @@ -0,0 +1,398 @@ +"""LevenbergMarquardt: the damped step, the metric's selection of the root, +and the implicit derivative of that selection. + +Everything here checks against a closed form or an independently computed +reference. Loop mechanics shared with the ridge solver (callbacks, save_steps, +multi-start) are covered once, in test_ridge_solve_features.py and +test_multi_start.py. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from nlls_gram import ( + CG, + QR, + SVD, + Cholesky, + CholeskyMetric, + DiagonalMetric, + GramCG, + IdentityPreconditioner, + LevenbergMarquardt, + LMStatus, + RepeatedFactorMetric, +) + +RNG = np.random.default_rng(11) +M, N = 4, 7 # underdetermined: which root comes back is a real choice +A_NP = RNG.normal(size=(M, N)) +B_NP = RNG.normal(size=M) +W_ROOT = RNG.normal(size=(N, N)) +W_NP = W_ROOT @ W_ROOT.T + N * np.eye(N) + +A = jnp.asarray(A_NP, jnp.float32) +B = jnp.asarray(B_NP, jnp.float32) +L_W = jnp.asarray(np.linalg.cholesky(W_NP), jnp.float32) + + +def linear_residual(x): + return A @ x - B + + +def nonlinear_residual(x, args, p): + return jnp.concatenate([A @ x - p["scale"] * B, jnp.array([x[0] * x[1] - 0.3])]) + + +def min_norm_solution(W, b=B_NP): + """argmin ||x||_W subject to A x = b.""" + Winv = np.linalg.inv(W) + return Winv @ A_NP.T @ np.linalg.solve(A_NP @ Winv @ A_NP.T, b) + + +def damped_step(W, x, damping): + """The exact solution of min ||r + J s||^2 + damping ||s||_W^2.""" + r = A_NP @ x - B_NP + return -np.linalg.solve(A_NP.T @ A_NP + damping * W, A_NP.T @ r) + + +FORWARD_SOLVERS = { + "cholesky_auto": Cholesky(), + "cholesky_gram": Cholesky(form="gram"), + "cholesky_normal": Cholesky(form="normal"), + "qr": QR(), + "cg": CG(IdentityPreconditioner(), tol=1e-12, maxiter=400), + "gram_cg": GramCG(IdentityPreconditioner(), tol=1e-12, maxiter=400), +} + + +@pytest.mark.parametrize("name", list(FORWARD_SOLVERS)) +def test_first_step_matches_the_closed_form_damped_solution(name): + damping = 0.07 + metric = CholeskyMetric(L_W) + solver = LevenbergMarquardt( + linear_residual, + metric=metric, + linear_solver=FORWARD_SOLVERS[name], + init_damping=damping, + geodesic_acceleration=False, + ) + x0 = jnp.asarray(RNG.normal(size=N), jnp.float32) + x1, _, info = solver.update(x0, solver.init(x0)) + expected = np.asarray(x0, np.float64) + damped_step( + W_NP, np.asarray(x0, np.float64), damping + ) + assert bool(info.accepted) + np.testing.assert_allclose(np.asarray(x1), expected, rtol=2e-4, atol=2e-5) + + +@pytest.mark.parametrize("name", list(FORWARD_SOLVERS)) +def test_converges_to_the_minimum_metric_norm_root(name): + # The damping -> 0 limit selects the minimum-W-norm interpolant, and the + # identity metric selects a demonstrably different one. + metric = CholeskyMetric(L_W) + solver = LevenbergMarquardt( + linear_residual, + metric=metric, + linear_solver=FORWARD_SOLVERS[name], + min_damping=1e-12, + ) + result = solver.solve(jnp.zeros(N), max_steps=200, atol=1e-6) + assert int(result.status) == int(LMStatus.CONVERGED) + expected = min_norm_solution(W_NP) + np.testing.assert_allclose(np.asarray(result.x), expected, rtol=2e-3, atol=2e-4) + # The selection is real: the Euclidean root differs well beyond tolerance. + euclidean = min_norm_solution(np.eye(N)) + assert np.linalg.norm(expected - euclidean) > 0.1 + + +def test_metric_forms_agree_at_positive_damping(): + # Push-through identity: the gram and normal factorizations of the same + # damped subproblem give the same step. + metric = CholeskyMetric(L_W) + x0 = jnp.asarray(RNG.normal(size=N), jnp.float32) + steps = {} + for form in ("gram", "normal"): + solver = LevenbergMarquardt( + linear_residual, + metric=metric, + linear_solver=Cholesky(form=form), + init_damping=0.3, + geodesic_acceleration=False, + ) + steps[form] = np.asarray(solver.update(x0, solver.init(x0))[0]) + np.testing.assert_allclose(steps["gram"], steps["normal"], rtol=1e-5, atol=1e-6) + + +def test_diagonal_and_dense_metrics_agree_on_the_same_geometry(): + weights = jnp.asarray(RNG.uniform(0.5, 3.0, size=N), jnp.float32) + dense = CholeskyMetric(jnp.diag(jnp.sqrt(weights))) + x0 = jnp.zeros(N) + results = [ + LevenbergMarquardt(linear_residual, metric=metric, min_damping=1e-12).solve( + x0, max_steps=200, atol=1e-6 + ) + for metric in (DiagonalMetric(weights), dense) + ] + np.testing.assert_allclose( + np.asarray(results[0].x), np.asarray(results[1].x), rtol=1e-4, atol=1e-5 + ) + np.testing.assert_allclose( + np.asarray(results[0].x), + min_norm_solution(np.diag(np.asarray(weights, np.float64))), + rtol=2e-3, + atol=2e-4, + ) + + +def test_repeated_factor_metric_matches_its_dense_block_diagonal(): + block, repeats = 3, 2 + root = RNG.normal(size=(block, block + 2)) + K = root @ root.T + 0.5 * np.eye(block) + free = N - block * repeats + dense = np.zeros((N, N)) + for j in range(repeats): + dense[j * block : (j + 1) * block, j * block : (j + 1) * block] = K + dense[block * repeats :, block * repeats :] = np.eye(free) + + repeated = RepeatedFactorMetric( + jnp.asarray(np.linalg.cholesky(K).T, jnp.float32), repeats=repeats + ) + solver = LevenbergMarquardt(linear_residual, metric=repeated, min_damping=1e-12) + result = solver.solve(jnp.zeros(N), max_steps=200, atol=1e-6) + np.testing.assert_allclose( + np.asarray(result.x), min_norm_solution(dense), rtol=3e-3, atol=3e-4 + ) + + +def test_default_metric_is_euclidean(): + plain = LevenbergMarquardt(linear_residual, min_damping=1e-12).solve( + jnp.zeros(N), max_steps=200, atol=1e-6 + ) + np.testing.assert_allclose( + np.asarray(plain.x), min_norm_solution(np.eye(N)), rtol=2e-3, atol=2e-4 + ) + + +def quadratic_residual(x): + # r(x) = [x0^2 - 2, x0 x1 - 1]: a curved residual where the geodesic + # correction has something to do. + return jnp.array([x[0] ** 2 - 2.0, x[0] * x[1] - 1.0]) + + +@pytest.mark.parametrize("name", list(FORWARD_SOLVERS)) +def test_geodesic_correction_matches_its_closed_form(name): + damping = 0.2 + solver = LevenbergMarquardt( + quadratic_residual, + linear_solver=FORWARD_SOLVERS[name], + init_damping=damping, + geodesic_acceptance_ratio=1e9, # always accept, so the value is checked + ) + x0 = jnp.asarray([1.6, 0.7], jnp.float32) + x1, _, info = solver.update(x0, solver.init(x0)) + x = np.asarray(x0, np.float64) + J = np.array([[2 * x[0], 0.0], [x[1], x[0]]]) + r = np.array([x[0] ** 2 - 2.0, x[0] * x[1] - 1.0]) + G = J.T @ J + damping * np.eye(2) + velocity = -np.linalg.solve(G, J.T @ r) + # Directional second derivative of r along the velocity. + f_vv = np.array([2 * velocity[0] ** 2, 2 * velocity[0] * velocity[1]]) + acceleration = -np.linalg.solve(G, J.T @ f_vv) + assert bool(info.used_geodesic) + np.testing.assert_allclose( + np.asarray(x1), x + velocity + 0.5 * acceleration, rtol=1e-4, atol=1e-5 + ) + + +def test_rejected_step_leaves_x_and_reuses_the_cached_jacobian(): + calls = [] + + def counting_residual(x): + calls.append(None) + return quadratic_residual(x) + + # A tiny max_damping forces the first step to overshoot and be rejected. + solver = LevenbergMarquardt( + counting_residual, init_damping=1e-8, geodesic_acceleration=False + ) + x0 = jnp.asarray([8.0, 8.0], jnp.float32) + state = solver.init(x0) + x1, state1, info1 = solver.update(x0, state) + if bool(info1.accepted): + pytest.skip("fixture no longer produces a rejected first step") + np.testing.assert_array_equal(np.asarray(x1), np.asarray(x0)) + assert bool(state1.jacobian_valid) + before = len(calls) + solver.update(x1, state1) + # The reused cache costs one trial evaluation, not a fresh linearization. + assert len(calls) - before <= 2 + + +def test_solve_and_manual_update_loop_agree(): + solver = LevenbergMarquardt(linear_residual, min_damping=1e-12) + x = jnp.zeros(N) + state = solver.init(x) + for _ in range(40): + x, state, _ = solver.update(x, state) + looped = LevenbergMarquardt(linear_residual, min_damping=1e-12).solve( + jnp.zeros(N), max_steps=40, atol=0.0, gtol=0.0, xtol=0.0 + ) + np.testing.assert_allclose( + np.asarray(looped.x), np.asarray(x), rtol=1e-5, atol=1e-6 + ) + + +def test_pytree_x_and_args_round_trip(): + def residual(x, args, p): + return jnp.concatenate( + [A @ x["head"] - args["target"], x["tail"] - p["anchor"]] + ) + + x0 = {"head": jnp.zeros(N), "tail": jnp.zeros(2)} + args = {"target": B} + p = {"anchor": jnp.asarray([0.25, -0.5], jnp.float32)} + result = LevenbergMarquardt(residual, min_damping=1e-12).solve( + x0, args, p=p, max_steps=200, atol=1e-6 + ) + assert int(result.status) == int(LMStatus.CONVERGED) + np.testing.assert_allclose( + np.asarray(result.x["tail"]), np.asarray(p["anchor"]), rtol=1e-4, atol=1e-5 + ) + + +# The undamped AD operator is singular on the side the problem is deficient +# in, so each Krylov rule is offered only where its operator is invertible: +# this fixture is underdetermined (m < n), which rules out plain CG. +AD_SOLVERS = { + "default": None, + "cholesky": Cholesky(), + "svd": SVD(), + "gram_cg": GramCG(IdentityPreconditioner(), tol=1e-12, maxiter=400), +} + + +@pytest.mark.parametrize("name", list(AD_SOLVERS)) +def test_implicit_jvp_matches_the_analytic_min_norm_map(name): + # x*(b) = W^-1 A' (A W^-1 A')^-1 b is linear in b, so the tangent is the + # same map applied to b_dot. + metric = CholeskyMetric(L_W) + solver = LevenbergMarquardt( + lambda x, args, p: A @ x - p["b"], + metric=metric, + ad_solver=AD_SOLVERS[name], + min_damping=1e-12, + ) + p = {"b": B} + p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} + + def run(p_value): + return solver.solve(jnp.zeros(N), p=p_value, max_steps=200, atol=1e-6).x + + tangent = jax.jvp(run, (p,), (p_dot,))[1] + expected = min_norm_solution(W_NP, np.asarray(p_dot["b"], np.float64)) + np.testing.assert_allclose(np.asarray(tangent), expected, rtol=2e-3, atol=2e-4) + + +@pytest.mark.parametrize("name", list(AD_SOLVERS)) +def test_implicit_vjp_is_the_transpose_of_the_jvp(name): + solver = LevenbergMarquardt( + lambda x, args, p: A @ x - p["b"], + metric=CholeskyMetric(L_W), + ad_solver=AD_SOLVERS[name], + min_damping=1e-12, + ) + p = {"b": B} + p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} + cotangent = jnp.asarray(RNG.normal(size=N), jnp.float32) + + def run(p_value): + return solver.solve(jnp.zeros(N), p=p_value, max_steps=200, atol=1e-6).x + + tangent = jax.jvp(run, (p,), (p_dot,))[1] + gradient = jax.vjp(run, p)[1](cotangent)[0]["b"] + np.testing.assert_allclose( + float(cotangent @ tangent), float(gradient @ p_dot["b"]), rtol=2e-3, atol=1e-5 + ) + + +def test_gram_cg_ad_rejects_the_overdetermined_shape(): + # The undamped dual is singular for m > n, where CG returns a wrong + # tangent rather than failing, so the resolution rejects it outright. + tall_A = jnp.asarray(RNG.normal(size=(9, 3)), jnp.float32) + solver = LevenbergMarquardt( + lambda x, args, p: tall_A @ x - p["b"], + ad_solver=GramCG(IdentityPreconditioner(), maxiter=16), + ) + p = {"b": jnp.asarray(RNG.normal(size=9), jnp.float32)} + with pytest.raises(ValueError, match="m <= n"): + jax.jvp(lambda pv: solver.solve(jnp.zeros(3), p=pv, max_steps=20).x, (p,), (p,)) + + +def test_nonlinear_residual_solves_and_differentiates(): + solver = LevenbergMarquardt(nonlinear_residual, min_damping=1e-12) + p = {"scale": jnp.asarray(1.0)} + result = solver.solve(jnp.zeros(N), p=p, max_steps=300, atol=1e-5) + assert int(result.status) == int(LMStatus.CONVERGED) + np.testing.assert_allclose( + np.asarray(nonlinear_residual(result.x, None, p)), 0.0, atol=1e-4 + ) + # Finite differences on a scalar summary of the solution. + summary = lambda s: jnp.sum( # noqa: E731 + solver.solve(jnp.zeros(N), p={"scale": s}, max_steps=300, atol=1e-5).x ** 2 + ) + analytic = float(jax.grad(summary)(jnp.asarray(1.0))) + h = 1e-3 + numeric = float( + (summary(jnp.asarray(1.0 + h)) - summary(jnp.asarray(1.0 - h))) / (2 * h) + ) + np.testing.assert_allclose(analytic, numeric, rtol=2e-2, atol=2e-3) + + +def test_padded_zero_residual_matches_the_unpadded_solve(): + # The fixed-residual-shape pattern: identically-zero rows keep compiled + # shapes stable and must not move the solution. The undamped dual is + # singular there, which is what SVD() is for. + pad = 3 + + def padded(x, args, p): + return jnp.concatenate([A @ x - p["b"], jnp.zeros(pad)]) + + p = {"b": B} + unpadded = LevenbergMarquardt( + lambda x, args, p: A @ x - p["b"], min_damping=1e-12 + ).solve(jnp.zeros(N), p=p, max_steps=200, atol=1e-6) + padded_result = LevenbergMarquardt( + padded, ad_solver=SVD(), min_damping=1e-12 + ).solve(jnp.zeros(N), p=p, max_steps=200, atol=1e-6) + # Two independently converged float32 solves, so the agreement is a + # measured property rather than a tolerance bound. + np.testing.assert_allclose( + np.asarray(padded_result.x), np.asarray(unpadded.x), rtol=2e-3, atol=2e-4 + ) + + +def test_has_aux_reports_pre_step_aux_and_a_final_value(): + def residual(x): + return linear_residual(x), {"norm": jnp.sum(x**2)} + + solver = LevenbergMarquardt(residual, has_aux=True, min_damping=1e-12) + x0 = jnp.ones(N) + _, _, info = solver.update(x0, solver.init(x0)) + np.testing.assert_allclose(float(info.aux["norm"]), float(N), rtol=1e-6) + result = solver.solve(x0, max_steps=200, atol=1e-6) + np.testing.assert_allclose( + float(result.aux["norm"]), float(jnp.sum(result.x**2)), rtol=1e-5 + ) + + +def test_equal_configs_share_one_compilation(): + def build(): + return LevenbergMarquardt( + linear_residual, linear_solver=Cholesky(), init_damping=1e-3 + ) + + assert build() == build() and hash(build()) == hash(build()) + assert build() != LevenbergMarquardt(linear_residual, linear_solver=QR()) diff --git a/tests/test_multi_start.py b/tests/test_multi_start.py index 62d0a94..ca91796 100644 --- a/tests/test_multi_start.py +++ b/tests/test_multi_start.py @@ -621,8 +621,6 @@ def test_multi_start_validation_errors(): solver = LevenbergMarquardt(residual_linear, init_damping=1e-2) x0 = jnp.zeros(2) - with pytest.raises(TypeError, match="MultiStart"): - solver.solve(x0, p=jnp.asarray(3.0), multi_start=42) def bad_draw(key, x, args): return x[:1], args diff --git a/tests/test_normal_solvers.py b/tests/test_normal_solvers.py deleted file mode 100644 index b62b9c2..0000000 --- a/tests/test_normal_solvers.py +++ /dev/null @@ -1,1343 +0,0 @@ -import subprocess -import sys -import textwrap - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import numpy as np -import pytest - -from nlls_gram import ( - GramMetric, - LevenbergMarquardt, - PreconditionerFactory, - RecycleConfig, - WhitenedPreconditioner, - identity_preconditioner, - metric_from_cholesky, - metric_from_diagonal, - repeated_shifted_dense_metric, -) - -# Rank-2 tall interpolation fixture: row 3 duplicates row 1 AND column 3 is -# column 1 + column 2, so the problem is rank-deficient in both directions; -# b = A @ theta_true keeps it consistent (a zero-residual root exists). -A_RD = jnp.array( - [ - [1.0, 2.0, 3.0], - [0.0, 1.0, 1.0], - [1.0, 2.0, 3.0], - [2.0, 1.0, 3.0], - ] -) -THETA_TRUE = jnp.array([1.0, -1.0, 2.0]) -B_RD = A_RD @ THETA_TRUE - -A_TALL = jnp.array([[1.0, 0.5], [0.3, 2.0], [-1.0, 1.0]]) -A_SQ = jnp.array([[2.0, 0.5], [-0.4, 1.5]]) -A_WIDE = jnp.array([[1.0, 2.0, -0.5, 0.3], [0.2, -1.0, 1.5, 2.0]]) - -L2 = jnp.array([[1.3, 0.0], [0.5, 0.8]]) -L3 = jnp.array([[1.5, 0.0, 0.0], [0.4, 1.2, 0.0], [-0.3, 0.2, 0.9]]) -L4 = jnp.array( - [ - [1.2, 0.0, 0.0, 0.0], - [0.3, 1.5, 0.0, 0.0], - [-0.2, 0.4, 0.9, 0.0], - [0.1, -0.1, 0.2, 1.4], - ] -) - - -def chol_S(L): - # metric_from_cholesky(L) has S = L^{-T} with S S' = (L L')^{-1}. - return jsp_linalg.solve_triangular(L.T, jnp.eye(L.shape[0]), lower=False) - - -def min_m_norm_root(A, b, S=None): - if S is None: - return jnp.linalg.pinv(A) @ b - return S @ jnp.linalg.pinv(A @ S) @ b - - -def normal_cg_kwargs(maxiter=100, tol=1e-7): - return dict( - linear_solver="normal_cg", - normal_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=tol, - iterative_maxiter=maxiter, - ) - - -def ad_kwargs(ad_solver): - if ad_solver in ("gram_cg", "normal_cg"): - return { - "ad_solver_preconditioner": identity_preconditioner(), - "ad_solver_maxiter": 50, - } - return {} - - -AD_FORMS = ["svd", "gram_cg", "normal_cg"] - - -# --- normal_cholesky closed-form steps --------------------------------------- - - -@pytest.mark.parametrize("A", [A_SQ, A_TALL], ids=["square", "tall"]) -@pytest.mark.parametrize("use_metric", [False, True], ids=["identity", "cholesky"]) -def test_normal_cholesky_step_matches_closed_form(A, use_metric): - lam = 1e-2 - b = jnp.arange(1.0, A.shape[0] + 1.0) - - def residual(theta, args, p): - return A @ theta - b - - solver = LevenbergMarquardt( - residual, - init_damping=lam, - linear_solver="normal_cholesky", - metric=metric_from_cholesky(L2) if use_metric else None, - geodesic_acceleration=False, - ) - theta0 = jnp.array([0.4, -0.3]) - theta1, _, info = solver.update(theta0, solver.init(theta0)) - - S = chol_S(L2) if use_metric else jnp.eye(2) - B = A @ S - r0 = A @ theta0 - b - u = jnp.linalg.solve(B.T @ B + lam * jnp.eye(2), -(B.T @ r0)) - assert bool(info.accepted) - assert jnp.allclose(theta1, theta0 + S @ u, atol=1e-5) - - -# --- gram <-> normal push-through identity at lambda > 0 --------------------- - - -@pytest.mark.parametrize( - "A", [A_RD, A_RD.T], ids=["tall_rank_deficient", "wide_rank_deficient"] -) -@pytest.mark.parametrize("use_metric", [False, True], ids=["identity", "cholesky"]) -def test_gram_and_normal_steps_agree_at_positive_damping(A, use_metric): - # Push-through identity: P J'(J P J' + lam I)^{-1} = S (B'B + lam I)^{-1} B' - # with B = J S, exact for every lam > 0 regardless of rank or shape -- this - # covers the gram form on a TALL residual and the normal form on a WIDE one. - m, n = A.shape - b = jnp.arange(1.0, m + 1.0) - L = {3: L3, 4: L4}[n] - - def residual(theta, args, p): - return A @ theta - b - - metric = metric_from_cholesky(L) if use_metric else None - common = dict(init_damping=1e-2, metric=metric, geodesic_acceleration=False) - gram = LevenbergMarquardt(residual, linear_solver="gram_cholesky", **common) - normal = LevenbergMarquardt(residual, linear_solver="normal_cholesky", **common) - - theta0 = 0.1 * jnp.arange(1.0, n + 1.0) - x_gram, _, info_gram = gram.update(theta0, gram.init(theta0)) - x_normal, _, info_normal = normal.update(theta0, normal.init(theta0)) - - assert bool(info_gram.accepted) == bool(info_normal.accepted) - # rtol 5e-4: the identity is exact (verified ~1e-13 at float64) but the two - # factorizations round differently in float32 at this rank-deficient - # conditioning, with measured rel diff ~1.2e-4 on the tall cases. - assert jnp.allclose(x_gram, x_normal, rtol=5e-4, atol=1e-5) - assert jnp.allclose(info_gram.loss, info_normal.loss, rtol=5e-4, atol=1e-6) - - -# --- normal_cg == normal_cholesky -------------------------------------------- - - -def exp_residual(theta, args, p): - ts, ys = args - return theta[0] * jnp.exp(theta[1] * ts) - ys - - -@pytest.mark.parametrize("preconditioned", [False, True], ids=["identity", "exact"]) -def test_normal_cg_step_matches_normal_cholesky(preconditioned): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - theta0 = jnp.array([1.0, 0.0]) - common = dict( - init_damping=1e-2, - metric=metric_from_cholesky(L2), - geodesic_acceleration=False, - ) - dense = LevenbergMarquardt(exp_residual, linear_solver="normal_cholesky", **common) - - if preconditioned: - # Exact n-space preconditioner (B'B + lam I)^{-1} frozen at theta0: SPD, - # linear, and inert at inner convergence -- the step must not move. - J0 = jax.jacobian(lambda th: exp_residual(th, (ts, ys), None))(theta0) - B0 = J0 @ chol_S(L2) - - def normal_preconditioner(v, damping): - return jnp.linalg.solve(B0.T @ B0 + damping * jnp.eye(2), v) - - else: - normal_preconditioner = identity_preconditioner() - - cg = LevenbergMarquardt( - exp_residual, - linear_solver="normal_cg", - normal_preconditioner=normal_preconditioner, - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-8, - iterative_maxiter=100, - **common, - ) - - x_dense, _, info_dense = dense.update( - theta0, dense.init(theta0, (ts, ys)), (ts, ys) - ) - x_cg, _, info_cg = cg.update(theta0, cg.init(theta0, (ts, ys)), (ts, ys)) - - assert bool(info_dense.accepted) - assert bool(info_cg.accepted) - assert jnp.allclose(x_cg, x_dense, rtol=1e-4, atol=1e-4) - - -# --- minimum-M-norm root selection ------------------------------------------- - - -@pytest.mark.parametrize("form", ["normal_cholesky", "normal_cg"]) -@pytest.mark.parametrize("use_metric", [False, True], ids=["identity", "cholesky"]) -def test_normal_forms_converge_to_min_m_norm_root(form, use_metric): - def residual(theta, args, p): - return A_RD @ theta - B_RD - - metric = metric_from_cholesky(L3) if use_metric else None - if form == "normal_cg": - kwargs = normal_cg_kwargs(maxiter=100, tol=1e-7) - else: - kwargs = {"linear_solver": "normal_cholesky"} - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - metric=metric, - geodesic_acceleration=False, - **kwargs, - ) - result = solver.solve(jnp.zeros(3), atol=1e-5, max_steps=60) - - expected = min_m_norm_root(A_RD, B_RD, chol_S(L3) if use_metric else None) - assert float(result.info.loss) < 1e-5 - assert jnp.allclose(result.x, expected, atol=5e-3) - - -def test_lambda_zero_selection_matches_weighted_pseudoinverse_float64(): - # One update at damping -> 0 from theta0 = 0 must select the M-weighted - # pseudoinverse root S pinv(A S) b for every form -- including LSMR under a - # right-preconditioner, which the damping fix makes exactly I-damped in u. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg - -from nlls_gram import ( - LevenbergMarquardt, - WhitenedPreconditioner, - identity_preconditioner, - metric_from_cholesky, -) - -A = jnp.array( - [[1.0, 2.0, 3.0], [0.0, 1.0, 1.0], [1.0, 2.0, 3.0], [2.0, 1.0, 3.0]] -) -b = A @ jnp.array([1.0, -1.0, 2.0]) -L = jnp.array([[1.5, 0.0, 0.0], [0.4, 1.2, 0.0], [-0.3, 0.2, 0.9]]) -S = jsp_linalg.solve_triangular(L.T, jnp.eye(3), lower=False) -B = A @ S -expected = S @ jnp.linalg.pinv(B) @ b - - -def residual(theta, args, p): - return A @ theta - b - - -lam = 1e-10 -theta0 = jnp.zeros(3) -common = dict( - init_damping=lam, metric=metric_from_cholesky(L), geodesic_acceleration=False -) - -for form in ("gram_cholesky", "normal_cholesky"): - solver = LevenbergMarquardt(residual, linear_solver=form, **common) - theta1, _, info = solver.update(theta0, solver.init(theta0)) - assert bool(info.accepted), form - assert jnp.allclose(theta1, expected, atol=1e-7), (form, theta1, expected) - -gram_cg = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-12, - iterative_maxiter=100, - **common, -) -theta1, _, _ = gram_cg.update(theta0, gram_cg.init(theta0)) -assert jnp.allclose(theta1, expected, atol=1e-6), ("gram_cg", theta1, expected) - -normal_cg = LevenbergMarquardt( - residual, - linear_solver="normal_cg", - normal_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-12, - iterative_maxiter=100, - **common, -) -theta1, _, _ = normal_cg.update(theta0, normal_cg.init(theta0)) -assert jnp.allclose(theta1, expected, atol=1e-6), ("normal_cg", theta1, expected) - -# The right-preconditioner acts in the whitened u coordinates, so approximate -# B.T @ B rather than the unwhitened A.T @ A. -R = jnp.linalg.cholesky(B.T @ B + jnp.eye(3)).T -lsmr_common = dict(iterative_tol=1e-14, iterative_atol=0.0, iterative_maxiter=400) -plain = LevenbergMarquardt(residual, linear_solver="lsmr", **lsmr_common, **common) -preconditioned = LevenbergMarquardt( - residual, - linear_solver="lsmr", - whitened_preconditioner=WhitenedPreconditioner( - lambda v, damping: jsp_linalg.solve_triangular(R, v, lower=False), - lambda w, damping: jsp_linalg.solve_triangular(R.T, w, lower=True), - ), - **lsmr_common, - **common, -) -for name, solver in (("lsmr", plain), ("lsmr_preconditioned", preconditioned)): - theta1, _, _ = solver.update(theta0, solver.init(theta0)) - assert jnp.allclose(theta1, expected, atol=1e-6), (name, theta1, expected) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -# --- auto resolution --------------------------------------------------------- - - -@pytest.mark.parametrize( - "A,explicit", - [ - (A_TALL, "normal_cholesky"), - (A_SQ, "normal_cholesky"), - (A_WIDE, "gram_cholesky"), - ], - ids=["tall", "square", "wide"], -) -def test_auto_matches_explicit_form_per_shape(A, explicit): - # auto resolves at trace time to gram_cholesky iff n_params > n_residuals, - # else normal_cholesky -- the SAME branch, so the update is bitwise equal. - m, n = A.shape - b = jnp.arange(1.0, m + 1.0) - - def residual(theta, args, p): - return A @ theta - b - - auto = LevenbergMarquardt(residual, init_damping=1e-2) - explicit_solver = LevenbergMarquardt( - residual, init_damping=1e-2, linear_solver=explicit - ) - theta0 = 0.1 * jnp.arange(1.0, n + 1.0) - x_auto, state_auto, info_auto = auto.update(theta0, auto.init(theta0)) - x_expl, state_expl, info_expl = explicit_solver.update( - theta0, explicit_solver.init(theta0) - ) - - assert jnp.array_equal(x_auto, x_expl) - assert jnp.array_equal(state_auto.damping, state_expl.damping) - assert jnp.array_equal(info_auto.loss, info_expl.loss) - - -def test_auto_reuses_trace_within_shape_and_recompiles_on_shape_change(): - traces = {"count": 0} - - def residual(theta, args, p): - traces["count"] += 1 - A, b = args - return A @ theta - b - - solver = LevenbergMarquardt( - residual, init_damping=1e-2, geodesic_acceleration=False - ) - step = jax.jit(lambda x, s, args: solver.update(x, s, args)) - - tall = (A_TALL, jnp.array([1.0, -0.5, 2.0])) - theta = jnp.zeros(2) - state = solver.init(theta, tall) - step(theta, state, tall) - count_after_trace = traces["count"] - assert count_after_trace > 0 - - # Same shapes, new values: the auto resolution is a trace-time constant, so - # the compiled update is reused with no retrace. - step(theta + 0.1, state, (A_TALL, jnp.array([0.3, 0.1, -1.0]))) - assert traces["count"] == count_after_trace - - # Shape flip (wide problem): a fresh trace resolves the other branch. - wide = (A_WIDE, jnp.array([0.7, -0.2])) - theta_wide = jnp.zeros(4) - state_wide = solver.init(theta_wide, wide) - count_before_wide_trace = traces["count"] - step(theta_wide, state_wide, wide) - assert traces["count"] > count_before_wide_trace - - -# --- constructor validation matrix ------------------------------------------- - - -def test_old_solver_names_are_unknown(): - with pytest.raises(ValueError, match="unknown linear_solver"): - LevenbergMarquardt(exp_residual, linear_solver="cholesky") - with pytest.raises(ValueError, match="unknown linear_solver"): - LevenbergMarquardt(exp_residual, linear_solver="cg") - with pytest.raises(ValueError, match="unknown ad_solver"): - LevenbergMarquardt(exp_residual, ad_solver="cholesky") - with pytest.raises(ValueError, match="unknown ad_solver"): - LevenbergMarquardt(exp_residual, ad_solver="cg") - with pytest.raises(TypeError, match="dual_solve_dtype"): - LevenbergMarquardt(exp_residual, dual_solve_dtype=jnp.float64) - # The pre-rename implicit_* kwarg family must not be silently accepted by - # a future **kwargs/compat shim. - for old_kwarg in ( - "implicit_solver", - "implicit_penalty", - "implicit_preconditioner", - "implicit_tol", - "implicit_atol", - "implicit_maxiter", - ): - with pytest.raises(TypeError, match=old_kwarg): - LevenbergMarquardt(exp_residual, **{old_kwarg: None}) - - -def test_gram_cg_only_hooks_rejected_elsewhere(): - for kwargs in ( - {"dual_preconditioner": identity_preconditioner()}, - { - "preconditioner_factory": PreconditionerFactory( - prepare=lambda x, args, p, aux: jnp.ones(2), - apply=lambda state, v, damping: v, - ) - }, - {"recycle": RecycleConfig(rank=2)}, - ): - (name,) = kwargs - with pytest.raises(ValueError, match=name): - LevenbergMarquardt(exp_residual, linear_solver="normal_cholesky", **kwargs) - with pytest.raises(ValueError, match=name): - LevenbergMarquardt( - exp_residual, - **normal_cg_kwargs(), - **kwargs, - ) - - -def test_normal_preconditioner_required_by_and_exclusive_to_normal_cg(): - with pytest.raises(ValueError, match="normal_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="normal_cg", - iterative_tol=1e-7, - iterative_maxiter=30, - ) - with pytest.raises(ValueError, match="normal_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=30, - normal_preconditioner=identity_preconditioner(), - ) - with pytest.raises(ValueError, match="normal_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="normal_cholesky", - normal_preconditioner=identity_preconditioner(), - ) - - -def test_whitened_preconditioner_still_lsmr_only(): - hook = WhitenedPreconditioner(lambda v, damping: v, lambda w, damping: w) - with pytest.raises(ValueError, match="whitened_preconditioner"): - LevenbergMarquardt( - exp_residual, linear_solver="normal_cholesky", whitened_preconditioner=hook - ) - - -def test_gram_cg_still_requires_dual_preconditioner(): - with pytest.raises(ValueError, match="dual_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=30, - ) - - -def test_ad_solver_preconditioner_requires_cg_resolved_implicit(): - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="normal_cholesky", - ad_solver_preconditioner=identity_preconditioner(), - ) - with pytest.raises(ValueError, match="ad_solver_preconditioner"): - LevenbergMarquardt( - exp_residual, - linear_solver="normal_cholesky", - ad_solver="svd", - ad_solver_preconditioner=identity_preconditioner(), - ) - - -def test_dtype_knobs_require_x64_and_float64(): - # This suite runs with x64 disabled, so a legal target still trips the - # x64 gate; non-float64 values are rejected outright. - with pytest.raises(ValueError, match="x64"): - LevenbergMarquardt(exp_residual, linear_solve_dtype=jnp.float64) - with pytest.raises(ValueError, match="x64"): - LevenbergMarquardt( - exp_residual, - metric=metric_from_cholesky(L2), - metric_solve_dtype=jnp.float64, - ) - with pytest.raises(ValueError, match="float64"): - LevenbergMarquardt(exp_residual, linear_solve_dtype=jnp.float32) - with pytest.raises(ValueError, match="float64"): - LevenbergMarquardt( - exp_residual, - metric=metric_from_cholesky(L2), - metric_solve_dtype=jnp.float32, - ) - - -def test_dtype_knob_legality_and_wiring_float64_subprocess(): - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import ( - LevenbergMarquardt, - MetricFactory, - GramMetric, - identity_preconditioner, - metric_from_cholesky, -) - -L = jnp.array([[1.3, 0.0], [0.5, 0.8]], dtype=jnp.float32) - - -def residual(theta, args, p): - A, b = args - return A @ theta - b - - -# Fully matrix-free pipeline (lsmr forward + normal_cg implicit): no dense -# linear-solve path exists for linear_solve_dtype to promote. -try: - LevenbergMarquardt( - residual, - linear_solver="lsmr", - ad_solver="normal_cg", - ad_solver_preconditioner=identity_preconditioner(), - ad_solver_maxiter=30, - iterative_maxiter=30, - linear_solve_dtype=jnp.float64, - ) -except ValueError as error: - assert "linear_solve_dtype" in str(error), error -else: - raise AssertionError("matrix-free linear_solve_dtype must be rejected") - -# metric_solve_dtype without a custom metric or factory has nothing to wrap. -try: - LevenbergMarquardt(residual, metric_solve_dtype=jnp.float64) -except ValueError as error: - assert "metric_solve_dtype" in str(error), error -else: - raise AssertionError("metric_solve_dtype without a metric must be rejected") - -# lsmr forward with implicit auto resolves densely by shape, a legal target. -LevenbergMarquardt( - residual, linear_solver="lsmr", iterative_maxiter=30, - linear_solve_dtype=jnp.float64, -) - -A32 = jnp.array([[1.0, 0.5], [0.3, 2.0], [-1.0, 1.0]], dtype=jnp.float32) -b32 = jnp.array([1.0, -2.0, 0.5], dtype=jnp.float32) -theta0 = jnp.zeros(2, dtype=jnp.float32) - -# linear_solve_dtype: float32 data in, float32 step out, wide solve inside. -promoted = LevenbergMarquardt( - residual, - linear_solver="normal_cholesky", - linear_solve_dtype=jnp.float64, - geodesic_acceleration=False, -) -theta1, state1, info1 = promoted.update( - theta0, promoted.init(theta0, (A32, b32)), (A32, b32) -) -assert theta1.dtype == jnp.float32, theta1.dtype -assert bool(jnp.all(jnp.isfinite(theta1))) - -# metric_solve_dtype wraps the resolved metric callbacks: they see float64 -# inputs while the returned step stays at the residual dtype. -seen = {} -base = metric_from_cholesky(L) - - -def recording_inv_sqrt(v): - seen["inv_sqrt"] = v.dtype - return base.inv_sqrt(v) - - -def recording_inv_sqrt_transpose(v): - seen["inv_sqrt_transpose"] = v.dtype - return base.inv_sqrt_transpose(v) - - -recording = GramMetric( - solve=base.solve, - norm=base.norm, - inv_sqrt=recording_inv_sqrt, - inv_sqrt_transpose=recording_inv_sqrt_transpose, -) -wrapped = LevenbergMarquardt( - residual, - linear_solver="normal_cholesky", - metric=recording, - metric_solve_dtype=jnp.float64, - geodesic_acceleration=False, -) -theta1, _, _ = wrapped.update(theta0, wrapped.init(theta0, (A32, b32)), (A32, b32)) -assert theta1.dtype == jnp.float32, theta1.dtype -assert seen["inv_sqrt"] == jnp.float64, seen -assert seen["inv_sqrt_transpose"] == jnp.float64, seen - -# A factory-built metric is wrapped the same way, after build. -factory = MetricFactory( - prepare=lambda x, args, p, aux: jnp.zeros(()), - build=lambda state: recording, -) -seen.clear() -factory_solver = LevenbergMarquardt( - residual, - linear_solver="normal_cholesky", - metric_factory=factory, - metric_solve_dtype=jnp.float64, - geodesic_acceleration=False, -) -theta1, _, _ = factory_solver.update( - theta0, factory_solver.init(theta0, (A32, b32)), (A32, b32) -) -assert seen["inv_sqrt"] == jnp.float64, seen -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -# --- S / S' adjoint consistency for every shipped builder -------------------- - - -def shipped_inv_sqrt_metrics(): - K = jnp.array([[2.0, 0.3], [0.3, 1.5]]) - return [ - ("cholesky", metric_from_cholesky(L3), 3), - ("diagonal", metric_from_diagonal(jnp.array([2.0, 0.5, 1.5])), 3), - ( - "repeated_shifted_dense", - repeated_shifted_dense_metric(K, repeats=2, zero_pad_size=1, epsilon=0.2), - 5, - ), - ] - - -@pytest.mark.parametrize( - "metric,n", - [case[1:] for case in shipped_inv_sqrt_metrics()], - ids=[case[0] for case in shipped_inv_sqrt_metrics()], -) -def test_metric_builders_inv_sqrt_adjoint_consistency(metric, n): - # The normal forms apply S and S' as a transpose PAIR: = - # and S S' = M^{-1} must hold for every shipped builder, or the normal-form - # steps and the implicit S-transpose rule silently use a wrong adjoint. - u = jax.random.normal(jax.random.key(0), (n,)) - w = jax.random.normal(jax.random.key(1), (n,)) - assert jnp.allclose( - metric.inv_sqrt(u) @ w, u @ metric.inv_sqrt_transpose(w), rtol=1e-4, atol=1e-5 - ) - assert jnp.allclose( - metric.inv_sqrt(metric.inv_sqrt_transpose(w)), - metric.solve(w), - rtol=1e-4, - atol=1e-5, - ) - - -# --- descent on an inconsistent residual ------------------------------------- - - -@pytest.mark.parametrize("form", ["normal_cholesky", "normal_cg"]) -def test_normal_forms_descend_on_inconsistent_residual(form): - # Tall full-rank with b outside range(A): no root exists, the forward r is - # never consistent, and the damped normal step must still be a descent - # direction converging to the least-squares solution. - b = jnp.array([1.0, -2.0, 0.5]) - - def residual(theta, args, p): - return A_TALL @ theta - b - - if form == "normal_cg": - kwargs = normal_cg_kwargs(maxiter=100, tol=1e-7) - else: - kwargs = {"linear_solver": form} - solver = LevenbergMarquardt( - residual, init_damping=1e-2, geodesic_acceleration=False, **kwargs - ) - theta = jnp.array([2.0, 1.0]) - state = solver.init(theta) - _, _, first = solver.update(theta, state) - assert bool(first.accepted) - assert float(first.loss) < float(first.loss_old) - - for _ in range(40): - theta, state, info = solver.update(theta, state) - expected = jnp.linalg.lstsq(A_TALL, b)[0] - assert jnp.allclose(theta, expected, atol=1e-3) - - -# --- range-violating preconditioner loses min-norm selection ----------------- - - -def test_range_violating_normal_preconditioner_loses_min_norm_selection(): - # Pins DOCUMENTED behavior (the Codex counterexample): a budget-truncated - # normal_cg iterate lies in the C-preconditioned Krylov space, so an SPD C - # with C(range(B')) not within range(B') leaks nullspace components into - # the step and minimum-M-norm selection is lost. The identity keeps every - # iterate in range(B'). maxiter=2 < n=3 keeps CG genuinely truncated. - def residual(theta, args, p): - return A_RD @ theta - B_RD - - weights = jnp.array([1.0, 1.0, 25.0]) - range_projector = A_RD.T @ jnp.linalg.pinv(A_RD.T) - steps = {} - for name, hook in ( - ("identity", identity_preconditioner()), - ("violating", lambda v, damping: v / weights), - ): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="normal_cg", - normal_preconditioner=hook, - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=2, - geodesic_acceleration=False, - ) - theta0 = jnp.zeros(3) - theta1, _, info = solver.update(theta0, solver.init(theta0)) - assert bool(info.accepted) - steps[name] = theta1 - theta0 - - out_of_range_identity = steps["identity"] - range_projector @ steps["identity"] - out_of_range_violating = steps["violating"] - range_projector @ steps["violating"] - assert float(jnp.linalg.norm(out_of_range_identity)) < 1e-4 - assert float(jnp.linalg.norm(out_of_range_violating)) > 1e-2 - - -# --- LSMR damping fix -------------------------------------------------------- - - -def test_lsmr_preconditioned_step_matches_plain_after_damping_fix(): - # The augmented operator damps sqrt(damping) * R^{-1} z = sqrt(damping) u, - # so every lambda > 0 subproblem is exactly I-damped in u and the converged - # step is R-invariant; a large lambda makes any leftover R'R-damping - # surrogate visible immediately. - def residual(theta, args, p): - return A_RD @ theta - B_RD - - R = jnp.linalg.cholesky(A_RD.T @ A_RD + jnp.eye(3)).T - hook = WhitenedPreconditioner( - lambda v, damping: jsp_linalg.solve_triangular(R, v, lower=False), - lambda w, damping: jsp_linalg.solve_triangular(R.T, w, lower=True), - ) - common = dict( - init_damping=0.1, - geodesic_acceleration=False, - iterative_tol=0.0, - iterative_atol=0.0, - iterative_maxiter=200, - ) - plain = LevenbergMarquardt(residual, linear_solver="lsmr", **common) - preconditioned = LevenbergMarquardt( - residual, linear_solver="lsmr", whitened_preconditioner=hook, **common - ) - theta0 = jnp.array([0.2, -0.1, 0.4]) - x_plain, _, _ = plain.update(theta0, plain.init(theta0)) - x_prec, _, _ = preconditioned.update(theta0, preconditioned.init(theta0)) - assert jnp.allclose(x_prec, x_plain, rtol=1e-4, atol=1e-4) - - -# --- reverse-mode grad through a normal_cg update ---------------------------- - - -def test_reverse_grad_through_normal_cg_update_matches_normal_cholesky(): - # Non-diagonal metric: S = L^{-T} is NOT self-adjoint, so any code path - # that transposes S as itself produces a wrong reverse-mode gradient here. - w = jnp.array([0.3, -0.7, 1.1]) - - def residual(theta, args, p): - return A_RD @ theta - p * B_RD - - common = dict( - init_damping=1e-2, - metric=metric_from_cholesky(L3), - geodesic_acceleration=False, - ) - dense = LevenbergMarquardt(residual, linear_solver="normal_cholesky", **common) - cg = LevenbergMarquardt( - residual, **normal_cg_kwargs(maxiter=100, tol=1e-8), **common - ) - - def stepped(solver, p): - theta0 = jnp.array([0.2, -0.1, 0.3]) - theta1, _, _ = solver.update(theta0, solver.init(theta0, p=p), None, p) - return theta1 @ w - - p = jnp.asarray(1.3) - grad_dense = jax.grad(lambda q: stepped(dense, q))(p) - grad_cg = jax.grad(lambda q: stepped(cg, q))(p) - assert jnp.allclose(grad_cg, grad_dense, rtol=1e-3, atol=1e-4) - - -# --- geodesic parity --------------------------------------------------------- - - -def test_geodesic_parity_across_forms(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - theta0 = jnp.array([1.0, 0.0]) - common = dict(init_damping=1e-2, metric=metric_from_cholesky(L2)) - gram = LevenbergMarquardt(exp_residual, linear_solver="gram_cholesky", **common) - normal = LevenbergMarquardt(exp_residual, linear_solver="normal_cholesky", **common) - cg = LevenbergMarquardt( - exp_residual, **normal_cg_kwargs(maxiter=100, tol=1e-8), **common - ) - - results = {} - for name, solver in (("gram", gram), ("normal", normal), ("normal_cg", cg)): - x1, _, info = solver.update(theta0, solver.init(theta0, (ts, ys)), (ts, ys)) - results[name] = (x1, info) - - x_ref, info_ref = results["gram"] - for name in ("normal", "normal_cg"): - x1, info = results[name] - assert bool(info.used_geodesic) == bool(info_ref.used_geodesic) - assert jnp.allclose(x1, x_ref, rtol=1e-4, atol=1e-4) - assert jnp.allclose( - info.acceleration_ratio, info_ref.acceleration_ratio, rtol=1e-3, atol=1e-4 - ) - - -# --- implicit AD: four forms x three regimes --------------------------------- - - -@pytest.mark.parametrize("ad_solver", AD_FORMS) -def test_implicit_forms_underdetermined_min_norm(ad_solver): - def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - ad_solver=ad_solver, - **ad_kwargs(ad_solver), - ) - theta0 = jnp.zeros(2) - - def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - p = jnp.asarray(3.0) - p_dot = jnp.asarray(0.7) - x, x_dot = jax.jvp(solved_x, (p,), (p_dot,)) - _, pullback = jax.vjp(solved_x, p) - (p_bar,) = pullback(jnp.array([3.0, 4.0])) - - assert jnp.allclose(x, jnp.array([3.0 / 5.0, 6.0 / 5.0]), atol=1e-5) - assert jnp.allclose(x_dot, jnp.array([p_dot / 5.0, 2.0 * p_dot / 5.0]), atol=1e-5) - assert jnp.allclose(p_bar, (3.0 + 2.0 * 4.0) / 5.0, atol=1e-5) - - -@pytest.mark.parametrize("ad_solver", AD_FORMS) -def test_implicit_forms_square_full_rank_jvp_and_vjp(ad_solver): - # Square nonsingular Jacobian: the ridge -> 0 sensitivity is exactly - # -J^{-1} J_p p_dot = A^{-1} c p_dot. - c = jnp.array([1.0, -0.7]) - - def residual(theta, _, p): - return A_SQ @ theta - c * p - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - ad_solver=ad_solver, - **ad_kwargs(ad_solver), - ) - theta0 = jnp.zeros(2) - - def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-7).x - - p = jnp.asarray(1.5) - p_dot = jnp.asarray(0.6) - dx_dp = jnp.linalg.solve(A_SQ, c) - x, x_dot = jax.jvp(solved_x, (p,), (p_dot,)) - _, pullback = jax.vjp(solved_x, p) - w = jnp.array([0.4, -0.2]) - (p_bar,) = pullback(w) - - # Measured 6e-8 float32 across all three forms. - assert jnp.allclose(x, dx_dp * p, atol=1e-6) - assert jnp.allclose(x_dot, dx_dp * p_dot, atol=1e-6) - assert jnp.allclose(p_bar, w @ dx_dp, atol=1e-6) - - -@pytest.mark.parametrize("ad_solver", AD_FORMS) -def test_implicit_forms_tall_rank_deficient_consistent_min_norm_tangent( - ad_solver, -): - # Interpolation keeps the system consistent for every p (r_p p_dot lies in - # range(B) by construction), so all four forms return the min-norm tangent - # root * p_dot. - def residual(theta, _, p): - return A_RD @ theta - p * B_RD - - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver=ad_solver, - geodesic_acceleration=False, - **ad_kwargs(ad_solver), - ) - theta0 = jnp.zeros(3) - - def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - root = min_m_norm_root(A_RD, B_RD) - p = jnp.asarray(1.2) - p_dot = jnp.asarray(0.5) - x, x_dot = jax.jvp(solved_x, (p,), (p_dot,)) - - # x is forward-convergence-limited (measured 2.5e-4 at solve atol 1e-6); - # the tangent itself is filter/CG-exact (measured <= 8.3e-7 float32). - assert jnp.allclose(x, p * root, atol=1e-3) - assert jnp.allclose(x_dot, p_dot * root, atol=1e-5) - - -def test_implicit_normal_cg_reverse_grad_nondiagonal_metric_matches_closed_form(): - # The implicit rule's final step applies S through a custom_linear_solve; - # with a non-diagonal metric S is not self-adjoint, so reverse mode is only - # correct if that solve declares its true transpose S'. - a = jnp.array([1.0, 2.0, 0.5]) - w = jnp.array([0.4, -0.2, 0.7]) - - def residual(theta, _, p): - return jnp.array([a @ theta - p]) - - def make_solver(ad_solver): - return LevenbergMarquardt( - residual, - init_damping=1e-2, - metric=metric_from_cholesky(L3), - geodesic_acceleration=False, - ad_solver=ad_solver, - **ad_kwargs(ad_solver), - ) - - def solved_dot_w(solver, p): - return solver.solve(jnp.zeros(3), p=p, max_steps=80, atol=1e-6).x @ w - - P = jnp.linalg.inv(L3 @ L3.T) - direction = P @ a / (a @ P @ a) - p = jnp.asarray(2.0) - grad_svd = jax.grad(lambda q: solved_dot_w(make_solver("svd"), q))(p) - grad_cg = jax.grad(lambda q: solved_dot_w(make_solver("normal_cg"), q))(p) - - # Measured 3e-8 float32 for both forms. - assert jnp.allclose(grad_svd, w @ direction, atol=1e-6) - assert jnp.allclose(grad_cg, w @ direction, atol=1e-6) - - -def test_svd_ad_under_lsmr_produces_min_norm_tangent_at_both_shapes(): - # A matrix-free forward (lsmr) uses SVD AD on non-square systems: - # the wide and the tall problem both must produce the min-norm tangent - # through the same rule (the small-side factorization is a cost choice, - # never a semantic one). - def wide_residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) - - def tall_residual(theta, _, p): - return A_RD @ theta - p * B_RD - - def make_solver(residual): - return LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="lsmr", - iterative_tol=1e-10, - iterative_maxiter=100, - geodesic_acceleration=False, - ) - - wide = make_solver(wide_residual) - _, x_dot = jax.jvp( - lambda p: wide.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).x, - (jnp.asarray(3.0),), - (jnp.asarray(1.0),), - ) - # Measured 4.5e-8 (wide) and 1.7e-6 (tall) float32. - assert jnp.allclose(x_dot, jnp.array([1.0 / 5.0, 2.0 / 5.0]), atol=1e-6) - - tall = make_solver(tall_residual) - root = min_m_norm_root(A_RD, B_RD) - _, x_dot = jax.jvp( - lambda p: tall.solve(jnp.zeros(3), p=p, max_steps=80, atol=1e-6).x, - (jnp.asarray(1.2),), - (jnp.asarray(1.0),), - ) - assert jnp.allclose(x_dot, root, atol=2e-5) - - -def make_ridged_normal_cg_solver(): - def residual(theta, _, p): - return A_RD @ theta - p * B_RD - - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver="regularized_normal_cg", - ad_solver_penalty=1e-4, - ad_solver_preconditioner=identity_preconditioner(), - ad_solver_maxiter=50, - geodesic_acceleration=False, - ) - # The three ridge guards below pin the normal_cg Rayleigh-probe ridge; a - # silent reroute to a different method would void them. - assert solver._resolved_ad_solver == "regularized_normal_cg" - return solver - - -def test_regularized_normal_cg_tangent_is_linear(): - # The explicit-positive normal_cg ridge is scaled by a Rayleigh quotient - # over a FIXED probe, not the rhs: an rhs-scaled ridge makes the tangent - # map T(p_dot) affine-but-not-linear, breaking T(a) + T(b) = T(a + b) and - # homogeneity on exactly this rank-deficient shape. - solver = make_ridged_normal_cg_solver() - p = jnp.asarray(1.2) - - def T(p_dot): - return jax.jvp( - lambda q: solver.solve(jnp.zeros(3), p=q, max_steps=80, atol=1e-6).x, - (p,), - (jnp.asarray(p_dot),), - )[1] - - t_a, t_b = T(0.3), T(0.5) - assert jnp.allclose(T(0.8), t_a + t_b, rtol=1e-4, atol=1e-5) - assert jnp.allclose(T(0.9), 3.0 * t_a, rtol=1e-4, atol=1e-5) - # And the ridge stays a small perturbation of the min-norm tangent. - assert jnp.allclose(t_b, 0.5 * min_m_norm_root(A_RD, B_RD), atol=5e-3) - - -def test_regularized_normal_cg_vjp_runs_and_is_finite(): - # Reverse mode transposes the tangent map; the rhs-scaled ridge was not - # linear, so this vjp used to raise NotImplementedError. - solver = make_ridged_normal_cg_solver() - w = jnp.array([0.4, -0.2, 0.7]) - - grad = jax.grad( - lambda q: solver.solve(jnp.zeros(3), p=q, max_steps=80, atol=1e-6).x @ w - )(jnp.asarray(1.2)) - assert bool(jnp.isfinite(grad)) - assert jnp.allclose(grad, min_m_norm_root(A_RD, B_RD) @ w, atol=5e-3) - - -def test_regularized_normal_cg_zero_seed_gives_zero_tangent(): - # A zero p_dot must map to an exactly-zero tangent even with the ridge - # live (the fixed-probe scale is seed-independent, the rhs is zero). - solver = make_ridged_normal_cg_solver() - _, t_zero = jax.jvp( - lambda q: solver.solve(jnp.zeros(3), p=q, max_steps=80, atol=1e-6).x, - (jnp.asarray(1.2),), - (jnp.asarray(0.0),), - ) - assert jnp.array_equal(t_zero, jnp.zeros(3)) - - -def test_default_implicit_tangent_has_no_ridge_bias_float64(): - # Guard-rail over all three unregularized AD forms: the tangent must be the - # exact min-norm tangent (SVD-of-B spectral filter / unridged CG). - # Measured error is ~4e-15 at float64; any hidden default ridge (a 1e-12 - # trace-scaled one biases ~1e-11) fails the 1e-12 bound. - script = r""" -import jax -jax.config.update("jax_enable_x64", True) -import jax.numpy as jnp - -from nlls_gram import LevenbergMarquardt, identity_preconditioner - -A = jnp.array( - [[1.0, 2.0, 3.0], [0.0, 1.0, 1.0], [1.0, 2.0, 3.0], [2.0, 1.0, 3.0]] -) -b = A @ jnp.array([1.0, -1.0, 2.0]) -root = jnp.linalg.pinv(A) @ b - - -def residual(theta, _, p): - return A @ theta - p * b - - -def tangent(ad_solver, **kwargs): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver=ad_solver, - geodesic_acceleration=False, - **kwargs, - ) - assert solver._resolved_ad_solver == ad_solver, ad_solver - return jax.jvp( - lambda p: solver.solve(jnp.zeros(3), p=p, max_steps=80, atol=1e-9).x, - (jnp.asarray(1.2),), - (jnp.asarray(0.5),), - )[1] - - -expected = 0.5 * root -cg_kwargs = dict( - ad_solver_preconditioner=identity_preconditioner(), - ad_solver_tol=1e-14, - ad_solver_maxiter=100, -) -for form, kwargs in ( - ("svd", {}), - ("gram_cg", cg_kwargs), - ("normal_cg", cg_kwargs), -): - t = tangent(form, **kwargs) - assert jnp.allclose(t, expected, atol=1e-12), (form, t - expected) -""" - result = subprocess.run( - [sys.executable, "-c", textwrap.dedent(script)], - check=False, - capture_output=True, - text=True, - ) - assert result.returncode == 0, result.stderr + result.stdout - - -def test_explicit_factorizations_on_rank_deficient_tall_system(): - def residual(theta, _, p): - return A_RD @ theta - p * B_RD - - def tangent(ad_solver, ad_solver_penalty=None): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver=ad_solver, - ad_solver_penalty=ad_solver_penalty, - geodesic_acceleration=False, - ) - return jax.jvp( - lambda p: solver.solve(jnp.zeros(3), p=p, max_steps=80, atol=1e-6).x, - (jnp.asarray(1.2),), - (jnp.asarray(0.5),), - )[1] - - expected = 0.5 * min_m_norm_root(A_RD, B_RD) - default_tangent = tangent("svd") - assert bool(jnp.all(jnp.isfinite(default_tangent))) - # Measured 1.8e-7 float32: the filter default carries no ridge bias. - assert jnp.allclose(default_tangent, expected, atol=2e-6) - ridged_tangent = tangent("augmented_qr", 1e-4) - assert bool(jnp.all(jnp.isfinite(ridged_tangent))) - # O(penalty) bias against the min-norm tangent, but tight (measured - # 2.9e-5) against the float64 analytic ridge it claims to solve. - assert jnp.allclose(ridged_tangent, expected, atol=5e-3) - G64 = np.asarray(A_RD, np.float64).T @ np.asarray(A_RD, np.float64) - analytic_ridged = 0.5 * np.linalg.solve( - G64 + 1e-4 * np.trace(G64) * np.eye(3), - np.asarray(A_RD, np.float64).T @ np.asarray(B_RD, np.float64), - ) - assert np.allclose( - np.asarray(ridged_tangent, np.float64), analytic_ridged, atol=3e-4 - ) - assert bool(jnp.all(jnp.isnan(tangent("qr")))) - - -def test_qr_nan_is_the_guard_not_roundoff_on_inconsistent_rhs(): - # The integer-valued A_RD is EXACTLY rank-deficient, yet a factorization - # can round it through to a finite solve -- which on this INCONSISTENT - # system (c outside range(A_RD), so the tangent rhs leaves the dual's - # range) would be a silently wrong finite tangent. The |R_ii| rank guard, - # not factorization roundoff, must deterministically poison it. - c = jnp.array([1.0, 0.0, 0.0, 0.0]) - - def residual(theta, _, p): - return A_RD @ theta - p * c - - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver="qr", - geodesic_acceleration=False, - ) - _, t = jax.jvp( - lambda p: solver.solve(jnp.zeros(3), p=p, max_steps=80, atol=0.0).x, - (jnp.asarray(1.2),), - (jnp.asarray(0.5),), - ) - assert bool(jnp.all(jnp.isnan(t))) - - -def test_explicit_factorizations_on_wide_rank_deficient_fixture(): - # The fat-side factorization (m = 3 < n = 4, rank 2) runs on the dual: - # small-side factorization runs on the dual and pushes through, but the - # semantics must match the tall side): default None is the exact min-norm - # tangent, an explicit penalty matches the analytic ridge exactly -- - # B'(BB' + penalty tr I)^{-1} = (B'B + penalty tr I)^{-1} B' with the - # same trace either side -- and 0.0 is the rank-guard NaN. - A_W = A_RD.T - b_w = A_W @ jnp.array([1.0, -1.0, 2.0, 0.5]) - - def residual(theta, _, p): - return A_W @ theta - p * b_w - - def tangent(ad_solver, ad_solver_penalty=None): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver=ad_solver, - ad_solver_penalty=ad_solver_penalty, - geodesic_acceleration=False, - ) - return jax.jvp( - lambda p: solver.solve(jnp.zeros(4), p=p, max_steps=80, atol=1e-6).x, - (jnp.asarray(1.2),), - (jnp.asarray(0.5),), - )[1] - - default_tangent = tangent("svd") - assert bool(jnp.all(jnp.isfinite(default_tangent))) - # Measured 6e-7 float32 against the exact min-norm tangent. - assert jnp.allclose(default_tangent, 0.5 * min_m_norm_root(A_W, b_w), atol=5e-6) - - delta = 1e-4 - G64 = np.asarray(A_W, np.float64).T @ np.asarray(A_W, np.float64) - analytic_ridged = 0.5 * np.linalg.solve( - G64 + delta * np.trace(G64) * np.eye(4), - np.asarray(A_W, np.float64).T @ np.asarray(b_w, np.float64), - ) - ridged_tangent = tangent("augmented_qr", delta) - assert bool(jnp.all(jnp.isfinite(ridged_tangent))) - # Measured 5.7e-8 float32 against the float64 analytic ridge. - assert np.allclose( - np.asarray(ridged_tangent, np.float64), analytic_ridged, atol=1e-6 - ) - - assert bool(jnp.all(jnp.isnan(tangent("qr")))) - - -def test_svd_reverse_mode_through_opaque_inv_sqrt(): - # A metric whose inv_sqrt is forward-correct but NOT reverse-differentiable - # (a lax.while_loop) with an explicit inv_sqrt_transpose: the SVD AD - # rule's final -S step declares that transpose, so jax.grad routes reverse - # mode through inv_sqrt_transpose. A bare -inv_sqrt(...) would instead try - # to reverse-differentiate the while_loop and raise (Codex counterexample). - L = jnp.array([[2.0, 0.0], [1.0, 3.0]], dtype=jnp.float32) - - def opaque_inv_sqrt(v): - def body(carry): - i, _ = carry - return i + 1, jsp_linalg.solve_triangular(L.T, v, lower=False) - - _, out = jax.lax.while_loop(lambda c: c[0] < 1, body, (0, jnp.zeros_like(v))) - return out - - def inv_sqrt_transpose(w): - return jsp_linalg.solve_triangular(L, w, lower=True) - - opaque_metric = GramMetric( - inv_sqrt=opaque_inv_sqrt, inv_sqrt_transpose=inv_sqrt_transpose - ) - - A = jnp.array([[1.0, 0.5], [0.5, 2.0], [1.0, 1.0]], dtype=jnp.float32) - - def residual(theta, _, p): - return A @ theta - p - - def scalar_of(metric): - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver="svd", - metric=metric, - geodesic_acceleration=False, - ) - return lambda p: jnp.sum( - solver.solve(jnp.zeros(2), p=p, max_steps=60, atol=1e-6).x ** 2 - ) - - p0 = jnp.array([1.0, 2.0, 0.5], dtype=jnp.float32) - grad_opaque = jax.grad(scalar_of(opaque_metric))(p0) - assert bool(jnp.all(jnp.isfinite(grad_opaque))) - # metric_from_cholesky(L) is the differentiable-inv_sqrt twin (same S, S'). - grad_reference = jax.grad(scalar_of(metric_from_cholesky(L)))(p0) - assert jnp.allclose(grad_opaque, grad_reference, atol=1e-4) - - -def test_qr_rank_guard_catches_exact_singularity(): - # Codex counterexample: B with column 2 == -3 * column 1 is exactly rank 1, - # but unpivoted-QR |R_ii| diagonals do not flag it. The svdvals(R) guard - # must poison the 0.0 tangent to NaN, not return a finite null-space- - # inflated tangent. - A = jnp.array([[2.0, -6.0], [7.0, -21.0]], dtype=jnp.float32) - - def residual(theta, _, p): - return A @ theta - p - - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - ad_solver="qr", - geodesic_acceleration=False, - ) - p0 = A @ jnp.array([1.0, 0.0], dtype=jnp.float32) # in range(A): solve converges - tangent = jax.jvp( - lambda p: solver.solve(jnp.zeros(2), p=p, max_steps=40, atol=1e-6).x, - (p0,), - (jnp.array([1.0, 0.0], dtype=jnp.float32),), - )[1] - assert bool(jnp.all(jnp.isnan(tangent))) diff --git a/tests/test_preconditioner_factory.py b/tests/test_preconditioner_factory.py deleted file mode 100644 index 8b74427..0000000 --- a/tests/test_preconditioner_factory.py +++ /dev/null @@ -1,556 +0,0 @@ -import dataclasses -import subprocess -import sys -import textwrap - -import jax -import jax.numpy as jnp -import pytest - -from nlls_gram import ( - LevenbergMarquardt, - LMStatus, - MultiStart, - PreconditionerFactory, - RecycleConfig, - identity_preconditioner, -) - - -def residual_fn(x, args, p): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -# A residual whose Jacobian rotates with x: with orthogonal A the dual operator -# J J' = D(x)^2 is exactly diagonal (D = diag(exp(a_i . x))), so the exact-current -# diagonal is a perfect inverse while the same diagonal frozen at x0 mismatches once -# the row scales drift. The canonical setting the factory is built for. -def rotating_problem(n=12): - A, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (n, n))) - x_true = 1.2 * jax.random.normal(jax.random.key(1), (n,)) - target = jnp.exp(A @ x_true) - - def residual(x): - return jnp.exp(A @ x) - target - - def prepare(x, args, p, aux): - d = jnp.exp(A @ x) - return d * d # exact diag(J J') at the current x - - def apply(state, v, damping): - return v / (state + damping) - - return residual, jnp.zeros(n), prepare, apply - - -# --- validation -------------------------------------------------------------- - - -def test_factory_requires_cg(): - factory = PreconditionerFactory(lambda *a: jnp.zeros(()), lambda *a: a[1]) - with pytest.raises(ValueError, match="preconditioner_factory requires"): - LevenbergMarquardt( - lambda x: x, linear_solver="gram_cholesky", preconditioner_factory=factory - ) - - -def test_factory_and_dual_preconditioner_mutually_exclusive(): - factory = PreconditionerFactory(lambda *a: jnp.zeros(()), lambda *a: a[1]) - with pytest.raises(ValueError, match="exactly one"): - LevenbergMarquardt( - lambda x: x, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - preconditioner_factory=factory, - ) - - -def test_factory_satisfies_cg_and_implicit_requirements(): - # With neither dual_preconditioner nor ad_solver_preconditioner, a factory alone - # satisfies both the forward-cg and cg-implicit preconditioner requirements. - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - assert solver.preconditioner_factory is not None - - -def test_factory_hashing_shares_compilation(): - # Equal (prepare, apply) identities -> equal solver static key -> shared jit - # cache; a different apply is a different compiled program. - residual, x0, prepare, apply = rotating_problem() - other_apply = lambda state, v, damping: v / (state + damping) # noqa: E731 - common = dict(linear_solver="gram_cg", iterative_maxiter=4) - a = LevenbergMarquardt( - residual, preconditioner_factory=PreconditionerFactory(prepare, apply), **common - ) - b = LevenbergMarquardt( - residual, preconditioner_factory=PreconditionerFactory(prepare, apply), **common - ) - c = LevenbergMarquardt( - residual, - preconditioner_factory=PreconditionerFactory(prepare, other_apply), - **common, - ) - assert a == b and hash(a) == hash(b) - assert a != c - - -# --- init / state threading -------------------------------------------------- - - -def test_init_builds_precond_state(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - state = solver.init(x0) - assert state.precond is not None - assert bool(state.precond_valid) - assert jnp.array_equal(state.precond, prepare(x0, None, None, None)) - - -def test_update_without_init_state_raises(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - from nlls_gram import LMState - - with pytest.raises(ValueError, match="no preconditioner state"): - solver.update(x0, LMState(jnp.asarray(1e-3))) - - -# --- equivalence: prepare ignoring x reproduces the frozen preconditioner ---- - - -def test_factory_matches_frozen_when_theta_independent(): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - weights = 1.0 + jnp.arange(20, dtype=jnp.float32) / 10.0 - - def prepare(x, args, p, aux): - return weights # ignores x -> a constant preconditioner - - def apply(state, v, damping): - return v / (state + damping) - - def frozen(v, damping): - return v / (weights + damping) - - common = dict( - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=40, - ) - frozen_solver = LevenbergMarquardt( - residual_fn, dual_preconditioner=frozen, **common - ) - factory_solver = LevenbergMarquardt( - residual_fn, - preconditioner_factory=PreconditionerFactory(prepare, apply), - **common, - ) - - # Identical arithmetic graph -> bitwise identical step and full solve. - xf, _, info_f = frozen_solver.update(x, frozen_solver.init(x, (ts, ys)), (ts, ys)) - xa, _, info_a = factory_solver.update(x, factory_solver.init(x, (ts, ys)), (ts, ys)) - assert jnp.array_equal(xf["a"], xa["a"]) - assert jnp.array_equal(xf["b"], xa["b"]) - assert jnp.array_equal(info_f.loss, info_a.loss) - - rf = frozen_solver.solve(x, (ts, ys), max_steps=30, atol=1e-6) - ra = factory_solver.solve(x, (ts, ys), max_steps=30, atol=1e-6) - assert jnp.array_equal(rf.x["a"], ra.x["a"]) - assert jnp.array_equal(rf.x["b"], ra.x["b"]) - - -# --- the measured need: frozen stalls, factory converges --------------------- - - -def test_factory_converges_where_frozen_stalls(): - residual, x0, prepare, apply = rotating_problem() - diag0 = prepare(x0, None, None, None) - - def frozen(v, damping): - return v / (diag0 + damping) # exact diagonal, frozen at x0 - - common = dict( - init_damping=1e-3, - linear_solver="gram_cg", - geodesic_acceleration=False, - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=2, - iterative_tol=1e-12, - ) - frozen_solver = LevenbergMarquardt(residual, dual_preconditioner=frozen, **common) - factory_solver = LevenbergMarquardt( - residual, preconditioner_factory=PreconditionerFactory(prepare, apply), **common - ) - - frozen_result = frozen_solver.solve(x0, max_steps=80, atol=1e-5) - factory_result = factory_solver.solve(x0, max_steps=80, atol=1e-5) - - assert int(factory_result.status) == LMStatus.CONVERGED - assert float(factory_result.info.loss) < 1e-6 - assert int(frozen_result.status) != LMStatus.CONVERGED - assert float(frozen_result.info.loss) > 1e-4 - - -# --- rejected-step reuse vs accepted-step rebuild ---------------------------- - - -def test_rejected_step_reuses_carried_precond_state(): - # precond_valid gates reuse-vs-rebuild. Injecting a deliberately wrong (but - # SPD) carried state distinguishes the branches through the threaded-out state: - # valid=True carries the wrong state through (reuse, no rebuild), valid=False - # replaces it with the freshly built prepare(x) (rebuild). - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - state = solver.init(x0) - correct = prepare(x0, None, None, None) - wrong = correct * 1000.0 + 1.0 - - reuse_in = dataclasses.replace( - state, precond=wrong, precond_valid=jnp.asarray(True) - ) - _, reuse_out, reuse_info = solver.update(x0, reuse_in) - assert jnp.array_equal(reuse_out.precond, wrong) # reused, not rebuilt - # precond_valid tracks acceptance: True iff the step was rejected (x fixed). - assert bool(reuse_out.precond_valid) == (not bool(reuse_info.accepted)) - - rebuild_in = dataclasses.replace( - state, precond=wrong, precond_valid=jnp.asarray(False) - ) - _, rebuild_out, _ = solver.update(x0, rebuild_in) - assert jnp.array_equal(rebuild_out.precond, correct) # rebuilt at x0 - assert not jnp.array_equal(rebuild_out.precond, wrong) - - -def test_update_jits(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - - @jax.jit - def step(x, lm_state): - return solver.update(x, lm_state) - - x, lm_state, info = step(x0, solver.init(x0)) - assert jnp.isfinite(info.loss) - assert lm_state.precond.shape == (12,) - - -# --- composition with recycle ------------------------------------------------ - - -def test_factory_composes_with_recycle(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="gram_cg", - geodesic_acceleration=False, - preconditioner_factory=PreconditionerFactory(prepare, apply), - recycle=RecycleConfig(rank=3), - iterative_maxiter=4, - iterative_tol=1e-10, - ) - result = solver.solve(x0, max_steps=80, atol=1e-6) - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.loss) < 1e-6 - assert result.lm_state.precond is not None - assert result.lm_state.recycle is not None - - -# --- multi_start ------------------------------------------------------------- - - -def test_factory_multi_start_vmap(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="gram_cg", - geodesic_acceleration=False, - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - iterative_tol=1e-10, - ) - - def draw(key, x, args): - return x + 0.01 * jax.random.normal(key, x.shape), args - - for parallel in (False, True): - ms = MultiStart( - key=jax.random.key(0), num_starts=3, draw=draw, parallel=parallel - ) - result = solver.solve(x0, max_steps=80, atol=1e-6, multi_start=ms) - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.loss) < 1e-6 - - -def test_multi_start_cold_resets_precond(): - # _cold_lm_state must invalidate the carried preconditioner state so a drawn - # start rebuilds prepare() at its own x rather than reusing another x's state. - from nlls_gram import gram_lm - - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - state = solver.init(x0) - _, warmed, _ = solver.update(x0, state) - cold = gram_lm._cold_lm_state(warmed) - assert not bool(cold.precond_valid) - assert jnp.all(cold.precond == 0) - - -# --- differentiation --------------------------------------------------------- - - -def test_factory_update_reverse_ad_matches_cholesky(): - # update()'s factory path stays reverse-differentiable and matches the dense - # cholesky reference: the preconditioner state is stop_gradient'd, so only the - # (converged) step carries gradient. Differentiate w.r.t. the target data. - ts = jnp.linspace(0.0, 2.0, 20) - - def residual_data(x, args, p): - return x["a"] * jnp.exp(x["b"] * ts) - args - - def prepare(x, args, p, aux): - e = jnp.exp(x["b"] * ts) - return e**2 + (x["a"] * ts * e) ** 2 # exact diag(J J') at x - - def apply(state, v, damping): - return v / (state + damping) - - x = {"a": 1.0, "b": 0.0} - cholesky = LevenbergMarquardt(residual_data, init_damping=1e-2) - factory = LevenbergMarquardt( - residual_data, - init_damping=1e-2, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_tol=1e-9, - iterative_maxiter=60, - ) - - def loss_of(solver): - def loss(ys): - new_x, _, _ = solver.update(x, solver.init(x, ys), ys) - return jnp.sum(new_x["a"] ** 2 + new_x["b"] ** 2) - - return loss - - ys = 2.0 * jnp.exp(-1.0 * ts) - g_factory = jax.grad(loss_of(factory))(ys) - g_cholesky = jax.grad(loss_of(cholesky))(ys) - assert jnp.allclose(g_factory, g_cholesky, rtol=1e-3, atol=1e-4) - - -# A full-rank underdetermined-style dual so the implicit derivative is -# preconditioner-independent: residual exp(A x) - p with orthogonal A gives -# J J' = D(x)^2 (full rank, all positive), the regime the package targets. -def target_problem(n=12): - A, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (n, n))) - - def residual_p(x, args, p): - return jnp.exp(A @ x) - p - - def prepare(x, args, p, aux): - d = jnp.exp(A @ x) - return d * d - - def apply(state, v, damping): - return v / (state + damping) - - p = jnp.exp(0.3 * jax.random.normal(jax.random.key(2), (n,))) - return residual_p, jnp.zeros(n), prepare, apply, p - - -def test_factory_implicit_p_derivative_matches_cholesky(): - # solve()'s p-derivative comes from the implicit rule at the converged root. - # With a factory and no explicit ad_solver_preconditioner, the implicit cg rule - # seeds its preconditioner from prepare(result.x) at the solution; on a - # full-rank dual the derivative is preconditioner-independent, so it must match - # both the dense cholesky rule and an explicit identity ad_solver_preconditioner. - residual_p, x0, prepare, apply, p = target_problem() - common = dict(init_damping=1e-3, geodesic_acceleration=False) - cholesky = LevenbergMarquardt(residual_p, linear_solver="gram_cholesky", **common) - factory = LevenbergMarquardt( - residual_p, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_tol=1e-12, - iterative_maxiter=40, - **common, - ) - explicit = LevenbergMarquardt( - residual_p, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-12, - iterative_maxiter=40, - **common, - ) - - def solved(solver, q): - return solver.solve(x0, p=q, max_steps=80, atol=1e-8).x - - j_cholesky = jax.jacobian(lambda q: solved(cholesky, q))(p) - j_factory = jax.jacobian(lambda q: solved(factory, q))(p) - j_explicit = jax.jacobian(lambda q: solved(explicit, q))(p) - assert jnp.allclose(j_factory, j_cholesky, rtol=1e-3, atol=1e-4) - assert jnp.allclose(j_factory, j_explicit, rtol=1e-3, atol=1e-4) - - -def test_factory_implicit_p_derivative_no_recompile_across_p(): - # The implicit rule builds prepare(result.x) from the TRACED solution, so - # differentiating at different p values shares one compilation instead of - # baking a closure constant. Cache-size counting is fragile under full-suite - # cache pressure (global eviction), so assert the key-stability property - # directly: the traced jaxpr is identical across p values, i.e. p enters as - # an input, never as an embedded constant. - n = 8 - A, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (n, n))) - p = jnp.exp(0.3 * jax.random.normal(jax.random.key(2), (n,))) - - def residual_p(x, args, q): - return jnp.exp(A @ x) - q - - def prepare(x, args, q, aux): - d = jnp.exp(A @ x) - return d * d - - def apply(state, v, damping): - return v / (state + damping) - - solver = LevenbergMarquardt( - residual_p, - init_damping=1e-3, - geodesic_acceleration=False, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_tol=1e-12, - iterative_maxiter=30, - ) - - def jac_fn(q): - return jax.jacobian( - lambda qq: solver.solve(jnp.zeros(n), p=qq, max_steps=60, atol=1e-8).x - )(q) - - jac = jax.jit(jac_fn) - j1 = jac(p) - j1.block_until_ready() - j2 = jac(p * 1.3) - j2.block_until_ready() - assert bool(jnp.all(jnp.isfinite(j1))) and bool(jnp.all(jnp.isfinite(j2))) - jaxpr_a = str(jax.make_jaxpr(jac_fn)(p)) - jaxpr_b = str(jax.make_jaxpr(jac_fn)(p * 1.3)) - assert jaxpr_a == jaxpr_b # p is a traced input, not a baked constant - - -# --- callback action must preserve the precond fields ------------------------ - - -def test_callback_dropping_precond_raises(): - residual, x0, prepare, apply = rotating_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=4, - ) - from nlls_gram import LMSolveAction, LMState - - def callback(ctx): - # A bare LMState lacks the precond fields -> loud failure. - return LMSolveAction(lm_state=LMState(ctx.lm_state.damping)) - - with pytest.raises(ValueError, match="without the preconditioner state"): - solver.solve(x0, max_steps=3, callback=callback, jit=False) - - -# --- x64 in a clean subprocess ----------------------------------------------- - - -def test_factory_float64_subprocess(): - script = textwrap.dedent( - """ - import jax - jax.config.update("jax_enable_x64", True) - import jax.numpy as jnp - from nlls_gram import LevenbergMarquardt, PreconditionerFactory, LMStatus - - n = 10 - A, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(0), (n, n))) - x_true = 1.2 * jax.random.normal(jax.random.key(1), (n,)) - target = jnp.exp(A @ x_true) - - def residual(x): - return jnp.exp(A @ x) - target - - def prepare(x, args, p, aux): - d = jnp.exp(A @ x) - return d * d - - def apply(state, v, damping): - return v / (state + damping) - - x0 = jnp.zeros(n, dtype=jnp.float64) - solver = LevenbergMarquardt( - residual, - init_damping=1e-3, - linear_solver="gram_cg", - geodesic_acceleration=False, - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=2, - iterative_tol=1e-14, - ) - state = solver.init(x0) - assert state.precond.dtype == jnp.float64 - result = solver.solve(x0, max_steps=80, atol=1e-10) - assert int(result.status) == LMStatus.CONVERGED - assert result.x.dtype == jnp.float64 - assert float(result.info.loss) < 1e-12 - jaxpr = str(jax.make_jaxpr(lambda x, s: solver.update(x, s))(x0, state)) - assert "f32" not in jaxpr, jaxpr - print("OK") - """ - ) - completed = subprocess.run( - [sys.executable, "-c", script], capture_output=True, text=True - ) - assert completed.returncode == 0, completed.stderr - assert "OK" in completed.stdout diff --git a/tests/test_recycled_cg.py b/tests/test_recycled_cg.py deleted file mode 100644 index d994b35..0000000 --- a/tests/test_recycled_cg.py +++ /dev/null @@ -1,1194 +0,0 @@ -import dataclasses -import types - -import jax -import jax.numpy as jnp -import jax.scipy.linalg as jsp_linalg -import jax.scipy.sparse.linalg as jsp_sparse_linalg -import pytest - -from nlls_gram import ( - LevenbergMarquardt, - LMSolveAction, - LMStatus, - MultiStart, - RecycleConfig, - RecycleState, - gram_lm, - identity_preconditioner, - metric_from_cholesky, - recycled_cg, -) -from nlls_gram.recycled_cg import ( - HarvestState, - build_coarse_operator, - deflated_pcg, -) - - -def residual_fn(x, args, p): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -REGRESSION_ATOL = 5e-5 -REGRESSION_RTOL = 1e-5 - - -@pytest.fixture -def use_recycled_cg(monkeypatch): - # Swap the fork in for jax's cg at both gram_lm call sites (forward dual - # solve and implicit tangent solve) without touching jax's own module. - monkeypatch.setattr( - gram_lm, "jsp_sparse_linalg", types.SimpleNamespace(cg=recycled_cg) - ) - - -def spd_test_system(n=30): - W = jax.random.normal(jax.random.key(0), (n, n)) - A = W @ W.T + n * jnp.eye(n) - b = jax.random.normal(jax.random.key(1), (n,)) - return A, b - - -# --- direct parity with jax.scipy.sparse.linalg.cg (identical graphs, so the -# --- results must match bitwise, not just to tolerance) - - -def test_recycled_cg_matches_jax_cg_bitwise(): - A, b = spd_test_system() - - def matvec(v): - return A @ v - - expected, expected_info = jsp_sparse_linalg.cg(matvec, b, tol=1e-5, maxiter=100) - got, info = recycled_cg(matvec, b, tol=1e-5, maxiter=100) - - assert info is expected_info is None - assert jnp.array_equal(got, expected) - - -def test_recycled_cg_preconditioned_warm_start_matches_jax_cg(): - A, b = spd_test_system() - weights = jnp.diag(A) - x0 = 0.1 * jnp.ones_like(b) - - def matvec(v): - return A @ v - - def preconditioner(v): - return v / weights - - expected, _ = jsp_sparse_linalg.cg( - matvec, b, x0=x0, tol=1e-5, atol=1e-8, maxiter=50, M=preconditioner - ) - got, _ = recycled_cg( - matvec, b, x0=x0, tol=1e-5, atol=1e-8, maxiter=50, M=preconditioner - ) - - assert jnp.array_equal(got, expected) - - -def test_recycled_cg_gradient_matches_jax_cg(): - # Exercises the imported _isolve/custom_linear_solve wrapper: derivatives - # come from an implicit transpose solve, not from unrolling the loop. - A, b = spd_test_system() - - def matvec(v): - return A @ v - - def loss_fork(b): - x, _ = recycled_cg(matvec, b, tol=1e-6, maxiter=200) - return jnp.sum(x**2) - - def loss_jax(b): - x, _ = jsp_sparse_linalg.cg(matvec, b, tol=1e-6, maxiter=200) - return jnp.sum(x**2) - - assert jnp.array_equal(jax.grad(loss_fork)(b), jax.grad(loss_jax)(b)) - - -def test_recycled_cg_jits(): - A, b = spd_test_system() - - @jax.jit - def solve(b): - return recycled_cg(lambda v: A @ v, b, tol=1e-5, maxiter=100)[0] - - eager, _ = recycled_cg(lambda v: A @ v, b, tol=1e-5, maxiter=100) - - assert jnp.allclose(solve(b), eager, rtol=1e-6, atol=1e-6) - - -def test_swap_fixture_reaches_forked_cg(monkeypatch): - # Guard that the SimpleNamespace swap is not a silent no-op: count trace- - # time calls through the patched attribute during a cg update. - calls = [] - - def counting_cg(*args, **kwargs): - calls.append(1) - return recycled_cg(*args, **kwargs) - - monkeypatch.setattr( - gram_lm, "jsp_sparse_linalg", types.SimpleNamespace(cg=counting_cg) - ) - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ) - - solver.update(x, solver.init(x, (ts, ys)), (ts, ys)) - - assert calls - - -# --- copies of the basic CG tests from test_gram_lm.py, run with the fork -# --- swapped in for jax's cg - - -def test_cg_step_matches_cholesky_identity_step(use_recycled_cg): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - - cholesky_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - cg_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ) - - cholesky_x, cholesky_state, cholesky_info = cholesky_solver.update( - x, cholesky_solver.init(x, (ts, ys)), (ts, ys) - ) - cg_x, cg_state, cg_info = cg_solver.update(x, cg_solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(cg_info.accepted) == bool(cholesky_info.accepted) - assert not bool(cg_info.used_geodesic) - assert jnp.allclose(cg_x["a"], cholesky_x["a"], rtol=1e-5, atol=1e-5) - assert jnp.allclose(cg_x["b"], cholesky_x["b"], rtol=1e-5, atol=1e-5) - assert jnp.allclose(cg_state.damping, cholesky_state.damping) - assert jnp.allclose( - cg_info.loss, - cholesky_info.loss, - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - assert cg_x["a"].dtype == jnp.float32 - assert cg_info.loss.dtype == jnp.float32 - - -def test_cg_update_jits(use_recycled_cg): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=20, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(lm_state.damping) - assert x["a"].dtype == jnp.float32 - - -def test_cg_geodesic_acceleration_matches_cholesky(use_recycled_cg): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - cg_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=10, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, target), target - ) - cg_theta, _, cg_info = cg_solver.update( - theta0, cg_solver.init(theta0, target), target - ) - - assert bool(cg_info.accepted) - assert bool(cg_info.used_geodesic) - assert jnp.allclose(cg_theta, cholesky_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose( - cg_info.acceleration_ratio, - cholesky_info.acceleration_ratio, - rtol=1e-6, - atol=1e-6, - ) - - -def test_cg_preconditioned_step_matches_cholesky_identity_step(use_recycled_cg): - # A valid SPD preconditioner changes only the inner Krylov iteration, not - # the step the inner solve converges to. - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": 1.0, "b": 0.0} - weights = 1.0 + jnp.arange(20, dtype=jnp.float32) / 10.0 - - cholesky_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) - cg_solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=40, - dual_preconditioner=lambda v, damping: v / weights, - ) - - cholesky_x, cholesky_state, cholesky_info = cholesky_solver.update( - x, cholesky_solver.init(x, (ts, ys)), (ts, ys) - ) - cg_x, cg_state, cg_info = cg_solver.update(x, cg_solver.init(x, (ts, ys)), (ts, ys)) - - assert bool(cg_info.accepted) == bool(cholesky_info.accepted) - # float32 across BLAS/SIMD variants: CI runners land ~2e-5 off macOS. - assert jnp.allclose(cg_x["a"], cholesky_x["a"], rtol=1e-4, atol=1e-4) - assert jnp.allclose(cg_x["b"], cholesky_x["b"], rtol=1e-4, atol=1e-4) - assert jnp.allclose(cg_state.damping, cholesky_state.damping) - assert jnp.allclose( - cg_info.loss, - cholesky_info.loss, - rtol=REGRESSION_RTOL, - atol=REGRESSION_ATOL, - ) - - -def test_cg_preconditioned_update_jits(use_recycled_cg): - ts = jnp.linspace(0.0, 2.0, 20) - ys = 2.0 * jnp.exp(-1.0 * ts) - x = {"a": jnp.asarray(1.0), "b": jnp.asarray(0.0)} - weights = 1.0 + jnp.arange(20, dtype=jnp.float32) / 10.0 - solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=40, - dual_preconditioner=lambda v, damping: v / weights, - ) - - @jax.jit - def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - x, lm_state, info = train_step(x, solver.init(x, (ts, ys))) - - assert bool(info.accepted) - assert jnp.isfinite(info.loss) - assert jnp.isfinite(lm_state.damping) - - -def test_cg_preconditioned_geodesic_matches_cholesky(use_recycled_cg): - def residual(theta, target, p): - return jnp.array([theta[0] ** 2 - target]) - - theta0 = jnp.array([1.9]) - target = 4.0 - - cholesky_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - ) - cg_solver = LevenbergMarquardt( - residual, - init_damping=1e-6, - linear_solver="gram_cg", - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-7, - iterative_maxiter=10, - geodesic_acceleration=True, - geodesic_acceptance_ratio=1.0, - dual_preconditioner=lambda v, damping: v / (1.0 + damping), - ) - - cholesky_theta, _, cholesky_info = cholesky_solver.update( - theta0, cholesky_solver.init(theta0, target), target - ) - cg_theta, _, cg_info = cg_solver.update( - theta0, cg_solver.init(theta0, target), target - ) - - assert bool(cg_info.accepted) - assert bool(cg_info.used_geodesic) - assert jnp.allclose(cg_theta, cholesky_theta, rtol=1e-6, atol=1e-6) - assert jnp.allclose( - cg_info.acceleration_ratio, - cholesky_info.acceleration_ratio, - rtol=1e-6, - atol=1e-6, - ) - - -def test_cg_dual_preconditioner_enables_ill_conditioned_convergence(use_recycled_cg): - # Kernel-collocation miniature: affine residual K x - b with metric M = K, - # so the dual operator is K K^{-1} K = K itself -- as ill-conditioned as - # the kernel (cond ~ 1e4 here). At a tight inner-iteration budget plain CG - # stalls, while the exact preconditioner (a K-solve) recovers - # Gauss-Newton-quality steps and converges immediately. - n = 40 - rho = 0.98 - idx = jnp.arange(n) - K = rho ** jnp.abs(idx[:, None] - idx[None, :]) - L = jnp.linalg.cholesky(K) - x_true = jnp.sin(idx / 3.0) - b = K @ x_true - - def residual(x): - return K @ x - b - - def preconditioner(v, damping): - y = jsp_linalg.solve_triangular(L, v, lower=True) - return jsp_linalg.solve_triangular(L.T, y, lower=False) - - common = dict( - init_damping=1e-6, - linear_solver="gram_cg", - iterative_maxiter=3, - ad_solver_preconditioner=identity_preconditioner(), - metric=metric_from_cholesky(L), - ) - plain = LevenbergMarquardt( - residual, dual_preconditioner=identity_preconditioner(), **common - ) - preconditioned = LevenbergMarquardt( - residual, dual_preconditioner=preconditioner, **common - ) - x0 = jnp.zeros(n) - - plain_result = plain.solve(x0, max_steps=20, atol=1e-3) - preconditioned_result = preconditioned.solve(x0, max_steps=20, atol=1e-3) - - assert int(preconditioned_result.status) == LMStatus.CONVERGED - assert int(plain_result.status) != LMStatus.CONVERGED - - -# --- deflated / recycled PCG ------------------------------------------------ -# -# The additive two-level preconditioner M_defl = P + U E^-1 U' shifts each -# deflated eigenvalue lambda -> lambda + P|_u, so it CLUSTERS (and speeds CG) -# when the deflated modes are small outliers near 0 and the first-level P -# normalizes the bulk near 1. The fixtures below use that regime: a few tiny -# isolated eigenvalues plus a tight bulk near 1. - - -def clustered_spd(n, small_eigs, bulk=1.0, bulk_spread=1e-4, seed=0): - key = jax.random.key(seed) - Q, _ = jnp.linalg.qr(jax.random.normal(key, (n, n))) - k = small_eigs.shape[0] - bulk_eigs = bulk + bulk_spread * jax.random.uniform( - jax.random.key(seed + 1), (n - k,) - ) - eigs = jnp.concatenate([small_eigs, bulk_eigs]) - A = (Q * eigs) @ Q.T - A = 0.5 * (A + A.T) - return A, Q, eigs - - -def max_subspace_angle_deg(U, V): - # Largest principal angle between range(U) and range(V) (both orthonormal). - cos_angles = jnp.linalg.svd(U.T @ V, compute_uv=False) - return float(jnp.degrees(jnp.arccos(jnp.clip(jnp.min(cos_angles), 0.0, 1.0)))) - - -def test_deflated_pcg_cold_matches_recycled_cg_bitwise(): - # U=0 with a non-identity first-level P: the coarse correction and deflated - # init vanish exactly (ridge floor keeps E finite while U'r=0), and the two - # cond-functions both read ||r||^2, so the iterates are bitwise identical. - n, k = 40, 4 - A, _, _ = clustered_spd(n, jnp.array([0.01, 0.02, 0.04, 0.08])) - b = jax.random.normal(jax.random.key(1), (n,)) - weights = jnp.diag(A) - - def matvec(v): - return A @ v - - def P(v): - return v / weights - - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(matvec, U0) - got, harvest = deflated_pcg( - matvec, - b, - U=U0, - E_factor=E_factor, - M=P, - tol=1e-5, - atol=0.0, - maxiter=300, - window=3 * k, - rank=k, - ) - expected, _ = recycled_cg(matvec, b, tol=1e-5, atol=0.0, maxiter=300, M=P) - - assert isinstance(harvest, HarvestState) - assert jnp.array_equal(got, expected) - - -def test_deflated_pcg_solves_spd_system(): - A, b = spd_test_system() - n, k = b.shape[0], 3 - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - got, _ = deflated_pcg( - lambda v: A @ v, - b, - U=U0, - E_factor=E_factor, - tol=1e-7, - atol=0.0, - maxiter=200, - window=2 * k, - rank=k, - ) - assert jnp.allclose(got, jnp.linalg.solve(A, b), rtol=1e-4, atol=1e-4) - - -def test_exact_basis_reduces_iterations(): - # A supplied basis spanning the k smallest eigenvectors clusters those modes - # and cuts the iteration count to a fixed tolerance well below undeflated CG. - n, k = 50, 4 - small = jnp.array([0.01, 0.02, 0.04, 0.08]) - A, Q, eigs = clustered_spd(n, small) - b = jax.random.normal(jax.random.key(1), (n,)) - order = jnp.argsort(eigs) - U_exact = Q[:, order[:k]] - - def matvec(v): - return A @ v - - common = dict(tol=1e-6, atol=0.0, maxiter=300, window=3 * k, rank=k) - _, cold = deflated_pcg( - matvec, - b, - U=jnp.zeros((n, k)), - E_factor=build_coarse_operator(matvec, jnp.zeros((n, k)))[1], - **common, - ) - _, defl = deflated_pcg( - matvec, - b, - U=U_exact, - E_factor=build_coarse_operator(matvec, U_exact)[1], - **common, - ) - assert int(defl.iterations) <= int(cold.iterations) // 2 - assert int(defl.iterations) <= 3 - - -def test_harvest_approximates_smallest_eigenvectors(): - # One solve harvests a basis that approximates the true smallest eigenvectors - # of the operator (subspace angle vs dense eigh) and is orthonormal. - n, k = 50, 4 - small = jnp.array([0.01, 0.02, 0.04, 0.08]) - A, _, _ = clustered_spd(n, small) - b = jax.random.normal(jax.random.key(1), (n,)) - _, evecs = jnp.linalg.eigh(A) - true_small = evecs[:, :k] - - _, harvest = deflated_pcg( - lambda v: A @ v, - b, - U=jnp.zeros((n, k)), - E_factor=build_coarse_operator(lambda v: A @ v, jnp.zeros((n, k)))[1], - tol=1e-6, - atol=0.0, - maxiter=n, - window=3 * k, - rank=k, - ) - U = harvest.basis - assert float(jnp.max(jnp.abs(U.T @ U - jnp.eye(k)))) < 1e-4 - assert max_subspace_angle_deg(U, true_small) < 5.0 - - -def test_recycling_reduces_total_iterations(): - # A slowly drifting sequence A_j = A + t_j Delta: carrying the harvested basis - # across solves drops the total iteration count well below the no-recycle run. - n, k = 60, 4 - small = jnp.array([1e-3, 5e-3, 2e-2, 8e-2]) - A, _, _ = clustered_spd(n, small) - D = jax.random.normal(jax.random.key(7), (n, n)) - Delta = (D @ D.T) / n - b0 = jax.random.normal(jax.random.key(3), (n,)) - w = 2 * k - - def total_iterations(recycle): - total = 0 - U = jnp.zeros((n, k)) - for j in range(8): - Aj = A + (0.005 * j) * Delta - Aj = 0.5 * (Aj + Aj.T) - - def matvec(v, Aj=Aj): - return Aj @ v - - U_in = U if recycle else jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(matvec, U_in) - _, harvest = deflated_pcg( - matvec, - b0 + 0.02 * j, - U=U_in, - E_factor=E_factor, - tol=1e-6, - atol=0.0, - maxiter=500, - window=w, - rank=k, - ) - total += int(harvest.iterations) - U = harvest.basis - return total - - cold_total = total_iterations(recycle=False) - recycled_total = total_iterations(recycle=True) - assert recycled_total < 0.7 * cold_total - - -def test_deflated_pcg_gradient_matches_dense_solve(): - # Derivatives are implicit through the custom_linear_solve wrapper; the - # deflation and harvest are stop_gradient'd, so the gradient matches the dense - # linear solve regardless of the (populated) deflation basis. - n, k = 30, 3 - A, _, _ = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - b = jax.random.normal(jax.random.key(1), (n,)) - A_inv = jnp.linalg.inv(A) - w = 3 * k - - _, harvest = deflated_pcg( - lambda v: A @ v, - b, - U=jnp.zeros((n, k)), - E_factor=build_coarse_operator(lambda v: A @ v, jnp.zeros((n, k)))[1], - tol=1e-7, - atol=0.0, - maxiter=200, - window=w, - rank=k, - ) - U = harvest.basis - - def loss(rhs): - _, E_factor = build_coarse_operator(lambda v: A @ v, U) - x, _ = deflated_pcg( - lambda v: A @ v, - rhs, - U=U, - E_factor=E_factor, - tol=1e-7, - atol=0.0, - maxiter=300, - window=w, - rank=k, - ) - return jnp.sum(x**2) - - def loss_dense(rhs): - return jnp.sum((A_inv @ rhs) ** 2) - - got = jax.grad(loss)(b) - expected = jax.grad(loss_dense)(b) - assert jnp.allclose(got, expected, rtol=1e-3, atol=1e-3) - - -def test_deflated_pcg_jits(): - n, k = 30, 3 - A, _, _ = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - b = jax.random.normal(jax.random.key(1), (n,)) - w = 3 * k - - @jax.jit - def solve(rhs): - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - x, harvest = deflated_pcg( - lambda v: A @ v, - rhs, - U=U0, - E_factor=E_factor, - tol=1e-5, - atol=0.0, - maxiter=200, - window=w, - rank=k, - ) - return x, harvest.iterations - - x, iters = solve(b) - assert jnp.allclose(x, jnp.linalg.solve(A, b), rtol=1e-3, atol=1e-3) - assert int(iters) >= 1 - - -def test_reorthogonalize_false_also_solves(): - # The cheap coefficient-tridiagonal harvest still yields the correct solution - # (the harvest quality only affects the NEXT solve, never correctness). - n, k = 40, 4 - A, _, _ = clustered_spd(n, jnp.array([0.01, 0.02, 0.04, 0.08])) - b = jax.random.normal(jax.random.key(1), (n,)) - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - got, harvest = deflated_pcg( - lambda v: A @ v, - b, - U=U0, - E_factor=E_factor, - tol=1e-6, - atol=0.0, - maxiter=200, - window=2 * k, - rank=k, - reorthogonalize=False, - ) - assert jnp.allclose(got, jnp.linalg.solve(A, b), rtol=1e-3, atol=1e-3) - assert bool(jnp.all(jnp.isfinite(harvest.basis))) - - -def test_harvest_ring_wrap_indexing(): - # Force CG past the window so the ring buffer wraps (start = count - w > 0), - # exercising the perm / off-boundary indexing. The robust reorthogonalize=True - # harvest still resolves the smallest eigenvectors from the correct windowed - # sub-block (a buggy perm would send the subspace angle to ~90 deg); the cheap - # reorthogonalize=False route is polluted under wrap but must stay finite and - # orthonormal with Rayleigh quotients inside the spectrum. - n, k = 90, 3 - A, _, eigs = clustered_spd(n, jnp.array([1e-3, 1e-2, 1e-1]), seed=4) - b = jax.random.normal(jax.random.key(1), (n,)) - _, evecs = jnp.linalg.eigh(A) - true_small = evecs[:, :k] - lo, hi = float(jnp.min(eigs)), float(jnp.max(eigs)) - w = 6 - - _, robust = deflated_pcg( - lambda v: A @ v, - b, - U=jnp.zeros((n, k)), - E_factor=build_coarse_operator(lambda v: A @ v, jnp.zeros((n, k)))[1], - tol=1e-8, - atol=0.0, - maxiter=n, - window=w, - rank=k, - reorthogonalize=True, - ) - assert int(robust.iterations) > w # ring wrapped - assert float(jnp.max(jnp.abs(robust.basis.T @ robust.basis - jnp.eye(k)))) < 1e-5 - assert max_subspace_angle_deg(robust.basis, true_small) < 30.0 - - _, cheap = deflated_pcg( - lambda v: A @ v, - b, - U=jnp.zeros((n, k)), - E_factor=build_coarse_operator(lambda v: A @ v, jnp.zeros((n, k)))[1], - tol=1e-8, - atol=0.0, - maxiter=n, - window=w, - rank=k, - reorthogonalize=False, - ) - assert bool(jnp.all(jnp.isfinite(cheap.basis))) - assert float(jnp.max(jnp.abs(cheap.basis.T @ cheap.basis - jnp.eye(k)))) < 1e-5 - ritz = jnp.diag(cheap.basis.T @ (A @ cheap.basis)) - assert bool(jnp.all((ritz >= lo - 1e-6) & (ritz <= hi + 1e-6))) - - -def test_deflated_pcg_count_zero_warm_started(): - # Warm-starting at the exact solution with a cold U drives count == 0 (the - # loop never runs). The all-invalid harvest must return a finite orthonormal - # basis (via the sentinel finite fallback), and it must not poison the next - # build_coarse_operator. - n, k = 40, 4 - A, _, _ = clustered_spd(n, jnp.array([0.01, 0.02, 0.04, 0.08])) - b = jax.random.normal(jax.random.key(1), (n,)) - x_star = jnp.linalg.solve(A, b) - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - # tol loose enough that the (float32) warm start is already converged, so the - # loop never runs. - y, harvest = deflated_pcg( - lambda v: A @ v, - b, - U=U0, - E_factor=E_factor, - x0=x_star, - tol=1e-3, - atol=0.0, - maxiter=200, - window=3 * k, - rank=k, - ) - assert int(harvest.iterations) == 0 - assert bool(jnp.all(jnp.isfinite(harvest.basis))) - # the returned solution is converged to tol (the differentiable pass solves - # from zeros, independently of the warm-started harvest pass). - assert float(jnp.linalg.norm(A @ y - b)) <= 1e-3 * float(jnp.linalg.norm(b)) - _, next_factor = build_coarse_operator(lambda v: A @ v, harvest.basis) - assert bool(jnp.all(jnp.isfinite(next_factor[0]))) - - -def test_harvest_false_returns_carried_basis(): - # harvest=False skips the Rayleigh-Ritz and returns the carried U verbatim; the - # solution is unchanged from harvest=True (only the emitted basis differs). - n, k = 40, 4 - A, Q, eigs = clustered_spd(n, jnp.array([0.01, 0.02, 0.04, 0.08])) - b = jax.random.normal(jax.random.key(1), (n,)) - order = jnp.argsort(eigs) - U = Q[:, order[:k]] - _, E_factor = build_coarse_operator(lambda v: A @ v, U) - common = dict( - U=U, - E_factor=E_factor, - tol=1e-7, - atol=0.0, - maxiter=200, - window=3 * k, - rank=k, - ) - y_off, off = deflated_pcg(lambda v: A @ v, b, harvest=False, **common) - y_on, on = deflated_pcg(lambda v: A @ v, b, harvest=True, **common) - # harvest=False returns the carried basis and skips the harvest pass (0 - # reported iterations), but solves the same system. - assert jnp.array_equal(off.basis, U) - assert int(off.iterations) == 0 - assert int(on.iterations) > 0 - assert jnp.allclose(y_off, y_on, rtol=1e-5, atol=1e-5) - - -def test_build_coarse_operator_cold_is_finite(): - # Zero U -> E = 0; the trace-scaled ridge's absolute floor keeps the Cholesky - # factor finite and M_defl == P (since U'r = 0), so cold start is a no-op. - n, k = 20, 3 - A, _, _ = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - U0 = jnp.zeros((n, k)) - W, E_factor = build_coarse_operator(lambda v: A @ v, U0) - assert bool(jnp.all(jnp.isfinite(W))) - assert bool(jnp.all(jnp.isfinite(E_factor[0]))) - r = jax.random.normal(jax.random.key(2), (n,)) - coarse = U0 @ jsp_linalg.cho_solve(E_factor, U0.T @ r) - assert jnp.allclose(coarse, jnp.zeros(n)) - - -def test_degenerate_basis_stays_finite(): - # A rank-deficient U (duplicate columns) must not produce NaN: the ridge keeps - # E factorable and the solve still converges to the correct solution. - n, k = 30, 3 - A, Q, eigs = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - b = jax.random.normal(jax.random.key(1), (n,)) - order = jnp.argsort(eigs) - u = Q[:, order[0]] - U_dup = jnp.stack([u, u, Q[:, order[1]]], axis=1) # duplicate column - _, E_factor = build_coarse_operator(lambda v: A @ v, U_dup) - got, harvest = deflated_pcg( - lambda v: A @ v, - b, - U=U_dup, - E_factor=E_factor, - tol=1e-6, - atol=0.0, - maxiter=200, - window=2 * k, - rank=k, - ) - assert bool(jnp.all(jnp.isfinite(got))) - assert bool(jnp.all(jnp.isfinite(harvest.basis))) - assert jnp.allclose(got, jnp.linalg.solve(A, b), rtol=1e-3, atol=1e-3) - - -def test_deflated_pcg_nan_operator_propagates(): - # A NaN entering through the ITERATION path (not build_coarse_operator or the - # init) propagates to non-finite output; it is never clamped to a quiet - # pseudo-solution. E_factor is built from the FINITE operator; the matvec goes - # NaN only on nonzero inputs, so the init matvec on zeros stays finite and the - # NaN first appears at the first A(p) inside the loop. - n, k = 20, 3 - A, _, _ = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - b = jax.random.normal(jax.random.key(1), (n,)) - U0 = jnp.zeros((n, k)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - - def nan_matvec(v): - return jnp.where(jnp.any(v != 0), (A @ v) * jnp.nan, A @ v) - - got, _ = deflated_pcg( - nan_matvec, - b, - U=U0, - E_factor=E_factor, - tol=1e-5, - atol=0.0, - maxiter=20, - window=2 * k, - rank=k, - ) - assert bool(jnp.any(~jnp.isfinite(got))) - - -@pytest.mark.parametrize( - "kwargs", - [ - dict(rank=0), - dict(window=2, rank=5), - dict(window=100, rank=3), - ], -) -def test_deflated_pcg_rejects_bad_rank_window(kwargs): - n = 20 - A, _, _ = clustered_spd(n, jnp.array([0.02, 0.05, 0.1])) - b = jax.random.normal(jax.random.key(1), (n,)) - U0 = jnp.zeros((n, 3)) - _, E_factor = build_coarse_operator(lambda v: A @ v, U0) - with pytest.raises(ValueError): - deflated_pcg( - lambda v: A @ v, - b, - U=U0, - E_factor=E_factor, - tol=1e-5, - atol=0.0, - maxiter=10, - **kwargs, - ) - - -# --- LM-level recycling integration ----------------------------------------- - - -def isolated_mode_problem(m=24, n=30, num_small=3): - # A mildly nonlinear underdetermined least squares whose Gauss-Newton dual - # operator J J' has `num_small` isolated small eigenvalues plus a bulk near 1 - # -- the regime where the additive deflation clusters the spectrum. The - # nonlinearity forces several LM steps so a carried basis can pay off. - Um, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(1), (m, m))) - Vn, _ = jnp.linalg.qr(jax.random.normal(jax.random.key(2), (n, n))) - small = jnp.array([0.02, 0.05, 0.12])[:num_small] - sv = jnp.concatenate([small, jnp.ones(m - num_small)]) - G = Um @ (sv[:, None] * Vn[:m, :]) - b = jax.random.normal(jax.random.key(3), (m,)) - - def residual(x): - linear = G @ x - b - return linear + 0.03 * linear**2 - - return residual, jnp.zeros(n) - - -def _reset_recycle(lm_state): - recycle = lm_state.recycle - return dataclasses.replace( - lm_state, - recycle=RecycleState( - jnp.zeros_like(recycle.U), - jnp.zeros_like(recycle.dual_velocity), - jnp.zeros_like(recycle.dual_accel), - jnp.zeros_like(recycle.valid), - jnp.zeros_like(recycle.iterations), - jnp.zeros_like(recycle.residual_norm), - ), - ) - - -def test_recycle_requires_cg(): - with pytest.raises(ValueError, match="recycle requires"): - LevenbergMarquardt( - lambda x: x, linear_solver="gram_cholesky", recycle=RecycleConfig(rank=2) - ) - - -def test_recycle_config_hashing_shares_compilation(): - # Equal RecycleConfig -> equal solver static key -> shared jit cache; a - # different rank is a different compiled program. - residual, _ = isolated_mode_problem() - common = dict( - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - ) - a = LevenbergMarquardt(residual, recycle=RecycleConfig(rank=4), **common) - b = LevenbergMarquardt(residual, recycle=RecycleConfig(rank=4), **common) - c = LevenbergMarquardt(residual, recycle=RecycleConfig(rank=5), **common) - assert a == b and hash(a) == hash(b) - assert a != c - - -def test_init_allocates_cold_recycle_state(): - residual, x0 = isolated_mode_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - recycle=RecycleConfig(rank=4), - ) - state = solver.init(x0) - assert state.recycle is not None - assert not bool(state.recycle.valid) - assert state.recycle.U.shape == (24, 4) - assert jnp.all(state.recycle.U == 0) - assert int(state.recycle.iterations) == 0 - - -def test_recycling_reduces_total_inner_iterations(): - # A manual update() sequence: carrying the harvested basis across steps cuts - # the total inner (velocity) CG iterations vs the identical solver with the - # basis cold-reset each step (the controlled no-recycle baseline). - residual, x0 = isolated_mode_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-4, - linear_solver="gram_cg", - geodesic_acceleration=False, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=40, - iterative_tol=1e-8, - recycle=RecycleConfig(rank=3), - ) - - def total_inner(reset): - x, state = x0, solver.init(x0) - total = 0 - for _ in range(8): - x, state, info = solver.update(x, state) - total += int(state.recycle.iterations) - if reset: - state = _reset_recycle(state) - return total, float(info.loss) - - recycled_total, recycled_loss = total_inner(reset=False) - baseline_total, baseline_loss = total_inner(reset=True) - assert recycled_loss < 1e-8 and baseline_loss < 1e-8 - assert recycled_total < 0.75 * baseline_total - - -def test_recycled_solve_converges_ill_conditioned(): - residual, x0 = isolated_mode_problem() - common = dict( - init_damping=1e-4, - linear_solver="gram_cg", - geodesic_acceleration=False, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=6, - iterative_tol=1e-8, - ) - recycled = LevenbergMarquardt(residual, recycle=RecycleConfig(rank=3), **common) - result = recycled.solve(x0, max_steps=60, atol=1e-6) - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.loss) < 1e-6 - - -def test_recycled_update_reverse_ad_matches_cholesky(): - # update()'s recycled path stays reverse-differentiable and matches the dense - # cholesky reference: the deflation/harvest are stop_gradient'd, so only the - # (converged) step carries gradient. Differentiate w.r.t. the target data. - ts = jnp.linspace(0.0, 2.0, 20) - - def residual_data(x, args, p): - return x["a"] * jnp.exp(x["b"] * ts) - args - - x = {"a": 1.0, "b": 0.0} - cholesky = LevenbergMarquardt(residual_data, init_damping=1e-2) - recycled = LevenbergMarquardt( - residual_data, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-9, - iterative_maxiter=60, - recycle=RecycleConfig(rank=4), - ) - - def loss_of(solver): - def loss(ys): - new_x, _, _ = solver.update(x, solver.init(x, ys), ys) - return jnp.sum(new_x["a"] ** 2 + new_x["b"] ** 2) - - return loss - - ys = 2.0 * jnp.exp(-1.0 * ts) - g_recycled = jax.grad(loss_of(recycled))(ys) - g_cholesky = jax.grad(loss_of(cholesky))(ys) - assert jnp.allclose(g_recycled, g_cholesky, rtol=1e-3, atol=1e-4) - - -def test_recycled_solve_implicit_p_derivative_matches_plain(): - # solve()'s p-derivative comes from the implicit rule at the converged root; - # recycling only changes the forward path, so the jacobian matches plain cg. - ts = jnp.linspace(0.0, 2.0, 12) - - def residual_p(x, args, p): - return x * ts - p - - common = dict( - init_damping=1e-3, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_tol=1e-10, - iterative_maxiter=40, - ) - plain = LevenbergMarquardt(residual_p, **common) - recycled = LevenbergMarquardt(residual_p, recycle=RecycleConfig(rank=3), **common) - x0 = jnp.zeros(()) - - def solved(solver, p): - return solver.solve(x0, p=p, max_steps=40, atol=1e-9).x - - p = jnp.asarray(1.7) - j_plain = jax.jacobian(lambda q: solved(plain, q))(p) - j_recycled = jax.jacobian(lambda q: solved(recycled, q))(p) - assert jnp.allclose(j_recycled, j_plain, rtol=1e-4, atol=1e-5) - - -def test_recycled_multi_start_vmap(): - residual, x0 = isolated_mode_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-4, - linear_solver="gram_cg", - geodesic_acceleration=False, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=8, - iterative_tol=1e-8, - recycle=RecycleConfig(rank=3), - ) - - def draw(key, x, args): - return x + 0.01 * jax.random.normal(key, x.shape), args - - for parallel in (False, True): - ms = MultiStart( - key=jax.random.key(0), num_starts=3, draw=draw, parallel=parallel - ) - result = solver.solve(x0, max_steps=60, atol=1e-6, multi_start=ms) - assert int(result.status) == LMStatus.CONVERGED - assert float(result.info.loss) < 1e-6 - - -def test_recycled_callback_maxiter_schedule_composes(): - # A callback that grows iterative_maxiter mid-solve composes with recycling: - # rank/window are static (untouched), the traced maxiter rides hyper. - residual, x0 = isolated_mode_problem() - solver = LevenbergMarquardt( - residual, - init_damping=1e-4, - linear_solver="gram_cg", - geodesic_acceleration=False, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=2, - iterative_tol=1e-8, - recycle=RecycleConfig(rank=3), - ) - - def schedule(ctx): - grown = dataclasses.replace( - ctx.lm_state, - hyper=dataclasses.replace( - ctx.lm_state.hyper, - iterative_maxiter=jnp.where( - ctx.info.loss < 1e-2, jnp.int32(8), jnp.int32(2) - ), - ), - ) - return LMSolveAction(lm_state=grown) - - result = solver.solve(x0, max_steps=60, atol=1e-6, callback=schedule) - assert int(result.status) == LMStatus.CONVERGED - - -def test_recycled_multi_start_cold_resets_basis(): - # _cold_lm_state must reset the recycle basis for drawn starts. - residual, x0 = isolated_mode_problem() - solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - recycle=RecycleConfig(rank=3), - ) - state = solver.init(x0) - # populate a basis, then cold-reset - _, warmed, _ = solver.update(x0, state) - assert bool(warmed.recycle.valid) - cold = gram_lm._cold_lm_state(warmed) - assert not bool(cold.recycle.valid) - assert jnp.all(cold.recycle.U == 0) - assert jnp.all(cold.recycle.dual_velocity == 0) - - -def test_recycled_update_nan_residual_rejects_step(): - # A residual that goes non-finite makes the recycled dual solve non-finite; - # LM must reject the step (never accept a NaN candidate). - def residual(x): - return jnp.array( - [ - x[0] ** 2 - 4.0, - x[0] - 1.0, - x[0] + 2.0, - 2.0 * x[0], - 3.0 * x[0], - jnp.log(x[0]), - ] - ) - - solver = LevenbergMarquardt( - residual, - init_damping=1e-2, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), - iterative_maxiter=10, - recycle=RecycleConfig(rank=1), - ) - x0 = jnp.array([-1.0]) # log(-1) -> nan in the residual - _, _, info = solver.update(x0, solver.init(x0)) - assert not bool(info.accepted) diff --git a/tests/test_ridge_metrics.py b/tests/test_ridge_metrics.py index 1011ab7..78d4b0d 100644 --- a/tests/test_ridge_metrics.py +++ b/tests/test_ridge_metrics.py @@ -97,14 +97,8 @@ def test_constructor_and_input_validation(): RepeatedFactorMetric(jnp.eye(2), repeats=0) with pytest.raises(TypeError, match="floating"): RepeatedFactorMetric(jnp.eye(2, dtype=jnp.complex64)) - with pytest.raises(ValueError, match="positive"): - IdentityMetric(0) with pytest.raises(ValueError, match="leading size"): RepeatedFactorMetric(jnp.eye(2)).factor_apply(jnp.zeros(3), CTX) - with pytest.raises(ValueError, match="vector or matrix"): - IdentityMetric(3).factor_apply(jnp.zeros((3, 2, 2)), CTX) - with pytest.raises(ValueError, match="vector"): - IdentityMetric(3).norm(jnp.zeros((3, 2)), CTX) def test_solver_passes_live_context_to_the_factor_ops(): From d48195ffddc69ed1ec79ff9cb683ee68fe2a1a6d Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 01:34:45 -0700 Subject: [PATCH 05/22] fix: value-hashable continuation callback, and guards for the whole class of bug The solve loop marks the callback a jit STATIC argument, so ridge_continuation() returning a fresh closure meant every construction recompiled the entire loop. It now returns a frozen RidgeContinuation dataclass, value-hashable on (ridge_floor, decrease, grad_rtol, stall_rtol), so equal schedules share one compiled loop. tests/test_compilation.py pins the whole class of regression, measured against the jitted loop's own compilation cache rather than a proxy. It asserts one compilation for: solvers rebuilt repeatedly with equal configs, traced values and loop controls changing, a reused metric across solver rebuilds, a freshly constructed IdentityPreconditioner, a rebuilt continuation callback, and the realistic driver that reconstructs the solver every iteration. It also asserts the negative direction -- a changed shape, linear solver, static scalar, or continuation schedule IS a different program -- so the guards cannot pass by never compiling anything. Also confirmed while writing these: the +1 residual evaluation per solve is init()'s eager sizing pass, not a retrace. 161 passed, 13 skipped. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/__init__.py | 7 +- src/nlls_gram/ridge_lm.py | 110 +++++++++++++-------- tests/test_compilation.py | 194 ++++++++++++++++++++++++++++++++++++++ 3 files changed, 271 insertions(+), 40 deletions(-) create mode 100644 tests/test_compilation.py diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index 3600647..849673e 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -64,7 +64,11 @@ WoodburyPreconditioner, block_eigen_state, ) -from nlls_gram.ridge_lm import RidgeLevenbergMarquardt, ridge_continuation +from nlls_gram.ridge_lm import ( + RidgeContinuation, + RidgeLevenbergMarquardt, + ridge_continuation, +) __all__ = [ "CG", @@ -95,6 +99,7 @@ "Preconditioner", "QRCache", "RepeatedFactorMetric", + "RidgeContinuation", "RidgeLevenbergMarquardt", "ShermanMorrisonPreconditioner", "SolverContext", diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index c5b9b46..9cc356f 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -20,6 +20,7 @@ """ import dataclasses +from dataclasses import dataclass import jax import jax.numpy as jnp @@ -53,6 +54,7 @@ __all__ = [ "CholeskyCache", + "RidgeContinuation", "QRCache", "RidgeLevenbergMarquardt", "ridge_continuation", @@ -115,68 +117,98 @@ def ridge_continuation( under enabled x64). """ - if not 0 < decrease < 1: - raise ValueError("decrease must lie strictly between 0 and 1") - concrete_floor = not isinstance(ridge_floor, (jax.Array, jax.core.Tracer)) - if concrete_floor and float(ridge_floor) <= 0: - raise ValueError( - "ridge_floor must be strictly positive (ridge = 0 is " - "unsupported by RidgeLevenbergMarquardt)" - ) - if grad_rtol <= 0: - raise ValueError("grad_rtol must be positive") - if not 0 <= stall_rtol < 1: - raise ValueError("stall_rtol must lie in [0, 1)") - if dtype is None: - dtype = jnp.result_type(float) - infinity = jnp.asarray(jnp.inf, dtype=dtype) - user_state0 = {"reference": infinity, "previous": infinity} - - def callback(ctx): + schedule = RidgeContinuation( + decrease=decrease, + ridge_floor=ridge_floor, + grad_rtol=grad_rtol, + stall_rtol=stall_rtol, + ) + infinity = jnp.asarray( + jnp.inf, dtype=jnp.result_type(float) if dtype is None else dtype + ) + return schedule, {"reference": infinity, "previous": infinity} + + +@dataclass(frozen=True) +class RidgeContinuation: + """The callback :func:`ridge_continuation` builds; see it for the schedule. + + A frozen dataclass rather than a closure because ``solve`` marks the + callback a jit STATIC argument: a fresh closure would key a fresh + compilation of the whole solve loop on every construction. Two equal + schedules compare equal and share one compiled loop. ``ridge_floor`` must + be a concrete float for that sharing -- a traced value is unhashable and + falls back to identity. + """ + + ridge_floor: float + decrease: float = 0.1 + grad_rtol: float = 1e-2 + stall_rtol: float = 0.0 + + def __post_init__(self): + if not 0 < self.decrease < 1: + raise ValueError("decrease must lie strictly between 0 and 1") + if not isinstance(self.ridge_floor, (jax.Array, jax.core.Tracer)) and ( + float(self.ridge_floor) <= 0 + ): + raise ValueError( + "ridge_floor must be strictly positive (ridge = 0 is " + "unsupported by RidgeLevenbergMarquardt)" + ) + if self.grad_rtol <= 0: + raise ValueError("grad_rtol must be positive") + if not 0 <= self.stall_rtol < 1: + raise ValueError("stall_rtol must lie in [0, 1)") + + def __call__(self, ctx): ridge = ctx.lm_state.ridge - grad_norm = jnp.asarray(ctx.info.grad_norm, dtype=ridge.dtype) - reference = jnp.asarray(ctx.user_state["reference"], dtype=ridge.dtype) - previous = jnp.asarray(ctx.user_state["previous"], dtype=ridge.dtype) - # +inf marks "no observation at this level yet": the first step after - # a ridge decrease (or the initial step) sets the reference and can - # never read as stalled. + dtype = ridge.dtype + grad_norm = jnp.asarray(ctx.info.grad_norm, dtype=dtype) + reference = jnp.asarray(ctx.user_state["reference"], dtype=dtype) + previous = jnp.asarray(ctx.user_state["previous"], dtype=dtype) + # +inf marks "no observation at this level yet": the first step after a + # ridge decrease (or the initial step) sets the reference and can never + # read as stalled. reference = jnp.where(jnp.isfinite(reference), reference, grad_norm) - floor = jnp.asarray(ridge_floor, dtype=ridge.dtype) - stationary = grad_norm <= jnp.asarray(grad_rtol, ridge.dtype) * reference - if stall_rtol > 0: + stationary = grad_norm <= jnp.asarray(self.grad_rtol, dtype) * reference + if self.stall_rtol > 0: # ACCEPTED steps only: a rejected step leaves x (and so the - # gradient) unchanged -- that is the trust region adapting, not - # the level converging -- while an accepted step that improved - # the gradient by less than the stall factor means the level has + # gradient) unchanged -- that is the trust region adapting, not the + # level converging -- while an accepted step that improved the + # gradient by less than the stall factor means the level has # yielded what it can. stalled = ctx.info.accepted & ( - grad_norm >= jnp.asarray(stall_rtol, ridge.dtype) * previous + grad_norm >= jnp.asarray(self.stall_rtol, dtype) * previous ) else: stalled = jnp.asarray(False) new_ridge = jnp.where( stationary | stalled, - jnp.maximum(ridge * jnp.asarray(decrease, ridge.dtype), floor), + jnp.maximum( + ridge * jnp.asarray(self.decrease, dtype), + jnp.asarray(self.ridge_floor, dtype), + ), ridge, ) # Reset the trackers when the level actually changes; at the floor the # ridge is unchanged, so convergence is not suppressed and gtol/atol # can fire. advanced = new_ridge < ridge - fresh_level = jnp.asarray(jnp.inf, ridge.dtype) - new_reference = jnp.where(advanced, fresh_level, reference) - new_previous = jnp.where(advanced, fresh_level, grad_norm) + fresh_level = jnp.asarray(jnp.inf, dtype) state_dtype = jnp.asarray(ctx.user_state["reference"]).dtype return LMSolveAction( lm_state=dataclasses.replace(ctx.lm_state, ridge=new_ridge), user_state={ - "reference": new_reference.astype(state_dtype), - "previous": new_previous.astype(state_dtype), + "reference": jnp.where(advanced, fresh_level, reference).astype( + state_dtype + ), + "previous": jnp.where(advanced, fresh_level, grad_norm).astype( + state_dtype + ), }, ) - return callback, user_state0 - class RidgeLevenbergMarquardt(LevenbergMarquardtBase): """Levenberg-Marquardt for the ridge objective diff --git a/tests/test_compilation.py b/tests/test_compilation.py new file mode 100644 index 0000000..cc48458 --- /dev/null +++ b/tests/test_compilation.py @@ -0,0 +1,194 @@ +"""Recompilation guards. + +The jitted solve loop marks the SOLVER and the CALLBACK static, so anything +reaching the solver's static key by object identity recompiles the whole loop +per construction. Converting a closure to a class is not by itself enough -- +a class that hashes on an array or on a user closure has the same behavior, +just relocated. These tests pin what must and must not recompile. + +The instrument is the jitted loop's own compilation cache, so a "compilation" +here is exactly what JAX counts as one. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from nlls_gram import ( + CG, + QR, + Cholesky, + CholeskyMetric, + DiagonalMetric, + IdentityPreconditioner, + LevenbergMarquardt, + RepeatedFactorMetric, + RidgeLevenbergMarquardt, + ridge_continuation, +) +from nlls_gram.solve_loop import _solve_loop_jit + +N, M = 5, 3 +A = jnp.asarray(np.random.default_rng(3).normal(size=(M, N)), jnp.float32) +SOLVE = dict(max_steps=20, atol=1e-6) + + +def residual(x, args, p): + return A @ x - p["b"] + + +def make_p(scale=1.0): + return {"b": scale * jnp.ones(M, jnp.float32)} + + +@pytest.fixture(autouse=True) +def fresh_cache(): + _solve_loop_jit._clear_cache() + yield + _solve_loop_jit._clear_cache() + + +def compilations(): + return _solve_loop_jit._cache_size() + + +def test_equal_solvers_built_repeatedly_share_one_compilation(): + for scale in (1.0, 2.0, 3.0): + LevenbergMarquardt(residual, linear_solver=Cholesky()).solve( + jnp.zeros(N), p=make_p(scale), **SOLVE + ) + assert compilations() == 1 + + +def test_traced_values_and_loop_controls_do_not_recompile(): + solver = LevenbergMarquardt(residual) + solver.solve(jnp.zeros(N), p=make_p(), **SOLVE) + solver.solve(jnp.zeros(N), p=make_p(2.0), max_steps=20, atol=1e-8) + solver.solve(jnp.zeros(N), p=make_p(3.0), max_steps=40, atol=1e-6, gtol=1e-9) + solver.solve(jnp.zeros(N), p=make_p(4.0), max_steps=20, atol=1e-6, xtol=1e-9) + assert compilations() == 1 + + +def test_shape_change_compiles_one_extra_program_and_reuses_both(): + wide = jnp.asarray(np.random.default_rng(4).normal(size=(M, N + 2)), jnp.float32) + + def sized(x, args, p): + return (A if x.shape[0] == N else wide) @ x - p["b"] + + solver = LevenbergMarquardt(sized) + solver.solve(jnp.zeros(N), p=make_p(), **SOLVE) + solver.solve(jnp.zeros(N + 2), p=make_p(), **SOLVE) + assert compilations() == 2 + solver.solve(jnp.zeros(N), p=make_p(2.0), **SOLVE) + solver.solve(jnp.zeros(N + 2), p=make_p(2.0), **SOLVE) + assert compilations() == 2 + + +# Metrics hold arrays, so they hash by identity and the documented contract is +# build-once-at-setup-scope. What must not happen is a recompilation when the +# same metric is reused and only the solver around it is rebuilt. +METRICS = { + "cholesky": lambda: CholeskyMetric(jnp.eye(N, dtype=jnp.float32)), + "diagonal": lambda: DiagonalMetric(jnp.ones(N, jnp.float32)), + "repeated": lambda: RepeatedFactorMetric(jnp.eye(N, dtype=jnp.float32)), +} + + +@pytest.mark.parametrize("name", list(METRICS)) +def test_reused_metric_survives_solver_rebuilds(name): + metric = METRICS[name]() + for scale in (1.0, 2.0, 3.0): + LevenbergMarquardt(residual, metric=metric).solve( + jnp.zeros(N), p=make_p(scale), **SOLVE + ) + assert compilations() == 1 + + +def test_stateless_preconditioner_is_value_equal(): + # IdentityPreconditioner holds nothing, so even a freshly constructed one + # keys the same compilation -- the closure it replaced did not. + for _ in range(3): + LevenbergMarquardt( + residual, linear_solver=CG(IdentityPreconditioner(), tol=1e-8, maxiter=32) + ).solve(jnp.zeros(N), p=make_p(), **SOLVE) + assert compilations() == 1 + + +def ridge_solver(): + return RidgeLevenbergMarquardt( + residual, metric=DiagonalMetric(jnp.ones(N, jnp.float32)), ridge=1e-3 + ) + + +def run_continuation(solver, ridge_floor, scale=1.0): + callback, user_state = ridge_continuation(ridge_floor=ridge_floor) + return solver.solve( + jnp.zeros(N), + p=make_p(scale), + callback=callback, + user_state=user_state, + max_steps=20, + gtol=1e-6, + ) + + +def test_rebuilding_the_continuation_callback_does_not_recompile(): + # The callback is a jit STATIC argument, so the closure this used to + # return recompiled the whole solve loop on every construction. + solver = ridge_solver() + for scale in (1.0, 2.0, 3.0): + run_continuation(solver, 1e-8, scale) + assert compilations() == 1 + + +def test_a_different_continuation_schedule_is_a_different_program(): + solver = ridge_solver() + run_continuation(solver, 1e-8) + run_continuation(solver, 1e-9) + assert compilations() == 2 + + +def test_solver_rebuilt_inside_a_python_loop_compiles_once(): + # The realistic regression: a driver that constructs the solver each + # iteration must not pay a compilation each iteration. + metric = CholeskyMetric(jnp.eye(N, dtype=jnp.float32)) + for step in range(5): + LevenbergMarquardt( + residual, metric=metric, linear_solver=QR(), init_damping=1e-3 + ).solve(jnp.zeros(N), p=make_p(1.0 + step), **SOLVE) + assert compilations() == 1 + + +def test_a_changed_static_setting_is_a_different_program(): + metric = DiagonalMetric(jnp.ones(N, jnp.float32)) + + def solve(**kwargs): + LevenbergMarquardt(residual, metric=metric, **kwargs).solve( + jnp.zeros(N), p=make_p(), **SOLVE + ) + + solve(linear_solver=Cholesky()) + solve(linear_solver=Cholesky()) + assert compilations() == 1 + solve(linear_solver=QR()) # a different algorithm + assert compilations() == 2 + solve(linear_solver=QR(), damping_increase=8.0) # a static scalar + assert compilations() == 3 + + +def test_matrix_free_path_never_factorizes(): + # The dense path's signature is a Cholesky factorization of an assembled + # matrix; the matrix-free path must contain none. + def jaxpr_text(config): + solver = LevenbergMarquardt(residual, linear_solver=config) + return str( + jax.make_jaxpr( + lambda pv: solver.solve(jnp.zeros(N), p=pv, **SOLVE).x # noqa: B023 + )(make_p()) + ) + + assert "cholesky" in jaxpr_text(Cholesky()) + assert "cholesky" not in jaxpr_text( + CG(IdentityPreconditioner(), tol=1e-8, maxiter=16) + ) From bd41d257fd8e2fb6aba176c10b19fc1eb1985c84 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 01:43:19 -0700 Subject: [PATCH 06/22] docs: restructure around the two solvers; update benchmarks; 2.7.0 Docs go 4252 -> 1743 lines. index.md leads with the one thing that distinguishes the solvers (where the selection of the root lives) as a table, then the residual interface and the solver menu; the eight per-solver math subsections it used to carry duplicated tuning_guide and utilities. gauss_newton.md and metrics.md become metric_lm.md (the damping geometry and its minimum-norm limit, with the rank-deficiency table that says which ad_solver is valid at which shape). utilities.md -- a grab-bag of eleven unrelated helpers, a third of them for deleted features -- becomes metrics.md, covering just the two hook types and why one must be exact and the other need not be. Every mkdocstrings stub moves into api.md, so a removed name breaks one file instead of six. tuning_guide.md and implicit_ad.md are rewritten around what survives; llms.txt (orphaned, not in the nav) is deleted. Benchmarks move to the typed configs and the new metric constructors; the metric-factory case becomes a prepare()-based metric, which is what it was measuring. The augmented_qr benchmark goes with the feature. 37 CPU benchmarks run clean. Also deleted: FAILED_IMPLICIT_AD_PLAN.md and the stale benchmarks/results artifacts from the 2026-07 investigation. mkdocs build --strict passes. 161 passed, 13 skipped. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- FAILED_IMPLICIT_AD_PLAN.md | 164 - README.md | 263 +- benchmarks/results/.gitkeep | 0 .../2026-07-21_failed-ad-baseline.json | 763 - .../2026-07-21_failed-ad-comparison.md | 62 - ...2026-07-21_failed-ad-compile-baseline.json | 92 - ...26-07-21_failed-ad-compile-post-rerun.json | 93 - .../2026-07-21_failed-ad-compile-post.json | 92 - ...-21_failed-ad-compile-stable-baseline.json | 93 - .../2026-07-21_failed-ad-full-post.json | 243310 --------------- .../2026-07-21_failed-ad-post-rerun-1.json | 763 - .../2026-07-21_failed-ad-post-rerun-2.json | 763 - .../results/2026-07-21_failed-ad-post.json | 763 - .../2026-07-21_failed-ad-stable-baseline.json | 767 - ...026-07-21_failed-ad-stable-post-rerun.json | 767 - .../2026-07-21_failed-ad-stable-post.json | 763 - benchmarks/test_implicit_ad_benchmark.py | 39 +- .../test_large_interpolation_benchmark.py | 30 +- .../test_repeated_shifted_metric_benchmark.py | 58 +- benchmarks/test_ridge_lm_benchmark.py | 5 +- docs/api.md | 52 + docs/callbacks.md | 17 +- docs/gauss_newton.md | 320 - docs/implicit_ad.md | 616 +- docs/index.md | 684 +- docs/llms.txt | 15 - docs/metric_lm.md | 84 + docs/metrics.md | 290 +- docs/ridge_lm.md | 41 - docs/tuning_guide.md | 423 +- docs/utilities.md | 570 - mkdocs.yml | 10 +- pyproject.toml | 2 +- uv.lock | 2 +- 34 files changed, 546 insertions(+), 252230 deletions(-) delete mode 100644 FAILED_IMPLICIT_AD_PLAN.md delete mode 100644 benchmarks/results/.gitkeep delete mode 100644 benchmarks/results/2026-07-21_failed-ad-baseline.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-comparison.md delete mode 100644 benchmarks/results/2026-07-21_failed-ad-compile-baseline.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-compile-post-rerun.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-compile-post.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-compile-stable-baseline.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-full-post.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-post-rerun-1.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-post-rerun-2.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-post.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-stable-baseline.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-stable-post-rerun.json delete mode 100644 benchmarks/results/2026-07-21_failed-ad-stable-post.json create mode 100644 docs/api.md delete mode 100644 docs/gauss_newton.md delete mode 100644 docs/llms.txt create mode 100644 docs/metric_lm.md delete mode 100644 docs/utilities.md diff --git a/FAILED_IMPLICIT_AD_PLAN.md b/FAILED_IMPLICIT_AD_PLAN.md deleted file mode 100644 index 8da7ab1..0000000 --- a/FAILED_IMPLICIT_AD_PLAN.md +++ /dev/null @@ -1,164 +0,0 @@ -# Failed Implicit-AD Simplification Plan - -## Summary - -Retain the existing stable `jax.custom_jvp` architecture. JAX will continue -deriving the VJP by transposing the linear tangent rule. Do not introduce -`custom_vjp`, HiJAX, separate tangent/cotangent solvers, or new AD algorithms. - -Simplify failed-solve handling: - -- Remove `failure_ad_reference` from `LevenbergMarquardt.solve`. -- Add the solve-level `max_steps_is_success=True` policy. Keep the diagnostic - `MAX_STEPS` status, but treat it as usable for implicit AD and default - multi-start acceptance unless the caller opts into strict handling. -- On every failed result, use the original stop-gradient `(x0, args, p)` as the - finite AD evaluation point. -- Return zero tangents for `result.x` and `result.aux`; preserve the identity - tangent through `result.p`. -- Require the initial point to be valid for JVP evaluation of the residual and - any metric/preconditioner factories. -- Preserve all successful-solve mathematics, solver methods, tolerances, and - performance. -- Finish nlls completely, then pause for review before touching tinydiffeq. - -Keep version 2.4.0 and make this the final unreleased interface. - -## Mathematical and Public Contract - -For \(r(x,a,p)=0\), define \(J=r_x\), \(K=r_p\), \(P=M^{-1}\), and -\(G=JPJ^\top\). Preserve the implicit tangent - -\[ -\dot x=-PJ^\top G^+K\dot p, -\] - -with the square direct special case - -\[ -J\dot x=-K\dot p. -\] - -Document the automatically transposed cotangent explicitly: - -\[ -\bar p=-K^\top G^+JP\bar x, -\] - -or, for the square direct method, solve \(J^\top\lambda=\bar x\) and return -\(\bar p=-K^\top\lambda\). - -For `aux = h(x*(p), args, p)`, document - -\[ -\dot h=h_x\dot x+h_p\dot p, -\] - -and explain that transposition combines an aux cotangent with the root -cotangent before applying the implicit pullback. The pass-through `result.p` -remains independently differentiable. - -`LMStatus.CONVERGED` is always AD-successful. `LMStatus.MAX_STEPS` is also -AD-successful by default, preserving fixed-step implicit derivatives while the -returned status remains diagnostic. With `max_steps_is_success=False`, it is a -failure. For every failed status: - -- Evaluate the linear tangent program at stop-gradient copies of the original - `(x0, args, p)`. -- Mask `p_dot` to zero before the implicit solve. -- Return exactly zero `x` and `aux` tangents. -- Let automatic transposition produce zero implicit cotangents without - encountering invalid failed iterates. -- Keep the primal failed result, status, diagnostics, and possibly nonfinite - aux unchanged. - -The initial point must be JVP-safe, not merely finite: the residual, aux map, -metric factory, and applicable preconditioner factory must have valid -derivatives there. Multi-start uses the caller's original initial point when -the selected winner fails the implicit-AD status policy; this is independent -of whether a custom acceptance hook accepted or rejected the winner. - -## Phase 1: nlls Implementation - -- Remove `failure_ad_reference` from the public signature, docstring, - custom-JVP operands, validation helpers, README examples, and implicit-AD - documentation. Do not add a compatibility alias. -- Pass the original `(x0, args, p)` from both ordinary and multi-start - custom-JVP rules into the internal tangent construction. -- Add `max_steps_is_success=True` to `solve`; use the same policy for implicit - AD and built-in multi-start acceptance, while a custom `MultiStart.accept` - continues to override selection. -- Select returned solution data for converged lanes and stop-gradient initial - data for failed lanes before evaluating any residual-derived AD operator. -- Preserve all existing `ad_solver*` controls and all direct, SVD, QR, - augmented-QR, and CG behavior. -- Eliminate the unconditional failed-path aux rebuild: - - Fixed metrics and direct square solves must not rebuild aux. - - A `MetricFactory` rebuilds initial aux only when a non-direct AD method - actually consumes it. - - A `PreconditionerFactory` rebuilds initial aux only for `gram_cg` when it - supplies the AD preconditioner. - - Successful scalar solves reuse `result.aux`; do not add another residual - evaluation. - - The returned aux tangent is still computed at selected safe inputs and then - masked to zero on failure. -- Preserve the existing factory-metric first-order and higher-order contracts. -- Update the README, implicit-AD guide, API docstrings, multi-start - documentation, and `llms.txt`. - -## nlls Tests and Performance Gate - -Replace reference-option tests with behavior-focused tests covering mixed -successful/failed `vmap` lanes, deliberately invalid returned iterates, -`result.p` pass-through differentiation, direct and metric-aware methods, -factories, aux evaluation, multi-start, eager/jit execution, pytrees, float32, -float64, successful closed forms, higher-order fixed-metric AD, and zero -derivatives through the initial guess and fixed args. - -Before solver edits, add successful-solve implicit-AD benchmarks for direct -square JVP/VJP, aux without a factory, metric-factory AD, and vmapped solves. -Save pre/post CPU JSON and Markdown comparisons. Any successful JVP/VJP -slowdown larger than `max(5%, 1 us)` is a regression to fix. Compare cold -compilation separately and record environment metadata. - -Run: - -```bash -uv run ruff check . -uv run pytest -uv run --group docs mkdocs build --strict -uv build -JAX_PLATFORMS=cpu uv run --group benchmark pytest benchmarks \ - --benchmark-only \ - --benchmark-json=benchmarks/results/_failed-ad-post.json -``` - -## Mandatory nlls Review Checkpoint - -After nlls code, docs, tests, builds, and benchmarks are complete, do not edit -tinydiffeq. Report the exact API and initial-point precondition, JVP/VJP -equations, aux evaluation behavior, validation results, timing comparison, -diff summary, dirty files, and narrowed behavior. Wait for explicit approval -before committing/pushing nlls or beginning downstream migration. - -## Phase 2: tinydiffeq Migration After Approval - -- Remove the obsolete nlls argument while retaining tinydiffeq's model-level - reference for inactive field and aux evaluation. -- Substitute safe inputs before root calls that are already inactive under - vmapped control flow. -- Require every newly attempted root's actual initial point to be JVP-safe. -- Preserve `LMRootSolver`'s single `ad_solver*` configuration and square-system - `auto -> direct` behavior. -- Update DAE/SDAE/aux/API docs and tests, run all validation and performance - suites, and commit/push each repository separately after approval. - -## Explicit Non-Goals - -- No HiJAX or low-level custom primitive. -- No explicit custom VJP. -- No separate tangent/cotangent solver options. -- No new AD algorithms or regularization changes. -- No augmented-QR redesign. -- No compatibility layer for the removed nlls argument. -- No tinydiffeq work before the nlls review checkpoint. diff --git a/README.md b/README.md index 4501e7f..9210492 100644 --- a/README.md +++ b/README.md @@ -7,32 +7,26 @@ [![License: MIT](https://img.shields.io/github/license/HighDimensionalEconLab/nlls_gram)](https://github.com/HighDimensionalEconLab/nlls_gram/blob/main/LICENSE) [![Ruff](https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/astral-sh/ruff/main/assets/badge/v2.json)](https://github.com/astral-sh/ruff) -Levenberg-Marquardt nonlinear least-squares for JAX pytrees, aimed at -solving systems of equations (i.e., interpolation). The core use case is -underdetermined systems — more parameters than residuals — where something -must select *which* interpolating solution is returned. The package ships -two solvers with one shared `init`/`update`/`solve` protocol: - -- **`RidgeLevenbergMarquardt`** puts the selection in the **objective**: it - minimizes \(\|r(x)\|^2 + \lambda\,\|x_m\|_W^2\) for a user - positive-definite metric \(W\) on the metric block \(x_m\) of - \(x = [x_m; x_f]\) (the free block \(x_f\) stays unpenalized), with the - ridge weight \(\lambda\) annealed toward zero, so the limit is the - minimum-seminorm (e.g. minimum-RKHS-norm) interpolant by classical - nonlinear Tikhonov regularization ([Engl–Hanke–Neubauer 1996; - Kaltenbacher–Neubauer–Scherzer 2008](https://highdimensionaleconlab.github.io/nlls_gram/ridge_lm/)). - Every inner problem is a well-posed NLLS — plain Gauss-Newton alone would - converge to *some* interpolant without selecting the minimal-norm one - ([Campbell–Kunkel–Bobinyec 2012](https://highdimensionaleconlab.github.io/nlls_gram/ridge_lm/)). -- **`LevenbergMarquardt`** is standard damped LM for general nonlinear least - squares — square, tall, or underdetermined — with dense, QR, CG, and - matrix-free LSMR linear solvers and a swappable implicit-AD rule. - -Both take a residual over `(x)`, `(x, args)`, or `(x, args, p)` (always in -that order), flatten any pytree `x` with `jax.flatten_util.ravel_pytree`, -expose per-step `update(...)` and an internally jitted `solve(...)` loop -with callbacks and multi-start, and differentiate `solve(...).x` with -respect to `p` through a custom implicit rule. +Levenberg-Marquardt nonlinear least squares for JAX pytrees, aimed at solving +systems of equations. The core use case is **underdetermined** systems — more +parameters than residuals — where a zero-residual root is not unique and +something must select *which* interpolant is returned. Two solvers differ in +where that selection lives: + +- **`RidgeLevenbergMarquardt`** puts it in the **objective**, minimizing + \(\|r(x)\|^2 + \lambda\,\|x_m\|_W^2\) for a positive-definite metric + \(W\) on the metric block of \(x = [x_m; x_f]\) (the free block stays + unpenalized). Annealing \(\lambda\) toward zero converges to the + minimum-seminorm — e.g. minimum-RKHS-norm — interpolant, by classical + nonlinear Tikhonov regularization. Every inner problem is a well-posed NLLS. +- **`LevenbergMarquardt`** puts it in the **damping geometry**: standard + damped LM whose trust region is measured in \(W\), so the small-damping + Gauss-Newton limit is the minimum-\(W\)-norm correction. + +Both take a residual over `(x)`, `(x, args)`, or `(x, args, p)`, flatten any +pytree `x`, expose per-step `update(...)` and an internally jitted `solve(...)` +loop with callbacks and multi-start, and differentiate `solve(...).x` with +respect to `p` through a custom implicit rule — no unrolling. ## Install @@ -40,207 +34,66 @@ respect to `p` through a custom implicit rule. uv add nlls-gram ``` -For GPU use, install the JAX accelerator build that matches your hardware, for -example: +For GPU use, install the JAX accelerator build that matches your hardware: ```bash uv add nlls-gram "jax[cuda13]" ``` -## Ridge Example: Minimum-RKHS-Norm Interpolation - -For kernel coefficient problems -\(f_\alpha(x)=\sum_j \alpha_j K(x, x_j)\), the squared RKHS norm is -\(\alpha^\top K \alpha\), so the metric is a `RepeatedFactorMetric` -(`repeats` coefficient blocks sharing one upper-triangular factor \(F\) -with \(W = F^\top F\), plus unpenalized structural scalars in the free -block — no epsilon shift anywhere): +## Minimum-RKHS-norm interpolation ```python import jax.numpy as jnp +from nlls_gram import RidgeLevenbergMarquardt, RepeatedFactorMetric, ridge_continuation + +# W = blockdiag(K, K): the RKHS seminorm over two coefficient blocks. The +# constructor takes the FACTOR; from_gram(K, ...) shifts and factors a K. +metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=2) -from nlls_gram import ( - RepeatedFactorMetric, - RidgeLevenbergMarquardt, - ridge_continuation, -) - -F = jnp.linalg.cholesky(K, upper=True) # W = F'F per coefficient block -metric = RepeatedFactorMetric(F, repeats=3) # free block: len(x) - metric.size -solver = RidgeLevenbergMarquardt( - residual_fn, # (x) | (x, args) | (x, args, p) - metric=metric, - ridge=1e-8, # fixed small ridge; None = dtype default -) -result = solver.solve(theta_0, max_steps=400, gtol=1e-8, atol=1e-8) - -# optional homotopy (ridge annealed 1e-4 -> 1e-8 on stationarity): -cb, us0 = ridge_continuation(ridge_floor=1e-8, decrease=0.1) -result = solver.solve(theta_0, max_steps=400, gtol=1e-8, atol=1e-8, - callback=cb, user_state=us0) +solver = RidgeLevenbergMarquardt(collocation_residual, metric=metric, ridge=1e-4) + +# Anneal the ridge toward the interpolating limit on stationarity. +callback, user_state = ridge_continuation(ridge_floor=1e-10) +result = solver.solve(x0, callback=callback, user_state=user_state, + gtol=1e-8, atol=1e-8) ``` -The solver runs entirely in the whitened variable -\(y = \bar F x\) (\(\bar F = \mathrm{blockdiag}(F, I)\)): stock Euclidean -LM on the augmented residual \([r;\sqrt{\lambda}\,y_m]\), where the -penalty rows are constant. The trust-region damping and the selection -weight are fully decoupled, the assembled whitened normal matrix -\(\tilde J^\top \tilde J + \lambda E\) is cached across rejected steps -and keeps a clean spectral floor at \(\lambda\) — so the default cholesky -path stays accurate at deep ridge — and a damping-row QR path -(`linear_solver=QR()`) covers the extreme tiny-ridge/tiny-damping regime. -`IdentityMetric(size)` is plain ridge; `jnp.eye` never appears. -`info.loss` is the ridge objective; `info.resid_loss` is the equation error. -Stopping is conjunctive: `gtol` means "stationary at this ridge", `atol` -additionally demands the equations solved (it never stops the solve alone). -Steps are measured in the W-norm and gradients in the dual W⁻¹-norm, which -makes calibration clean: `gtol ~ 1e-3 * ridge * sqrt(q(x*))` with -\(q = \|x_m\|_W^2\) the solution's squared seminorm -(`info.penalty_grad_norm` reports `sqrt(penalty_value)`). -The [Ridge LM docs](https://highdimensionaleconlab.github.io/nlls_gram/ridge_lm/) -derive the selection theorem, the whitened change of variables, the -continuation schedule, and the solver table. - -## General Nonlinear Least Squares +## General nonlinear least squares ```python -import jax -import jax.numpy as jnp - +import jax, jax.numpy as jnp from nlls_gram import LevenbergMarquardt +def residual(x, args, p): + return args["design"] @ x - p["target"] -def residual_fn(x, args): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -ts = jnp.linspace(0.0, 2.0, 20) -ys = 2.0 * jnp.exp(-1.0 * ts) -x = {"a": 1.0, "b": 0.0} +solver = LevenbergMarquardt(residual) +result = solver.solve(jnp.zeros(8), {"design": design}, p={"target": y}, + max_steps=200, atol=1e-8) -solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) -lm_state = solver.init(x, (ts, ys)) - - -@jax.jit -def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) +# The solution is differentiable in p, at a cost independent of max_steps. +sensitivity = jax.grad( + lambda p: jnp.sum(solver.solve(jnp.zeros(8), {"design": design}, p=p, + max_steps=200, atol=1e-8).x ** 2) +)({"target": y}) +``` +Pass `metric=` to weight the damping geometry. -for _ in range(50): - x, lm_state, info = train_step(x, lm_state) +## Linear solvers -print(x["a"], x["b"]) # approximately 2.0, -1.0 -``` +The same typed configs serve both solvers, forward and in the implicit-AD +role: `Cholesky()` (the default, auto-selecting the smaller of the dual and +normal systems), `QR()` (damping-row QR — stable at tiny damping and +rank-safe), `CG(precond)` and `GramCG(precond)` (matrix-free in parameter and +residual space), and `SVD()` for rank-deficient tangents. A knob that exists +for only one method is a field on that method, so it cannot be passed with +another. -For a simple full solve loop: - -```python -result = solver.solve(x, (ts, ys), max_steps=50, atol=1e-8) -x = result.x -``` +## Docs -`solve` stops on a residual-norm `atol`, gradient-norm `gtol`, or -accepted-step-norm `xtol` (each `0.0` disables), always enforces `max_steps`, -and takes a traceable callback for custom stopping, epoch-style data -resampling, and per-step history recording; the docs have a cookbook. - -`solve(...).x` also supports custom implicit JVP/VJP with respect to `p`; -the docs give the metric-minimum-norm formula and a minimal `jax.jvp` / -`jax.vjp` example. The default `ad_solver="auto"` uses a direct solve for -every square system, preserves the forward CG space for nonsquare CG systems, -and uses SVD otherwise. Every method is independently swappable (an `lsmr` forward solve with -`ad_solver="normal_cg"` is fully matrix-free end to end). The metric -matters for underdetermined roots because it selects which tangent is the -minimum-norm solution. The per-step `update(...)` interface does not define -the implicit AD rule. By default, both `CONVERGED` and `MAX_STEPS` results are -usable: fixed-step solves retain their implicit derivative while the status -still reports `MAX_STEPS`. Pass `max_steps_is_success=False` for strict -failure semantics. A failed solve keeps its primal result and diagnostics but -contributes exactly zero through `result.x` and `result.aux`; `result.p` -remains an identity pass-through. Its linear tangent program is evaluated -safely at differentiation-inert copies of the caller's original -`(x0, args, p)`, so those initial inputs must be JVP-safe for the residual, -aux map, and any metric or preconditioner factory used by the selected AD -method. This also keeps mixed successful/failed `vmap` lanes finite. - -### Advanced: metric damping - -`LevenbergMarquardt` optionally accepts a positive-definite parameter-space -`metric` (or an iterate-aware `MetricFactory`) that redefines the damping -geometry, so the small-damping Gauss-Newton limit selects -minimum-*metric*-norm corrections — the algorithmic-bias alternative to the -ridge objective, with `repeated_shifted_dense_metric` / -`repeated_shifted_state_space_metric` covering the kernel geometry -\(\operatorname{blockdiag}(K,\ldots,K,0_s)+\varepsilon I\). See the -[metrics](https://highdimensionaleconlab.github.io/nlls_gram/metrics/) and -[metric Gauss-Newton](https://highdimensionaleconlab.github.io/nlls_gram/gauss_newton/) -docs pages; for new kernel problems prefer `RidgeLevenbergMarquardt`. - -## LevenbergMarquardt Solvers - -- `linear_solver="auto"` (the default): resolves at trace time to the - smaller dense factorization — `gram_cholesky` when `n > m`, - `normal_cholesky` otherwise. A shape rule, and safely so: the two forms - compute the same step. -- `linear_solver="gram_cholesky"`: dense `m × m` residual-space Gram solve. -- `linear_solver="normal_cholesky"`: dense `n × n` whitened normal solve; - its small-damping limit is the minimum-metric-norm least-squares step at - every shape and rank. -- `linear_solver="qr"`: dense QR solve of the whitened-step problem (requires - a full-row-rank Jacobian). -- `linear_solver="augmented_qr"`: direct augmented QR in parameter space; - robust to rank-deficient Jacobians when damping is positive and best suited - to small systems. -- `linear_solver="gram_cg"`: matrix-free residual-space CG. A - `dual_preconditioner` is required (e.g. `sherman_morrison_preconditioner`, - or the randomized `nystrom_preconditioner` for neural-network duals; pass - `identity_preconditioner()` to run unpreconditioned CG explicitly); - on a nonsquare system `ad_solver="auto"` keeps `solve(...).x` matrix-free - under AD and requires `ad_solver_preconditioner` when the differentiated - solve is traced (an explicit `ad_solver="gram_cg"` validates it eagerly). - When the dual operator rotates as LM - drifts `x`, pass `preconditioner_factory=PreconditionerFactory(prepare, - apply)` instead — a θ-adaptive preconditioner rebuilt from the live iterate - each step — and `recycle=RecycleConfig(rank=k)` to carry a deflation basis - across steps, recycling each solve's Krylov subspace into the next. -- `linear_solver="normal_cg"`: matrix-free CG on the whitened normal system, - iterating in parameter space — the matrix-free form for square-to-tall - problems. A `normal_preconditioner` is required; on rank-deficient - problems it must preserve `range(Bᵀ)` or the minimum-norm selection is - lost (`identity_preconditioner()` always qualifies — the docs give the - full requirement). -- `linear_solver="lsmr"`: matrix-free LSMR on the whitened augmented system, - the iterative sibling of `augmented_qr`, using only J/Jᵀ products. It works - on the whitened Jacobian rather than a squared Gram/normal operator, so it - stays accurate at small damping where those solves hit their `eps·cond` - floor. An optional - `whitened_preconditioner=WhitenedPreconditioner(solve, solve_transpose)` - right-preconditions the operator to cluster its spectrum; every damped - posed subproblem stays exactly the identity-damped whitened one, so the - preconditioner changes the iteration path, never the converged step. - -All eight solve the same metric-damped linearized subproblem up to the -accuracy of the chosen linear solver. The dense paths materialize the -Jacobian from its small side (`jacobian_mode="auto"`; `"fwd"`/`"rev"` -force one AD mode), so tall systems never build an `m × m` residual basis. - -## Docs and Alternatives - -Full docs: https://highdimensionaleconlab.github.io/nlls_gram/ - -Working with an AI assistant? Point it at -[`docs/tuning_guide.md`](https://highdimensionaleconlab.github.io/nlls_gram/tuning_guide/) -if it doesn't pick it up automatically — solver selection, damping heuristics, -inner-solve scheduling, and failure signatures, written to be read by humans -and agents alike (also indexed via the site's `llms.txt`). - -For a broader JAX nonlinear solver library, see -[Optimistix](https://github.com/patrick-kidger/optimistix). `nlls_gram` is more -specialized: it focuses on underdetermined nonlinear least-squares, residual -space Gram solves, and explicit parameter-space metrics. + ## License -MIT +MIT. diff --git a/benchmarks/results/.gitkeep b/benchmarks/results/.gitkeep deleted file mode 100644 index e69de29..0000000 diff --git a/benchmarks/results/2026-07-21_failed-ad-baseline.json b/benchmarks/results/2026-07-21_failed-ad-baseline.json deleted file mode 100644 index 884ec3a..0000000 --- a/benchmarks/results/2026-07-21_failed-ad-baseline.json +++ /dev/null @@ -1,763 +0,0 @@ -{ - 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`bf22f01fb7ff91ead9e218c92217590f3e325be6` -- Post source: current failed-implicit-AD working tree on the same base commit -- Runtime method: 50 rounds, 100 blocked dispatches per round; medians below - are per dispatch -- Regression gate: slowdown greater than `max(5%, 1 us)` - -The original one-dispatch samples were too noisy for the 1 us gate. They are -retained as raw artifacts, but the gate uses the repeated-dispatch baseline and -post rerun: - -- `2026-07-21_failed-ad-stable-baseline.json` -- `2026-07-21_failed-ad-stable-post-rerun.json` - -## Successful implicit-AD runtime - -| Full benchmark suffix | Baseline (us) | Post (us) | Delta (us) | Delta | Gate crossing | -| --- | ---: | ---: | ---: | ---: | --- | -| `jvp-direct` | 10.0225 | 10.0013 | -0.0212 | -0.21% | no | -| `jvp-direct_aux` | 8.7723 | 7.7760 | -0.9963 | -11.36% | no | -| `jvp-metric_factory` | 23.6000 | 23.5610 | -0.0390 | -0.17% | no | -| `jvp-vmapped` | 27.4027 | 26.4317 | -0.9710 | -3.54% | no | -| `vjp-direct` | 10.6850 | 9.8560 | -0.8290 | -7.76% | no | -| `vjp-direct_aux` | 9.0592 | 9.1277 | +0.0685 | +0.76% | no | -| `vjp-metric_factory` | 24.2642 | 23.0433 | -1.2208 | -5.03% | no | -| `vjp-vmapped` | 37.0979 | 36.2494 | -0.8485 | -2.29% | no | - -No successful JVP/VJP runtime crosses the regression gate. - -## Cold compilation - -Cold compilation used five cache-cleared samples per case. These values are -recorded separately from the runtime gate. - -| Case | Baseline (ms) | Post (ms) | Delta (ms) | Delta | -| --- | ---: | ---: | ---: | ---: | -| `jvp-direct` | 72.788 | 81.589 | +8.802 | +12.09% | -| `jvp-direct_aux` | 76.288 | 82.298 | +6.011 | +7.88% | -| `jvp-metric_factory` | 75.872 | 82.959 | +7.088 | +9.34% | -| `jvp-vmapped` | 94.400 | 98.925 | +4.525 | +4.79% | -| `vjp-direct` | 76.881 | 82.598 | +5.717 | +7.44% | -| `vjp-direct_aux` | 80.087 | 86.689 | +6.602 | +8.24% | -| `vjp-metric_factory` | 83.700 | 93.249 | +9.549 | +11.41% | -| `vjp-vmapped` | 95.396 | 103.481 | +8.085 | +8.47% | - -The additional status selection and masking graph adds 4.5--9.5 ms to a cold -compile. It does not add a measurable hot-runtime regression in the cases -above. - -## Full benchmark suite - -`JAX_PLATFORMS=cpu uv run --group benchmark pytest benchmarks ---benchmark-only` completed with 70 passed and 93 skipped in 83.38 seconds. -The complete output is saved in -`2026-07-21_failed-ad-full-post.json`. diff --git a/benchmarks/results/2026-07-21_failed-ad-compile-baseline.json b/benchmarks/results/2026-07-21_failed-ad-compile-baseline.json deleted file mode 100644 index 0c61917..0000000 --- a/benchmarks/results/2026-07-21_failed-ad-compile-baseline.json +++ /dev/null @@ -1,92 +0,0 @@ -{ - "commit": "bf22f01fb7ff91ead9e218c92217590f3e325be6", - "host": "dh4.econ.ubc.ca", - "python": "3.13.2", - "jax": "0.10.1", - "platform": "cpu", - "machine": "arm64", - "system": "macOS-26.5.2-arm64-arm-64bit-Mach-O", - "repeat": 5, - "timings": { - "jvp-direct": { - "median_seconds": 0.06743350008036941, - "samples_seconds": [ - 0.13281870796345174, - 0.06713770900387317, - 0.0671046250499785, - 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p, {"weight": 1.0 + 0.1 * x**2} - factory = MetricFactory( - prepare=lambda x, args, p, aux: aux["weight"], - build=metric_from_diagonal, - ) solver = LevenbergMarquardt( residual, has_aux=True, - metric_factory=factory, - ad_solver="svd", + metric=PreparedDiagonalMetric(), + ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) @@ -102,8 +117,8 @@ def _make_problem(case): return _direct_problem(has_aux=False) if case == "direct_aux": return _direct_problem(has_aux=True) - if case == "metric_factory": - return _metric_factory_problem() + if case == "prepared_metric": + return _prepared_metric_problem() return _vmapped_problem() @@ -128,7 +143,7 @@ def transformed(parameter): return transformed, p -@pytest.mark.parametrize("case", ["direct", "direct_aux", "metric_factory", "vmapped"]) +@pytest.mark.parametrize("case", ["direct", "direct_aux", "prepared_metric", "vmapped"]) @pytest.mark.parametrize("transform", ["jvp", "vjp"]) def test_successful_implicit_ad(benchmark, case, transform): _, status_parameter, status = _make_problem(case) diff --git a/benchmarks/test_large_interpolation_benchmark.py b/benchmarks/test_large_interpolation_benchmark.py index bca5f99..e8c6af9 100644 --- a/benchmarks/test_large_interpolation_benchmark.py +++ b/benchmarks/test_large_interpolation_benchmark.py @@ -2,7 +2,13 @@ import jax.numpy as jnp import pytest -from nlls_gram import LevenbergMarquardt, identity_preconditioner +from nlls_gram import ( + QR, + Cholesky, + GramCG, + IdentityPreconditioner, + LevenbergMarquardt, +) ITERATIVE_MAXITER = 8 @@ -36,20 +42,7 @@ def residual(theta, args, p): features, ys = args return jnp.sin(features @ theta) - ys - solver_kwargs = { - "init_damping": 1e-2, - "linear_solver": linear_solver, - } - if linear_solver == "gram_cg": - solver_kwargs.update( - { - "iterative_tol": 0.0, - "iterative_atol": 0.0, - "iterative_maxiter": ITERATIVE_MAXITER, - "dual_preconditioner": identity_preconditioner(), - "ad_solver_preconditioner": identity_preconditioner(), - } - ) + solver_kwargs = {"init_damping": 1e-2, "linear_solver": linear_solver} base_solver = LevenbergMarquardt(residual, **solver_kwargs) solver = LevenbergMarquardt( @@ -78,10 +71,11 @@ def step(x, lm_state): @pytest.mark.parametrize( "linear_solver", [ - "gram_cholesky", - "qr", - "gram_cg", + Cholesky(form="gram"), + QR(), + GramCG(IdentityPreconditioner(), maxiter=ITERATIVE_MAXITER), ], + ids=["gram_cholesky", "qr", "gram_cg"], ) @pytest.mark.parametrize("geodesic_acceleration", [False, True]) def test_large_rbf_interpolation_second_update( diff --git a/benchmarks/test_repeated_shifted_metric_benchmark.py b/benchmarks/test_repeated_shifted_metric_benchmark.py index ff92d1d..bbe20a4 100644 --- a/benchmarks/test_repeated_shifted_metric_benchmark.py +++ b/benchmarks/test_repeated_shifted_metric_benchmark.py @@ -2,11 +2,8 @@ import jax.numpy as jnp import pytest -from nlls_gram import ( - matern_state_space, - repeated_shifted_dense_metric, - repeated_shifted_state_space_metric, -) +from nlls_gram import RepeatedFactorMetric +from nlls_gram.experimental import StateSpaceMetric, matern_state_space SIGMA = 1.0 ELL = 10.0 @@ -34,25 +31,20 @@ def _matern_gram(t, nu): @pytest.mark.parametrize("platform", ["cpu", "gpu"]) @pytest.mark.parametrize( - ("n", "repeats", "zero_pad_size", "rhs_columns", "nu"), + ("n", "repeats", "rhs_columns", "nu"), [ - (41, 3, 2, 123, 0.5), - (81, 7, 5, 567, 0.5), - (96, 5, 3, 480, 2.5), - (96, 9, 5, 865, 2.5), - (96, 201, 101, 1, 2.5), + (41, 3, 123, 0.5), + (81, 7, 567, 0.5), + (96, 5, 480, 2.5), + (96, 9, 865, 2.5), + (96, 201, 1, 2.5), ], ) -@pytest.mark.parametrize("callback", ["solve", "inv_sqrt", "inv_sqrt_transpose"]) -def test_repeated_shifted_dense_apply( - benchmark, - platform, - n, - repeats, - zero_pad_size, - rhs_columns, - nu, - callback, +@pytest.mark.parametrize( + "callback", ["factor_apply", "factor_solve", "factor_solve_transpose"] +) +def test_repeated_factor_metric_apply( + benchmark, platform, n, repeats, rhs_columns, nu, callback ): devices = _devices(platform) if not devices: @@ -60,18 +52,15 @@ def test_repeated_shifted_dense_apply( device = devices[0] t = jax.device_put(jnp.linspace(0.0, 40.0, n), device) K = _matern_gram(t, nu) - metric = repeated_shifted_dense_metric( - K, - repeats=repeats, - zero_pad_size=zero_pad_size, - epsilon=EPSILON, + metric = RepeatedFactorMetric.from_gram( + K, repeats=repeats, epsilon=EPSILON, free_scale=EPSILON ) - total_size = repeats * n + zero_pad_size + total_size = repeats * n shape = (total_size,) if rhs_columns == 1 else (total_size, rhs_columns) x = jax.device_put(jax.random.normal(jax.random.key(0), shape), device) - apply = jax.jit(getattr(metric, callback)) + apply = jax.jit(lambda v: getattr(metric, callback)(v, None)) jax.block_until_ready(apply(x)) - benchmark.group = f"repeated-shifted-dense-{callback}" + benchmark.group = f"repeated-factor-{callback}" def run(): out = apply(x) @@ -85,28 +74,27 @@ def run(): @pytest.mark.parametrize("n", [1_000, 10_000, 100_000]) @pytest.mark.parametrize("nu", [0.5, 1.5, 2.5]) @pytest.mark.parametrize("parallel", [False, True]) -def test_repeated_shifted_state_space_apply(benchmark, platform, n, nu, parallel): +def test_state_space_metric_apply(benchmark, platform, n, nu, parallel): devices = _devices(platform) if not devices: pytest.skip(f"JAX {platform!r} backend is not available") device = devices[0] t = jax.device_put(jnp.arange(n) * 1.0, device) - metric = repeated_shifted_state_space_metric( + metric = StateSpaceMetric( t, *matern_state_space(SIGMA, ELL, nu), repeats=3, - zero_pad_size=2, epsilon=EPSILON, parallel=parallel, ) - x = jax.device_put(jnp.sin(jnp.linspace(0.0, 20.0, 3 * n + 2)), device) + x = jax.device_put(jnp.sin(jnp.linspace(0.0, 20.0, 3 * n)), device) @jax.jit def apply(value): - return metric.solve(value), metric.norm(value) + return metric.factor_solve(value, None), metric.norm(value, None) jax.block_until_ready(apply(x)) - benchmark.group = "repeated-shifted-state-space" + benchmark.group = "state-space-metric" def run(): out = apply(x) diff --git a/benchmarks/test_ridge_lm_benchmark.py b/benchmarks/test_ridge_lm_benchmark.py index e53c9a4..75d03d2 100644 --- a/benchmarks/test_ridge_lm_benchmark.py +++ b/benchmarks/test_ridge_lm_benchmark.py @@ -19,7 +19,6 @@ LevenbergMarquardt, RepeatedFactorMetric, RidgeLevenbergMarquardt, - repeated_shifted_dense_metric, ) SIGMA = 1.0 @@ -86,8 +85,8 @@ def test_update_step( device = devices[0] K, residual, x0 = _problem(n, repeats, free_size, m_resid, device) if configuration == "metric": - metric = repeated_shifted_dense_metric( - K, repeats=repeats, zero_pad_size=free_size, epsilon=EPSILON + metric = RepeatedFactorMetric.from_gram( + K, repeats=repeats, epsilon=EPSILON, free_scale=EPSILON ) solver = LevenbergMarquardt(residual, metric=metric) else: diff --git a/docs/api.md b/docs/api.md new file mode 100644 index 0000000..c752240 --- /dev/null +++ b/docs/api.md @@ -0,0 +1,52 @@ +# API + +## Solvers + +::: nlls_gram.RidgeLevenbergMarquardt +::: nlls_gram.LevenbergMarquardt +::: nlls_gram.RidgeContinuation +::: nlls_gram.ridge_continuation + +## Linear solvers + +::: nlls_gram.Cholesky +::: nlls_gram.QR +::: nlls_gram.CG +::: nlls_gram.GramCG +::: nlls_gram.SVD + +## Metrics + +::: nlls_gram.Metric +::: nlls_gram.IdentityMetric +::: nlls_gram.CholeskyMetric +::: nlls_gram.DiagonalMetric +::: nlls_gram.RepeatedFactorMetric + +## Preconditioners + +::: nlls_gram.Preconditioner +::: nlls_gram.IdentityPreconditioner +::: nlls_gram.BlockEigenPreconditioner +::: nlls_gram.block_eigen_state +::: nlls_gram.NystromPreconditioner +::: nlls_gram.ShermanMorrisonPreconditioner +::: nlls_gram.WoodburyPreconditioner +::: nlls_gram.PaddedPreconditioner + +## State and results + +::: nlls_gram.LMState +::: nlls_gram.LMInfo +::: nlls_gram.LMStatus +::: nlls_gram.LMHyperparams +::: nlls_gram.LMSolveContext +::: nlls_gram.LMSolveAction +::: nlls_gram.LMSolveResult +::: nlls_gram.SolverContext + +## Multi-start + +::: nlls_gram.MultiStart +::: nlls_gram.MultiStartInfo +::: nlls_gram.DrawNNXModule diff --git a/docs/callbacks.md b/docs/callbacks.md index 8133475..2d4586b 100644 --- a/docs/callbacks.md +++ b/docs/callbacks.md @@ -324,7 +324,7 @@ point on the next update. ### Scheduled Inner-Solve Accuracy -With `linear_solver="gram_cg"`, cheap inexact steps are fine far from the solution +With a Krylov `linear_solver`, cheap inexact steps are fine far from the solution (the accept/reject test absorbs them), but near convergence step quality limits the rate. Grow the CG budget once the loss crosses a threshold — one solve call, so implicit differentiation still applies: @@ -332,10 +332,7 @@ one solve call, so implicit differentiation still applies: ```python solver = LevenbergMarquardt( residual_fn, - linear_solver="gram_cg", - iterative_maxiter=2, - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), + linear_solver=GramCG(IdentityPreconditioner(), maxiter=2), ) @@ -355,18 +352,10 @@ result = solver.solve(x0, args, max_steps=200, atol=1e-8, callback=grow_budget) Alternatively, a relative `iterative_tol` adapts the inner accuracy automatically (CG's stopping test scales with the right-hand side, which is the shrinking outer residual). For a dense endgame instead, chain two solves: -a coarse CG stage, then a dense solver (`auto`) warm-started with `result.x` and +a coarse CG stage, then a `Cholesky()` solver warm-started with `result.x` and `result.lm_state` — the implicit derivative is unaffected since it is defined at the returned solution only. -This schedule composes unchanged with Krylov recycling -([`recycle=RecycleConfig(...)`](tuning_guide.md#recycling-and-deflation-across-steps)): -`rank`/`window` are static shapes the callback must not touch, while the carried -deflation basis shrinks the budget each step needs and the schedule then grows -it toward the endgame. The callback contract is the same — preserve the recycle -state with `dataclasses.replace(ctx.lm_state, ...)` (a fresh `LMState` that drops -it is rejected, exactly like the Jacobian cache). - ### Validation Early Stopping Compute held-out metrics in the callback and stop when they jointly clear diff --git a/docs/gauss_newton.md b/docs/gauss_newton.md deleted file mode 100644 index 20dfd31..0000000 --- a/docs/gauss_newton.md +++ /dev/null @@ -1,320 +0,0 @@ -# Metric Gauss-Newton and Minimum-Norm Steps - -This page explains the local behavior of the solver near the interpolation -threshold: with small damping, metric-aware Levenberg-Marquardt behaves like a -**metric Gauss-Newton** method, and the metric Gauss-Newton step is the -**minimum-\(M\)-norm** correction that solves the linearized residual -equations. Equivalently, ordinary Gauss-Newton in whitened coordinates is -metric Gauss-Newton in raw coordinates. For RKHS metrics this means the solver -selects minimum-RKHS-norm linearized corrections — and with kernel methods the -metric, hence the norm being minimized, can be carefully controlled. - -Notation follows the [mathematical contract](index.md#mathematical-contract): -at the current flattened parameters \(\theta \in \mathbb R^n\), the residual is -\(r \in \mathbb R^m\), the Jacobian is \(J \in \mathbb R^{m \times n}\), the -step is \(s\), the damping is \(\lambda > 0\), and the metric is -\(M \succ 0\) with \(P = M^{-1}\) and -\(\|s\|_M = \sqrt{s^\top M s}\). Residual entries are always measured in the -Euclidean norm; \(M\) defines the geometry of *parameter* perturbations only. - -## Why Gauss-Newton Is the Local Model Near Interpolation - -The Hessian of \(\tfrac12\|r(\theta)\|_2^2\) decomposes as - -$$ -\nabla_\theta^2 \tfrac12\|r(\theta)\|_2^2 -= J^\top J + \sum_{i=1}^m r_i \nabla_\theta^2 r_i. -$$ - -Near the interpolation threshold \(r_i \approx 0\), so the residual-weighted -curvature terms are negligible and \(J^\top J\) is the locally accurate model. -With a metric, the relevant local method is not Euclidean Gauss-Newton but its -metric version below. - -## The Metric Gauss-Newton Step Is the Minimum-Norm Correction - -Suppose the linearized equation \(J s = -r\) is feasible. With \(n > m\) it -typically has many solutions; metric Gauss-Newton selects the one with -minimum \(M\)-norm: - -$$ -s_{\mathrm{GN},M} -= \arg\min_{s} \tfrac12 \|s\|_M^2 -\quad\text{subject to}\quad -J s = -r. -$$ - -The Lagrangian \(\tfrac12 s^\top M s + y^\top (J s + r)\) has first-order -conditions \(M s + J^\top y = 0\), so \(s = -P J^\top y\); imposing the -constraint gives \(J P J^\top y = r\) (invertible for full-row-rank \(J\); -the [rank-deficient case](#rank-deficiency) replaces it with a -pseudoinverse), and therefore - -$$ -s_{\mathrm{GN},M} = -P J^\top \left(J P J^\top\right)^{-1} r. -$$ - -For \(M = I\) this is the ordinary underdetermined Gauss-Newton / -pseudoinverse step \(s = -J^\top (J J^\top)^{-1} r\). - -The \(m \times m\) matrix - -$$ -G_M = J P J^\top, -\qquad -(G_M)_{ij} = J_i P J_j^\top -$$ - -is the **metric Gram matrix**: the metric changes the induced inner product -between residual sensitivities \(J_i\), not the residual norm itself. - -## Damping Interpolates Between Two Metric Methods - -The solver's damped step (see the -[linear solver formulas](index.md#linear-solver-formulas)) is - -$$ -s_\lambda = -P J^\top \left(G_M + \lambda I_m\right)^{-1} r. -$$ - -**Small damping.** As \(\lambda \downarrow 0\) (with \(G_M\) nonsingular), -\(s_\lambda \to s_{\mathrm{GN},M}\): near interpolation, small-damping metric -LM is approximately the minimum-\(M\)-norm linearized residual correction. - -**Large damping.** As \(\lambda \to \infty\), -\((G_M + \lambda I)^{-1} \approx \tfrac1\lambda I\), so - -$$ -s_\lambda \approx -\tfrac1\lambda P J^\top r -= -\tfrac1\lambda M^{-1} \nabla_\theta \tfrac12\|r(\theta)\|_2^2, -$$ - -which is steepest descent in the \(M\)-metric (a natural-gradient-style step), -not Euclidean gradient descent. - -## Spectral Filter View - -Let \(S\) satisfy \(S S^\top = M^{-1}\) and let the whitened Jacobian -\(J S\) have SVD \(J S = U \Sigma V^\top\). In whitened coordinates -\(s = S z\), the damped step is - -$$ -z_\lambda = -\sum_i \frac{\sigma_i}{\sigma_i^2 + \lambda}\, v_i (u_i^\top r), -\qquad -s_\lambda = S z_\lambda. -$$ - -The filter factor \(\sigma_i / (\sigma_i^2 + \lambda)\) acts direction by -direction: where \(\sigma_i^2 \gg \lambda\) it is \(\approx 1/\sigma_i\) -(Gauss-Newton-like), and where \(\sigma_i^2 \ll \lambda\) it is -\(\approx \sigma_i/\lambda\) (gradient-descent-like). LM is therefore -direction-wise between metric Gauss-Newton and metric gradient descent: as -damping falls near interpolation, accepted steps become Gauss-Newton-like on -the well-identified directions while poorly identified directions stay damped. -The effective number of active directions at damping \(\lambda\) is - -$$ -d_{\mathrm{eff}}(\lambda) -= \operatorname{tr}\!\left(G_M (G_M + \lambda I)^{-1}\right) -= \sum_i \frac{\sigma_i^2}{\sigma_i^2 + \lambda}. -$$ - -**The pseudoinverse limit.** As \(\lambda \downarrow 0\) each filter factor -converges to \(\sigma_i^{+}\) — \(1/\sigma_i\) where \(\sigma_i > 0\), and -exactly \(0\) where \(\sigma_i = 0\) — so - -$$ -z_\lambda \to -(JS)^{+} r, -\qquad -s_\lambda \to -S\,(JS)^{+} r, -$$ - -the minimum-\(M\)-norm least-squares correction of the -[rank-deficiency section](#rank-deficiency), with **no rank or shape -assumption**: redundant rows and collinear columns are filtered out -direction by direction, never inverted. The full-row-rank dual formula of -the earlier sections is the special case where the linearized least-squares -residual is zero. This primal limit is what every damped solver realizes as -damping falls near interpolation; how *accurately* a solver tracks it at -small \(\lambda\) is a conditioning question — the Gram and normal forms -work at the squared condition number of \(JS\), `lsmr` at -\(\operatorname{cond}(JS)\) itself. - -## Whitened-Coordinate Equivalence - -Metric Gauss-Newton in raw coordinates is ordinary Gauss-Newton in whitened -coordinates. With \(M = L L^\top\) and whitened coordinates -\(z = L^\top \theta\), - -$$ -\|s\|_M^2 = \|L^\top s\|_2^2, -\qquad -J_z = J L^{-\top}, -$$ - -and the ordinary minimum-Euclidean-norm Gauss-Newton step -\(z\text{-step} = -J_z^\top (J_z J_z^\top)^{-1} r\) maps back to exactly -\(s_{\mathrm{GN},M}\). Passing whitened variables to an ordinary LM solver is -therefore equivalent to using the metric-aware solver in raw variables; the -metric-aware solver lets you stay in raw variables with the same -geometry. (This is precisely the substitution the whitened paths — -`normal_cholesky`, `normal_cg`, `qr`, `augmented_qr`, `lsmr` — make, with -\(S = L^{-\top}\).) - -## Rank Deficiency - -Without full row rank, replace the inverse with a pseudoinverse: writing -\(s = S z\) and \(A = J S\), the general metric Gauss-Newton step is - -$$ -s_{\mathrm{GN},M} = -S A^{+} r = -S (J S)^{+} r, -$$ - -the minimum-\(M\)-norm step among linearized least-squares minimizers. The -damped solvers remain well-posed for rank-deficient \(J\) (the `qr` path is -the exception — it [requires full row rank](index.md#qr)). - -## Choosing the Metric with Kernels - -The practical power of the metric is that kernel methods let you control it -exactly. Two standard parameterizations of a kernel function -\(f\) with Gram matrix \(K = [K(t_i, t_j)]_{ij}\): - -**Kernel coefficients.** With \(f_\alpha(t) = \sum_j \alpha_j K(t, t_j)\), the -RKHS norm is \(\|f_\alpha\|_{\mathcal H_K}^2 = \alpha^\top K \alpha\), so the -parameter metric is \(M = K\) and - -$$ -s_{\mathrm{GN},M} -= -K^{-1} J^\top \left(J K^{-1} J^\top\right)^{-1} r -$$ - -is the correction that solves the linearized equations while minimizing the -RKHS norm of the *function* perturbation. - -**Function values.** With parameters \(u_i = f(t_i)\), the minimum-norm -interpolant through \(u\) has \(\|f_u\|_{\mathcal H_K}^2 = u^\top K^{-1} u\), -so \(M = K^{-1}\) and \(P = K\): - -$$ -s_{\mathrm{GN},M} -= -K J^\top \left(J K J^\top\right)^{-1} r. -$$ - -| Parameterization | Function norm | Metric \(M\) | Inverse metric \(P\) | -| --- | --- | --- | --- | -| Kernel coefficients \(\alpha\) | \(\alpha^\top K \alpha\) | \(K\) | \(K^{-1}\) | -| Function values \(u = f(t)\) | \(u^\top K^{-1} u\) | \(K^{-1}\) | \(K\) | - -The same choice governs [implicit differentiation](implicit_ad.md): -in underdetermined problems the metric is part of the definition of the -derivative, selecting the minimum-\(M\)-norm solution tangent. - -## Shifted Metrics and the Seminorm Limit - -Kernel models often carry a few extra scalar parameters \(\beta\) (level -constants, initial values) alongside the coefficients \(\alpha\), and the -natural objective is the RKHS *seminorm* \(\alpha^\top K \alpha\) with -\(\beta\) free — which is not a metric (\(M \succ 0\) fails on the -\(\beta\) block, and \(K\) itself is numerically singular on fine grids). -The **unified shifted metric** - -$$ -M_\varepsilon -= \begin{bmatrix} K & 0 \\ 0 & 0 \end{bmatrix} + \varepsilon I -= \begin{bmatrix} K + \varepsilon I_n & 0 \\ 0 & \varepsilon I_k \end{bmatrix} -$$ - -completes it with a single spectral floor: the eigenvalues are -\(\{\lambda_i(K) + \varepsilon\} \cup \{\varepsilon\}\), so -\(\|M_\varepsilon^{-1}\|_2 = 1/\varepsilon\) exactly — uniformly in \(n\) -and in how singular \(K\) is. The metric norm it minimizes is - -$$ -\|s\|_{M_\varepsilon}^2 -= \alpha^\top K \alpha + \varepsilon \|s\|_2^2 , -$$ - -the seminorm plus a flat Tikhonov ridge on the whole parameter vector. - -**The \(\varepsilon \to 0\) limit.** When \(K \succ 0\), \(J\) has full row -rank, and the \(\beta\)-columns \(J_\beta\) have full column rank, the -seminorm-constrained problem \(\min_\theta \alpha^\top K \alpha\) s.t. -\(J\theta = b\) has a unique solution — the bordered KKT system - -$$ -\begin{bmatrix} 2K & 0 & J_\alpha^\top \\ 0 & 0 & J_\beta^\top \\ -J_\alpha & J_\beta & 0 \end{bmatrix} -\begin{bmatrix} \alpha \\ \beta \\ -y \end{bmatrix} -= \begin{bmatrix} 0 \\ 0 \\ b \end{bmatrix} -$$ - -— and the minimum-\(M_\varepsilon\)-norm solution (and its implicit -derivative) converges to it at rate \(O(\varepsilon)\). For **singular** -\(K\) the limit is *lexicographic*: the minimum-Euclidean-norm element -among the seminorm minimizers (the Tikhonov tie-break), not a distinguished -"\(\beta\)-free" solution. (With \(K = 0\) and one constraint -\(\alpha + \beta = 1\), every feasible pair has zero seminorm; -\(M_\varepsilon\) selects \(\alpha = \beta = 1/2\).) State uniqueness -assumptions before claiming the \(O(\varepsilon)\) perturbation. - -Compared to the two-knob block form \(\operatorname{blockdiag}(K + -\delta I, m_0 I_k)\), one \(\varepsilon\) is one dial: smaller -\(\varepsilon\) means less selection bias but a harder metric solve -(\(\kappa(K + \varepsilon I) = (\lambda_{\max} + \varepsilon)/\varepsilon\)) -and a larger scalar-block spike \((c^2/\varepsilon)\,uu^\top\) in the dual -operator — see the [Tuning Guide](tuning_guide.md#the-metric) and -[Utilities](utilities.md#repeated-shifted-kernel-metrics) for construction -and preconditioning. - -## Worked Example - -For the one-row residual \(r(\theta) = \theta_1 + \theta_2 - 1\) at -\(\theta = 0\): every interpolating step satisfies \(s_1 + s_2 = 1\). The -identity metric splits the correction evenly, \(s = (1/2, 1/2)\); the metric -\(M = \operatorname{diag}(1, 4)\) makes the second coordinate more expensive -and selects - -$$ -s = -P J^\top (J P J^\top)^{-1} r -= \frac{-r}{1 + 1/4}\begin{bmatrix}1\\[2pt]1/4\end{bmatrix} -= \begin{bmatrix}0.8\\[2pt]0.2\end{bmatrix}, -\qquad r = -1. -$$ - -With tiny damping, one `update` reproduces both: - -```python -import jax.numpy as jnp - -from nlls_gram import LevenbergMarquardt, metric_from_cholesky - - -def residual(theta, _, __): - return jnp.array([theta[0] + theta[1] - 1.0]) - - -theta0 = jnp.zeros(2) - -identity_solver = LevenbergMarquardt(residual, init_damping=1e-9) -x_identity, _, _ = identity_solver.update(theta0, identity_solver.init(theta0)) -# x_identity ≈ [0.5, 0.5] - -L = jnp.linalg.cholesky(jnp.diag(jnp.array([1.0, 4.0]))) -metric_solver = LevenbergMarquardt( - residual, init_damping=1e-9, metric=metric_from_cholesky(L) -) -x_metric, _, _ = metric_solver.update(theta0, metric_solver.init(theta0)) -# x_metric ≈ [0.8, 0.2] -``` - -## Scope of the Claim - -The minimum-norm statement is **local**: each small-damping step is the -minimum-\(M\)-norm correction to the *linearized* residual equations. -Nonlinear LM run to convergence does not globally solve -\(\min \|\theta\|_M\) subject to \(r(\theta) = 0\) — which root it reaches -depends on the initialization and the step history. The safe claims are that -near interpolation the steps are metric Gauss-Newton corrections, and that -the [implicit derivative](implicit_ad.md) at the returned -solution is exactly the minimum-\(M\)-norm tangent. diff --git a/docs/implicit_ad.md b/docs/implicit_ad.md index 2230515..9fe4811 100644 --- a/docs/implicit_ad.md +++ b/docs/implicit_ad.md @@ -1,587 +1,79 @@ -# Implicit Differentiation +# Implicit differentiation -`solve` has a custom implicit JVP/VJP with respect to `p` for the solved -parameters: +`solve(...).x` carries a custom JVP rule with respect to `p`, so gradients do +**not** unroll the LM iterations. They differentiate the converged root +through the implicit function theorem, at a cost independent of `max_steps`. -```python -solver.solve(x0, args, p=p).x -``` - -The custom rule is not defined on the per-step `update(...)` interface, and it -does not differentiate through the LM iterations. It differentiates the residual -equation at the returned solution. For implicit differentiation, use a fixed -`args` and read the differentiated value from `result.x`. - -Here `p` means the external pytree argument passed to the residual function: - -```python -residual_fn(x, args, p) -``` - -It does not mean LM hyperparameters such as `init_damping`, `max_steps`, -`atol`, callback choices, or metric callbacks. The custom rule treats `args` and -the initial guess `x0` as fixed for this derivative (their tangents are zero, -not an error). - -### Status policy and the initial AD point - -Implicit AD is defined for `LMStatus.CONVERGED` and, by default, -`LMStatus.MAX_STEPS`. The forgiving default supports fixed-step solves: a -result that exhausts its budget relinearizes at the returned -`(result.x, result.args, result.p)`, while its diagnostic status remains -`MAX_STEPS`. Pass `max_steps_is_success=False` to make `MAX_STEPS` strict: it -then follows the same failed-AD path as `NONFINITE`, `CALLBACK_STOP`, or any -other non-`CONVERGED` status. - -An AD-successful solve relinearizes at its returned values. A failed solve -keeps the primal result, status, aux, and diagnostics unchanged but returns -exactly zero tangents through `result.x` and `result.aux`. `result.p` remains -an independent identity pass-through. - -The failed lane's linear tangent program is evaluated at stop-gradient copies -of the caller's original `(x0, args, p)`, with the `p` tangent masked to zero -before the implicit solve. This gives automatic transposition a finite linear -program even when the returned failed iterate is nonfinite, and keeps a failed -lane from poisoning successful lanes under `vmap`. These initial values are a -safety point, not a fallback solution: the returned failed iterate is never -replaced. - -The original initial point must therefore be **JVP-safe**, not merely finite. -The residual and aux map must have valid derivatives there. A `MetricFactory` -must also be JVP-safe there when the resolved non-direct AD method consumes its -metric, and a `PreconditionerFactory` must be JVP-safe there when it supplies a -`gram_cg` AD preconditioner. A direct square AD solve ignores both factories, -so it does not rebuild aux for them. When a selected multi-start winner fails -the implicit-AD status policy, the safety point is the caller's original -`(x0, args, p)`, not one of the drawn starts; custom acceptance is independent. - -Aux is reevaluated for factory construction only when it is actually consumed: -a failed `MetricFactory` lane under a non-direct AD method, or a failed -`gram_cg` lane whose `PreconditionerFactory` supplies the AD preconditioner. -Fixed metrics, explicit AD preconditioners, and direct square solves do not -trigger that factory-only rebuild. An AD-successful lane always reuses -`result.aux` for factory construction. Independently, when `has_aux=True`, the -aux map is linearized once at the selected point to compute the returned aux -tangent itself. - -There is no setup stage that AD must trace through: the whole iteration — -every update, callback, and the final aux evaluation — sits inside one -`jax.custom_jvp` boundary, so derivative information flows only through the -implicit rule at the returned solution. `init` is differentiation-inert (its -outputs are constants whose shapes and dtypes come from one residual -evaluation), so calling it by hand inside a differentiated function, or -implicitly via `cache_jacobian=True`, contributes exactly zero to any -derivative. `result.aux` also participates in the implicit rule — see -[Aux outputs](#aux-outputs) below. One -construction-time caveat: the solver (including any `GramMetric` callbacks) is a -static object — do not build it from traced values. Constructing -`LevenbergMarquardt` *inside* a jitted function is supported: every -constructor argument is a static Python value (option strings, floats, -hooks) and the solver holds no arrays, so equal configurations share one -compilation. What must not happen is feeding a traced value into the -constructor, or rebuilding the *pieces* per call — an inline `lambda` -residual or a hook closed over fresh arrays keys a new compile by object -identity (see -[what is free to sweep](tuning_guide.md#what-is-free-to-sweep)). - -## Root Selection and the Metric - -In underdetermined interpolation problems there may be many roots -\(\theta\) satisfying - -$$ -r(\theta, a, p)=0, -$$ - -where \(a\) denotes fixed auxiliary data from `args`. A perturbation \(\dot p\) -does not determine a unique parameter tangent when the parameter dimension -exceeds the residual dimension: the linearized root constraint is - -$$ -J_\theta \dot\theta + J_p \dot p = 0, -$$ - -and any null-space vector \(z\) with \(J_\theta z=0\) can be added to a solution. -The metric \(M \succ 0\) selects the tangent with minimum metric norm: - -$$ -\dot\theta -= \arg\min_u \frac12 u^\top M u -\quad\text{subject to}\quad -J_\theta u = -J_p\dot p. -$$ - -This is why the metric matters for implicit AD: in underdetermined problems the -norm is part of the definition of the derivative of the selected solution -branch. With \(M=I\) this is the Euclidean minimum-norm tangent; with an RKHS or -kernel coefficient metric, it is the minimum RKHS-norm tangent. - -Let - -$$ -J_\theta = -\frac{\partial r}{\partial \theta}(\theta^\star, a, p) -\in \mathbb R^{m\times n}, -\qquad -J_p \dot p = -\frac{\partial r}{\partial p}(\theta^\star, a, p)\dot p -\in \mathbb R^m, -\qquad -P = M^{-1}. -$$ - -For a pytree `p`, \(J_p\dot p\) means the JAX JVP of the residual with respect -to the `p` argument only, evaluated at fixed \(\theta^\star\) and `args`. - -The Lagrange conditions for the minimum metric-norm problem give - -$$ -M\dot\theta + J_\theta^\top y = 0, -\qquad -J_\theta \dot\theta = -J_p\dot p, -$$ - -so - -$$ -\dot\theta -= -P J_\theta^\top -(J_\theta P J_\theta^\top)^{+} -J_p\dot p. -$$ - -In whitened variables — \(B = J_\theta S\) with \(S S^\top = P\) and -\(\dot\theta = S\dot u\) — the same tangent is the minimum-norm solution of - -$$ -B^\top B\,\dot u = -B^\top J_p\dot p, -\qquad -\dot u = -B^{+} J_p\dot p, -\qquad -\dot\theta = S\,\dot u, -$$ - -using \((B^\top B)^{+}B^\top = B^{+}\). In code, the **dense** AD rule -computes exactly this: it materializes \(B\) and applies \(B^{+}\) from its -SVD. The **gram_cg** rule solves the \(m \times m\) dual system above -matrix-free, applying \(P x\) with `metric.solve(x)` when available, else as -\(P x = S S^\top x\) through the square-root callbacks; the **normal_cg** -rule solves the whitened normal system matrix-free through -`metric.inv_sqrt`/`inv_sqrt_transpose`. - -### Iterate-Dependent Metrics Are Frozen per Solve - -With an iterate-dependent metric (`metric_factory=`), the metric is FROZEN at -the returned solution: `prepare`/`build` run once at -`(result.x, result.args, result.p, result.aux)` and the resulting \(P\) is -applied exactly as a fixed metric would be. The state-dependence of the metric -is deliberately not differentiated — the same contract as a fixed metric -closing over constants, matching the forward selection role the metric plays. -The built metric must stay self-adjoint and positive definite for that fixed -state. - -The freeze is a **first-order** statement. Each first-order implicit solve -applies the metric frozen at *its* solution — the verified contract -(first-order forward and reverse mode, fixed or factory-built metric). The -tangent field \(p \mapsto \dot\theta(p)\) so defined uses, at every \(p\), -the metric rebuilt at that point's solution. But **higher-order AD through -a factory-built metric's state dependence is unsupported in every AD rule**: -the metric-aware assembled and CG methods alike apply the frozen metric through -identity-matvec `custom_linear_solve` wrappers whose declared solves are -opaque to AD, so second derivatives do not account for the metric's point -dependence. Take higher-order derivatives of `solve` only with a fixed -metric (subject also to the spectral-filter caveat in -[the rank-deficiency section](#rank-deficiency-and-the-ridge)). Those same wrappers -declare each metric's transpose explicitly, so first-order reverse mode is -correct even when `inv_sqrt` is not reverse-differentiable but -`inv_sqrt_transpose` is supplied. - -## The AD Solver - -`ad_solver` selects how the implicit tangent and cotangent systems are -solved. Each method name selects exactly one algorithm: - -- **`direct`** assembles the general square Jacobian and solves - \(J_\theta\dot\theta=-J_p\dot p\) with `jnp.linalg.solve`. It is the - inexpensive choice for a square, nonsingular root and gives the correct - transpose solve in VJP even when \(J_\theta\) is nonsymmetric. A unique - square root has no metric-dependent tangent selection, so `direct` - intentionally ignores the metric. It rejects nonsquare systems. -- **`svd`** assembles the whitened Jacobian \(B=J_\theta S\) and applies its - spectral pseudoinverse. It is the robust dense choice for rank-deficient or - nearly rank-deficient problems and returns the minimum-\(M\)-norm tangent. -- **`qr`** factors the same \(B\) without regularization. It is cheaper than - SVD at full numerical rank and fails loudly with a NaN tangent when the - rank guard detects deficiency. -- **`augmented_qr`** factors - \([B;\sqrt{\delta}I]\), where - \(\delta=\texttt{ad\_solver\_penalty}\operatorname{tr}(B^\top B)\). - This is the explicitly regularized dense method. -- **`gram_cg`** applies \(J_\theta P J_\theta^\top\) matrix-free and solves - the residual-space system with CG. -- **`normal_cg`** applies \(B^\top B\) matrix-free. Its tangent right-hand - side lies in \(\operatorname{range}(B^\top)\), so CG from zero selects the - minimum-norm tangent without a ridge. -- **`regularized_normal_cg`** is the explicit matrix-free regularized method. - It scales its ridge by a Rayleigh quotient of \(B^\top B\) over a fixed - deterministic probe so the tangent remains linear in \(\dot p\). - -The default `ad_solver="auto"` dispatches from traced shapes first: - -| traced system / forward `linear_solver` | `auto` resolves to | -| --- | --- | -| square, for every forward solver | `direct` | -| nonsquare with `gram_cg` forward | `gram_cg` | -| nonsquare with `normal_cg` forward | `normal_cg` | -| any other nonsquare system | `svd` | - -The shape-first rule matters: a square algebraic system gets the direct -solve even if its primal step used CG. The AD method is otherwise independent -of the forward solver, so an `lsmr` forward with explicit -`ad_solver="normal_cg"` remains matrix-free end to end. - -The SVD and QR methods work from \(B\), never from a formed squared operator, -so their numerical accuracy is governed by \(\operatorname{cond}(B)\), not -\(\operatorname{cond}(B)^2\). They assemble the Jacobian from its small side; -see [`jacobian_mode`](tuning_guide.md#jacobian-assembly-jacobian_mode). -`direct`, `svd`, `qr`, and `augmented_qr` inherit `linear_solve_dtype`. - -For `normal_cg`, reverse mode cannot simply reuse CG on a possibly singular -normal operator with an arbitrary cotangent. Its declared transpose uses the -push-through identity \(N^+=B^\top(BB^\top)^{+2}B\), which keeps both dual -solves consistent. The final metric-square-root application declares -`inv_sqrt_transpose` explicitly, so triangular and other non-self-adjoint -square roots transpose correctly. - -Both CG forms assume the inner solve **converges**. -`jax.lax.custom_linear_solve` transposes the declared solve as an exact -linear map, but a truncated or early-stopped CG (a small bounded -`ad_solver_maxiter`) is not a linear function of its right-hand side — its -declared transpose then no longer matches what was computed, and -derivatives are silently inaccurate on top of the truncation error itself. -Run the AD CG solves to tolerance (the default -`ad_solver_maxiter=None`), and treat a bounded budget as valid only with a -preconditioner exact enough to converge within it. +## The rule -The undamped implicit system is often the most conditioning-sensitive solve in -the library. `linear_solve_dtype=jnp.float64` promotes the assembled AD methods -while leaving model inputs and returned tangents at their original dtype. - -### The AD Solver Preconditioner - -An explicit `gram_cg` AD method requires an `ad_solver_preconditioner` at -construction. With `ad_solver="auto"`, the requirement is checked when a -differentiated nonsquare forward `gram_cg` solve is traced; a square system -has already resolved to `direct`. The hook approximates the undamped -residual-space \((J_\theta P J_\theta^\top)^{-1} v\) on \(m\)-vectors, and -a forward `preconditioner_factory`'s state at the solution serves as the -default when no explicit hook is given. Under `normal_cg` the hook is -**optional**: the tangent right-hand side lies in -\(\operatorname{range}(B^\top)\), so unpreconditioned CG already selects -the minimum-norm tangent. A hook supplied there acts in *parameter* space — -an approximation of the undamped \((B^\top B)^{-1} v\) on \(n\)-vectors — -and on rank-deficient problems it must preserve -\(\operatorname{range}(B^\top)\), the same structural requirement as the -forward -[`normal_preconditioner`](utilities.md#the-normal-space-preconditioner-normal_cg); -the dual-space factory can never serve this parameter-space system. The -assembled methods use no preconditioner. - -The callback may take `(v)` or `(v, damping)`: a callable *requiring* the -damping argument is called with an explicit zero damping (the implicit -system is undamped), and one whose damping has a default passes through -unchanged — so `identity_preconditioner()`, -`sherman_morrison_preconditioner`, `woodbury_preconditioner`, and -`nystrom_preconditioner` all serve the hook directly. The one exception -is `pad_dual_preconditioner`, which divides by the live damping and is -rejected at construction. Pass `identity_preconditioner()` to run the -AD CG unpreconditioned, or `ad_solver="svd"` to use the assembled -pseudoinverse instead. The forward `dual_preconditioner` is never reused for AD: -it approximates the damped operator, and the implicit system is undamped — -reusing one is an explicit choice (pass the same callable to both -arguments). Any `ad_solver_preconditioner` must be linear, self-adjoint, and -positive definite for the operator of its resolved space, and the metric -inverse \(P\) must be linear, self-adjoint, and positive definite in -parameter space. - -## Rank Deficiency and the Ridge - -One invariant holds package-wide: **no default applies a ridge to an implicit -tangent solve.** Regularization requires an explicit algorithm name and an -explicit positive penalty. The primal solve's only regularizer remains the LM -damping itself. - -The implicit system is intentionally not damped — damping would change the -minimum-\(M\)-norm derivative. What happens on a rank-deficient system -depends on consistency, and interpolation problems produce **consistent** -linearized systems by construction: differentiating the root identity -\(r(\theta^\star(p), a, p) = 0\) along the solution branch gives -\(J_\theta\dot\theta^\star + J_p\dot p = 0\), i.e. -\(J_p\dot p \in \operatorname{range}(J_\theta)\) — redundant rows and -collinear columns included. The methods behave as follows: - -- **`direct`** is exact for a nonsingular square Jacobian and fails through the - underlying solve when the Jacobian is singular. -- **`svd`** applies \(B^+\) at the standard cutoff - \(\max(m,n)\,\mathrm{eps}\,\sigma_{\max}\). This is the robust choice for - a consistent rank-deficient system. The cutoff is numerical, so meaningful - singular values below it are treated as null directions. Higher derivatives - are exact only while the active singular subspace is locally constant. -- **`qr`** is exact at full numerical rank and returns NaNs when its rank guard - detects deficiency. -- **`augmented_qr`** is smooth across rank changes but biased by - O(`ad_solver_penalty` · dimension). Typical starting penalties are `1e-12` - in float64 and `1e-6` in float32. -- **`gram_cg`** is unregularized and can fail on a singular dual even when the - primal tangent equation is consistent. A small fixed iteration budget can - instead return a finite but inaccurate answer, so run it to tolerance. -- **`normal_cg`** remains unregularized and converges to the minimum-norm - tangent on singular-but-consistent systems in exact arithmetic. -- **`regularized_normal_cg`** supplies the explicit matrix-free ridge. - -`ad_solver_penalty` is required and must be positive for `augmented_qr` and -`regularized_normal_cg`. It is rejected for every other method, including -`auto`; it never switches algorithms. - -**Gauss–Newton semantics on inconsistent systems.** When the returned -point is a least-squares stationary point with nonzero residual rather than -an exact root, \(J_p\dot p\) need not lie in -\(\operatorname{range}(J_\theta)\). The default rules still return a finite -answer — the minimum-\(M\)-norm **Gauss–Newton sensitivity of the -linearized system**: the normal equations -\(B^\top B\dot u = -B^\top J_p\dot p\) are consistent regardless (any -\(B^\top\)-image is), and \(B^{+}\) applies their minimum-norm solution -directly. That tangent is *not* the exact optimizer -sensitivity — the exact derivative of a nonzero-residual stationary point -carries residual-weighted second-derivative (curvature) terms that the -frozen-Jacobian system drops. A one-line counterexample: -\(r(x, p) = (x - p,\ x^2 - 1)\) at the stationary point \(x = 0.5\), -\(p = -0.25\) has exact sensitivity \(dx/dp = 2\), while the Gauss–Newton -normal system gives \(0.5\). The implicit rules are exact at interpolating -(zero-residual) roots — the package's target — and Gauss–Newton -approximations away from them. The non-default modes differ: an opt-in -ridge returns a penalty-inflated finite tangent, and -`gram_cg` fails loudly (its Krylov solve faces the singular-inconsistent -dual). - -GramMetric callback requirements follow the factorization each form uses. -`svd`, `qr`, `augmented_qr`, `normal_cg`, and `regularized_normal_cg` work in -whitened variables and need the -square-root pair `metric.inv_sqrt`/`inv_sqrt_transpose`; the final -\(S\dot u\) map is not self-adjoint and declares that true transpose pair, -so triangular Cholesky factors differentiate correctly in reverse mode. -`direct` does not use the metric. `gram_cg` needs only `metric.solve`, and only ever *evaluates* it: the -final \(P J_\theta^\top y\) application acts on tangent data, and its -transpose in the VJP is declared to be \(P\) itself (a symmetric -`jax.lax.custom_linear_solve`, which also batches under `jax.vmap`). That -is what lets a hand-written iterative, solve-only `GramMetric.solve` participate -in both JVP and VJP even though transposing through JAX's CG is unsupported: -pair such a metric with `ad_solver="gram_cg"`. - -Accuracy of the CG forms is controlled separately from the forward -iterative solve: - -- `ad_solver_tol=None` uses a dtype-aware default (`1e-6` in float32, `1e-10` - in float64), chosen for derivative accuracy rather than forward-step speed. - The same attainable-floor bound as any CG applies: the residual stagnates - near `machine_eps` times the operator's condition number, so at small - `eps` (spike weight \(c^2/\varepsilon\)) the float64 default is reachable - only with the spike preconditioner below. -- `ad_solver_atol=0.0` and `ad_solver_maxiter=None` are passed to JAX CG. - `None` leaves the iteration budget to JAX's CG policy. -- `ad_solver_preconditioner` is deliberately a separate argument from the - forward preconditioner hooks — see - [above](#the-ad-solver-preconditioner). - -For the -[repeated shifted metric](gauss_newton.md#shifted-metrics-and-the-seminorm-limit) -\(M = \operatorname{blockdiag}(K, 0) + \varepsilon I\): - -- The scalar block injects its rank-\(k\) spike of weight \(c^2/\varepsilon\) - into the *undamped* implicit dual operator too — there is no LM damping - here to mask it — so at small \(\varepsilon\) a `gram_cg` AD solve - needs the same - [Sherman–Morrison/Woodbury spike preconditioner](utilities.md#shermanmorrison-dual-preconditioner) - as the forward solve — pass the helper directly; the AD hook calls - it with zero damping. -Example sketch for a large matrix-free residual: - -```python -from nlls_gram import LevenbergMarquardt - - -def residual(theta, _, p): - # `features(theta)` is evaluated by JVP/VJP closures; no dense Jacobian is - # formed by the forward CG solve or the CG-based AD rule. - return features(theta) - p - - -def ad_solver_preconditioner(v): - return approximate_undamped_dual_solve(v) - - -solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - iterative_tol=1e-3, - iterative_maxiter=20, - dual_preconditioner=identity_preconditioner(), - ad_solver="auto", - ad_solver_tol=None, - ad_solver_preconditioner=ad_solver_preconditioner, -) -``` - -## VJP - -JAX derives the VJP by automatically transposing this solver's linear custom -JVP rule; there is no separate custom VJP or cotangent solver. Writing -\(K=J_p\), \(G=J_\theta P J_\theta^\top\), and using the same pseudoinverse or -filtered solve as the JVP, the maps are +For a root \(r(x, a, p) = 0\) with \(J = r_x\) and \(K = r_p\), differentiating +gives \(J\,\dot x = -K\,\dot p\). That is underdetermined at an interpolating +root, and the metric picks the solution: with \(W = F^\top F\) and +\(B = JF^{-1}\), $$ -\dot\theta=-P J_\theta^\top G^+ K\dot p, -\qquad -\bar p=-K^\top G^+ J_\theta P\bar\theta. +\dot x = -F^{-1}B^{+}K\dot p , $$ -Equivalently, for a cotangent \(\bar\theta\) on `result.x`, solve +the **minimum-\(W\)-norm** tangent — the same selection the forward solve +makes, so the derivative is consistent with the solution it differentiates. +For `RidgeLevenbergMarquardt` the ridge makes the system positive definite and +the rule is the plain solve of \((\tilde J^\top\tilde J + \lambda E)\dot y = +-\tilde J^\top K\dot p\). -$$ -(J_\theta P J_\theta^\top)y = J_\theta P\bar\theta, -\qquad -\bar p = -J_p^\top y. -$$ +Reverse mode comes from JAX transposing that linear tangent program, so `grad`, +`vjp`, `hessian`, and `vmap` all work without a separate implementation. -For the square direct method, the JVP solves -\(J_\theta\dot\theta=-K\dot p\). Its automatically transposed VJP solves -\(J_\theta^\top\lambda=\bar\theta\) and returns -\(\bar p=-K^\top\lambda\). +## Choosing an `ad_solver` -For a pytree `p`, \(J_p^\top y\) means the JAX VJP of the residual with respect -to the `p` argument only. The whitened rules compute the identical cotangent -by transposing the whitened map instead — the `svd` rule through -\((B^{+})^\top\) from the same factorization, the unridged `normal_cg` rule -through its declared push-through transpose, since a cotangent right-hand -side need not lie in \(\operatorname{range}(B^\top)\). Rank-deficient -systems behave as in [the ridge section](#rank-deficiency-and-the-ridge): -the VJP applies the transpose of the same regularized, filtered, or exact -solve the JVP uses. - -Example: - -```python -import jax -import jax.numpy as jnp +`None`, the default, matches the forward family. Override it when the shape +or the rank says otherwise — see +[Metric LM](metric_lm.md#rank-deficiency-and-implicit-ad) for the table of +which rule is valid where. The short version: -from nlls_gram import LevenbergMarquardt +- `SVD()` whenever the undamped system is singular by construction — padded + zero residuals are the common case; +- `GramCG(precond)` for \(m \le n\) and `CG(precond)` for \(n \le m\) when the + forward solve is matrix-free and you want the tangent to stay so; +- `Cholesky()` otherwise. +A Krylov rule used outside its valid shape raises rather than returning a +quietly wrong tangent. -# p without args still uses the three-argument form; the second argument is -# simply ignored. -def residual(theta, _, p): - return jnp.array([theta[0] + 2.0 * theta[1] - p]) +## Frozen hooks +Under differentiation the metric's and preconditioner's `prepare` run **once, +at the returned solution**, and their state-dependence is not differentiated — +the same contract as a fixed metric closing over constants. The solver state +rides along as inert conditioning data under `stop_gradient`. -solver = LevenbergMarquardt(residual, init_damping=1e-2) -theta0 = jnp.zeros(2) +## Failed solves +Implicit AD uses `CONVERGED`, and also `MAX_STEPS` when +`max_steps_is_success=True` (the default). Every other status returns **exact +zero tangents** for `result.x` and `result.aux`. To keep automatic VJP +transposition finite under `vmap`, a failed lane's linear tangent program is +evaluated at differentiation-inert copies of the original `(x0, args, p)`, so +those initial values must be valid for JVP evaluation of the residual. The +primal failed result is never replaced. -def solved_x(p): - return solver.solve(theta0, p=p, max_steps=80, atol=1e-6).x - - -theta, theta_dot = jax.jvp( - solved_x, - (jnp.asarray(3.0),), - (jnp.asarray(0.7),), -) - -theta, pullback = jax.vjp(solved_x, jnp.asarray(3.0)) -(p_bar,) = pullback(jnp.array([3.0, 4.0])) -``` - -Here \(J_\theta=[1,2]\), so the identity-metric tangent is -\(\dot\theta = [1,2]\dot p / 5\), and the VJP maps -\(\bar\theta\) to \((\bar\theta_0 + 2\bar\theta_1)/5\). +`x0` gets exactly zero tangent by contract: the returned root is a property of +the problem, not of where the search started. ## Aux outputs -With `has_aux=True` the residual returns \((r, a)\); write the aux output map -as - -$$ -a = g(\theta, \text{args}, p), -\qquad -a = g(\theta^\star, \text{args}, p) -\text{ at the returned solution,} -$$ - -and define its two Jacobians at the solution (with \(k\) the flattened aux -dimension): - -$$ -G_\theta = \frac{\partial g}{\partial \theta}(\theta^\star, \text{args}, p) -\in \mathbb R^{k \times n}, -\qquad -G_p = \frac{\partial g}{\partial p}(\theta^\star, \text{args}, p) -\in \mathbb R^{k \times \dim p}. -$$ - -For a pytree aux/`p`, \(G_\theta \dot\theta\) and \(G_p \dot p\) mean the JAX -JVP of the aux output with respect to that argument only (the same convention -as \(J_p \dot p\) above); transposes mean the corresponding VJP. - -`p` moves the aux through both paths — directly, and through the solution -\(\theta^\star(p)\) — and the implicit rule accounts for both. **JVP**: with -\(\dot\theta\) the minimum-\(M\)-norm implicit tangent above, - -$$ -\dot a = G_\theta\,\dot\theta + G_p\,\dot p -= \bigl(-G_\theta P J_\theta^\top (J_\theta P J_\theta^\top)^{+} J_p - + G_p\bigr)\,\dot p. -$$ - -**VJP**: cotangents \(\bar\theta\) on `result.x` and \(\bar a\) on -`result.aux` combine — the aux cotangent pulls back through -\(G_\theta^\top\) into the solution cotangent and through \(G_p^\top\) -directly: - -$$ -y=(J_\theta P J_\theta^\top)^+ -J_\theta P\,(\bar\theta + G_\theta^\top \bar a), -\qquad -\bar p = -J_p^\top y + G_p^\top \bar a. -$$ - -Setting \(\bar a = 0\) recovers the `x`-only VJP above; setting -\(\bar\theta = 0\) gives the pure aux pullback. - -On a failed solve both \(\dot\theta\) and \(\dot a\) are masked to exact zero -after this tangent program is evaluated at the original JVP-safe initial -point. Automatic transposition therefore contributes zero implicit cotangents -from `result.x` and `result.aux`, while any cotangent on the independently -returned `result.p` still passes through unchanged. - -Example — the residual from above with an aux that depends on `p` both ways: +With `has_aux=True`, `result.aux` is evaluated at the returned `(x, args, p)` +and is differentiable with respect to `p` both directly and through +\(x^*(p)\). ```python -def residual(theta, _, p): - r = jnp.array([theta[0] + 2.0 * theta[1] - p]) - return r, {"m": theta[0] * theta[1] + p**2} - - -solver = LevenbergMarquardt(residual, init_damping=1e-2, has_aux=True) - - -def solved_aux_m(p): - return solver.solve(jnp.zeros(2), p=p, max_steps=80, atol=1e-6).aux["m"] - +def residual(x, args, p): + value = model_residual(x, args, p) + return value, {"fit": summary(x, p)} -da_dp = jax.grad(solved_aux_m)(jnp.asarray(3.0)) +solver = LevenbergMarquardt(residual, has_aux=True) +grad = jax.grad(lambda p: solver.solve(x0, args, p=p, atol=1e-8).aux["fit"])(p) ``` -Here \(\theta^\star = (p/5, 2p/5)\), so the aux value is -\(2p^2/25 + p^2\) and its derivative is \(4p/25 + 2p = 6.48\) at \(p=3\): -the \(4p/25\) comes through the solution path \(G_\theta\dot\theta\) and the -\(2p\) through the direct path \(G_p\dot p\). +`args`, `user_state`, the histories, and the multi-start diagnostics are all +differentiation-inert. diff --git a/docs/index.md b/docs/index.md index 808438a..58a5ded 100644 --- a/docs/index.md +++ b/docs/index.md @@ -1,635 +1,105 @@ # nlls_gram -`nlls_gram` provides metric-aware Levenberg-Marquardt nonlinear least-squares for -JAX pytrees, aimed at solving systems of equations (i.e., interpolation). The -core use cases are underdetermined systems — more parameters than residuals — -where LM is solved in its Gram form, and square or redundant tall nonlinear -systems where regularization is needed to select among the interpolating -solutions, with the selection controlled by a user-chosen metric. +Levenberg-Marquardt nonlinear least squares for JAX, built for +**underdetermined interpolation**: problems whose residual has many more +parameters than equations, so a zero-residual root is not unique and *which* +root you get is part of the contract. -The solver is intentionally small: users provide `residual_fn(x, args, p)`, -and `LevenbergMarquardt` exposes `init()`, `update(...)`, and -`solve(...)`. It does not depend on Flax, NNX, Optax, or any model framework. +Two solvers differ in where that selection lives. -## Install +| | `RidgeLevenbergMarquardt` | `LevenbergMarquardt` | +|---|---|---| +| minimizes | \(\|r(x)\|^2 + \lambda\,\|x_m\|_W^2\) | \(\|r(x)\|^2\) | +| selection lives in | the **objective** | the **damping geometry** | +| converges to | the minimum-\(W\)-seminorm interpolant | the minimum-\(W\)-norm correction limit | +| use when | the interpolant is the deliverable | the root is a means to an end | -```bash -uv add nlls-gram -``` +Both share one `init`/`update`/`solve` protocol, one `Metric`, one linear-solver +menu, and one implicit-AD contract. -For accelerator use, install the JAX build matching your hardware alongside -`nlls-gram`, for example: +## Install ```bash -uv add nlls-gram "jax[cuda13]" -``` - -## Residual and Data Interface - -The residual function takes one, two, or three positional arguments — always -in this order: - -```python -residual_fn(x) # closes over its data -residual_fn(x, args) -residual_fn(x, args, p) +uv add nlls-gram # or: pip install nlls-gram ``` -- `x` is the pytree optimized by LM. -- `args` is arbitrary auxiliary data passed to `update(...)` or `solve(...)`. -- `p` is optional read-only data, useful for fixed deep parameters or outer - perturbations; the implicit differentiation of `solve` is with respect to - `p`, so that requires the three-argument form. - -`args` and `p` may be any JAX pytree. The arity is inspected once at -construction and the function is wrapped into the canonical three-argument -form, so the compiled code is identical for all three; callables whose -signature cannot be inspected (or that take `*args`) are assumed to take all -three. The order is fixed: a two-argument residual always means -`(x, args)` — to use `p` without `args`, write the three-argument form and -ignore the second argument. Passing `args` or `p` to `update`/`solve` when the -residual does not accept it raises a `ValueError` rather than silently -dropping it. - -`update(x, lm_state, args=None, p=None)` performs one LM step. The higher-level -`solve(x0, args=None, *, p=None, ...)` loop repeatedly calls `update` and -returns an `LMSolveResult`. Pass `save_steps=True` to also record the full -iterate history on the result (`x_history`, plus the row-aligned -`args_history` and, with `has_aux=True`, `aux_history`) — see -[history recording](callbacks.md#fixed-size-history-recording) for the layout -and a plotting recipe. Pass `multi_start=MultiStart(...)` to retry failed -solves from fresh initial conditions or race several starts under `vmap`, -returning the single best result — see [multi-start](multi_start.md). - -### Auxiliary Outputs (`has_aux`) - -With `has_aux=True` (the same convention as Optimistix and `jax.grad`), the -residual returns a pair `(residual, aux)`, where `aux` is a pytree of extra -outputs the optimizer ignores — per-block diagnostics, validation metrics, -anything already computed inside the residual. Its structure is arbitrary, -but every leaf must be a JAX numeric type (an array, or a Python/NumPy -scalar), with fixed shape and dtype across iterations like any jitted value: -aux rides through the jitted solve loop and the implicit differentiation -rule, so a non-numeric leaf such as a string raises a `TypeError` at the -first evaluation. For example: - -```python -def residual_fn(x, args): - r = model(x, args) - return r, {"max_abs": jnp.max(jnp.abs(r))} - - -solver = LevenbergMarquardt(residual_fn, has_aux=True) -``` - -Each step's `LMInfo.aux` holds the aux from the residual evaluation at the -**pre-step** `x` (the linearization point — same convention as `loss_old` -and `grad_norm`), at no extra cost; callbacks read it as `ctx.info.aux`, -e.g. to early-stop on a diagnostic. The solve result additionally carries -`result.aux`: the aux evaluated at the returned `(result.x, result.args, result.p)` -with one extra residual evaluation after the loop. This is well-defined for -every status — the returned `x` is always the last accepted iterate — so it -holds the final diagnostics whether or not the solve converged, and it -participates in the implicit differentiation with respect to `p` (see -[Aux outputs](implicit_ad.md#aux-outputs)). With -`has_aux=False`, both are `None` and nothing is added to the compiled -program. - -Callbacks passed to `solve` can replace `args` for later iterations, for example -to regenerate collocation points or refresh simulation data. They receive `p` -but cannot replace it; this keeps the optimized solution's dependence on -external parameters explicit for implicit differentiation. - -## Mathematical Contract - -At a parameter vector \(\theta\), let - -- \(r \in \mathbb R^m\) be the flattened residual, -- \(J \in \mathbb R^{m \times n}\) be the Jacobian with respect to the flattened - parameter vector, -- \(s \in \mathbb R^n\) be the proposed step, -- \(\lambda > 0\) be the current damping scalar, -- \(M \succ 0\) be the parameter-space metric. - -Each linear solver targets the same metric-damped LM subproblem: - -$$ -\min_s \frac12\|r + Js\|_2^2 + \frac{\lambda}{2}s^\top M s. -$$ - -The normal equations are - -$$ -(J^\top J + \lambda M)s = -J^\top r. -$$ - -The default metric is \(M=I\), which recovers the usual Euclidean LM damping. -For kernel coefficient problems, - -$$ -f_\alpha(x)=\sum_{j=1}^n \alpha_j K(x,x_j) -$$ - -has RKHS norm - -$$ -\|f_\alpha\|_{\mathcal H_K}^2 = \alpha^\top K\alpha, -$$ - -so the natural parameter metric is \(M=K\). - -The actual nonlinear step is accepted only if the unregularized residual sum of -squares decreases. On acceptance, damping is multiplied by `damping_decrease`; -on rejection, it is multiplied by `damping_increase`. `min_damping=None` -clamps it to the smallest positive normal value of the residual dtype, avoiding -backend flush-to-zero behavior without imposing a larger regularization floor. - -Near the interpolation threshold, small-damping LM becomes metric -Gauss-Newton, whose step is the minimum-\(M\)-norm solution of the linearized -residual equations; large damping is steepest descent in the \(M\)-metric. -[Metric Gauss-Newton and Minimum-Norm Steps](gauss_newton.md) derives both -limits, the spectral-filter view, and the kernel/RKHS metric choices. - -## Metrics +JAX is the only dependency. -A custom positive-definite parameter-space metric is passed as a single -`metric=GramMetric(...)` argument. See [Gram Metrics](metrics.md) for the -`GramMetric` callback contract and validation rules. The public -constructors cover dense, diagonal, and repeated shifted kernel metrics, -including a structured state-space representation that does not materialize -the kernel Gram. For a metric that depends on the current iterate or on -residual aux outputs, pass a `metric_factory=MetricFactory(prepare, build)` -instead — the state is rebuilt once per accepted step and `build` returns a -plain `GramMetric` -([Iterate-Dependent Metrics](metrics.md#iterate-dependent-metrics-metricfactory)). -(The ridge solver's `Metric` — factor callbacks for \(W = F^\top F\) on the -metric block — is a different contract, documented on the -[Ridge LM page](ridge_lm.md#the-metric-interface).) +## Residual interface -## Linear Solver Formulas +`residual_fn` takes `(x)`, `(x, args)`, or `(x, args, p)` — always in that +order — and returns a residual pytree, or `(residual, aux)` with +`has_aux=True`. `x` is any JAX pytree. -`linear_solver` selects among eight forms. Two families share the dense and -matrix-free slots: the **Gram** forms work in residual space on the -\(m \times m\) dual \(J P J^\top + \lambda I\), the **normal** forms in -parameter space on the \(n \times n\) whitened system -\(B^\top B + \lambda I\) with \(B = J S\), \(S S^\top = P\). For -\(\lambda > 0\) the two families produce the *same step* (the push-through -identity below); they differ in which dimension they factor or iterate in -and in which metric callbacks they need. - -### Auto - -`linear_solver="auto"` (the default) resolves to one of the two dense forms -at trace time, when the residual and parameter shapes are concrete: -`gram_cholesky` when \(n > m\) (strictly more parameters than residuals), -`normal_cholesky` otherwise. It factors the smaller of the two SPD systems. -The rule keys on shape only — it never inspects numerical rank — and since -both forms compute the same step, `auto` is a cost choice, not a semantics -choice. The resolution is a plain Python branch during tracing: one compiled -program per problem shape, no runtime branching. - -### Gram Cholesky - -`linear_solver="gram_cholesky"` materializes \(J^\top\), applies -`metric.solve`, and factors the residual-space dual system - -$$ -(J P J^\top + \lambda I_m)y = r, -\qquad s = -P J^\top y. -$$ - -This is the fastest dense path when \(m \ll n\): the factorization is -\(m \times m\) and \(n\) enters only through matvecs. - -### Normal Cholesky - -`linear_solver="normal_cholesky"` materializes -\(B^\top = S^\top J^\top\) via `metric.inv_sqrt_transpose` and factors the -whitened normal system in parameter space: - -$$ -(B^\top B + \lambda I_n)u = -B^\top r, -\qquad s = S u. -$$ - -The factorization is \(n \times n\), so this is the dense form for -square-to-tall problems (\(m \ge n\)). For \(\lambda > 0\) the step is -identical to the Gram form's by the push-through identity - -$$ -B^\top(B B^\top + \lambda I_m)^{-1} = (B^\top B + \lambda I_n)^{-1}B^\top, -$$ - -and its \(\lambda \to 0\) limit is the minimum-\(M\)-norm least-squares step -\(s = -S(JS)^{+}r\) at every shape and rank — tall problems that are still -rank-deficient along some directions (redundant rows, collinear columns) -keep the minimum-norm selection. See -[the pseudoinverse limit](gauss_newton.md#spectral-filter-view). - -### Gram CG - -`linear_solver="gram_cg"` applies the residual-space dual system matrix-free: - -$$ -y \mapsto J P J^\top y + \lambda y, -$$ - -using JAX linearization for JVPs/VJPs and `jax.scipy.sparse.linalg.cg`. -The iterative solve defaults to a small fixed budget: `iterative_tol=0.0`, -`iterative_atol=0.0`, and `iterative_maxiter=8`. -With the default `ad_solver="auto"`, differentiating a nonsquare -`solve(...).x` also stays matrix-free for forward `gram_cg` solves; a square -system resolves to `direct`. Pass `ad_solver="svd"` to use the robust -assembled pseudoinverse instead. - -`linear_solver="gram_cg"` requires a `dual_preconditioner(v, damping)` -callback, applied as the CG preconditioner (for the geodesic-acceleration -solve as well). It must be a jit-traceable, linear, SPD approximation of -\((J P J^\top + \lambda I)^{-1} v\). It never changes the subproblem being -solved: at inner convergence the step is identical, and a budget-truncated -step still lies in \(\operatorname{range}(P J^\top)\), preserving the -minimum-metric-norm structure — so approximations are safe. Nobody should -run Krylov methods without thinking about preconditioning; to opt out -explicitly, pass `identity_preconditioner()` for unpreconditioned CG. When -the AD solver resolves to `gram_cg` (the default -`ad_solver="auto"` does exactly that for a nonsquare -`linear_solver="gram_cg"` system), -an `ad_solver_preconditioner` is required as well — -`identity_preconditioner()` works there too, or pass -`ad_solver="svd"` for the assembled SVD rule. (A `normal_cg`-resolved -AD solve needs no preconditioner; see -[Implicit AD](implicit_ad.md#the-ad-solver-preconditioner).) See -[Utilities](utilities.md) for structural constructors -(`sherman_morrison_preconditioner`, `woodbury_preconditioner`) and the -randomized `nystrom_preconditioner`. Like `metric`, the preconditioner -*callable* is static configuration: it is not carried in `LMState` and no -callback action can replace it — construct a new solver to change one. A -`preconditioner_factory` is the exception in the other direction: the callable -pair stays static, but its *prepared state* (`precond`/`precond_valid`, rebuilt -from the live iterate each accepted step) IS carried on `LMState`, so a `solve` -callback that rebuilds `lm_state` must preserve those two fields. -`dual_preconditioner`, `preconditioner_factory`, and `recycle` are -`gram_cg`-only hooks — they live in residual space. - -### Normal CG - -`linear_solver="normal_cg"` applies the whitened normal system matrix-free: - -$$ -u \mapsto B^\top(B u) + \lambda u, -\qquad B u = J(S u),\quad B^\top w = S^\top(J^\top w), -$$ - -with right-hand side \(-B^\top r\) and step \(s = S u\), through the same -JVP/VJP closures and `jax.scipy.sparse.linalg.cg` machinery as `gram_cg` — -but the Krylov iteration lives in the \(n\)-dimensional parameter space, so -it is the matrix-free form for square-to-tall problems. It requires the -metric's `inv_sqrt`/`inv_sqrt_transpose` and a -`normal_preconditioner(v, damping)` callback: a jit-traceable, linear, SPD -parameter-space approximation of \((B^\top B + \lambda I_n)^{-1}v\) -(`identity_preconditioner()` is the explicit opt-out). One structural -requirement has no Gram-side analogue: the preconditioner must map -\(\operatorname{range}(B^\top)\) into itself, or the minimum-norm selection -is silently lost on rank-deficient problems — see the -[normal-space preconditioner](utilities.md#the-normal-space-preconditioner-normal_cg) -for why, and for which constructions are safe. - -### QR - -`linear_solver="qr"` uses the square-root metric form. With \(s = Sz\), solve - -$$ -\min_z \frac12\|r + JSz\|_2^2 + \frac{\lambda}{2}\|z\|_2^2. -$$ - -The implementation materializes \(S^\top J^\top\) via -`metric.inv_sqrt_transpose(J.T)` and solves the resulting augmented QR problem. -The returned parameter step is mapped back with `metric.inv_sqrt`. - -The triangular solves require \(S^\top J^\top\) to have full column rank -(equivalently, \(J\) full row rank): a rank-deficient Jacobian produces a -non-finite step even though the damped subproblem remains well-posed. Every -other solver handles rank deficiency — the Gram/normal forms through their -damped SPD systems, `augmented_qr` / `lsmr` through the damping block that -keeps the augmented matrix full column rank for \(\lambda>0\). - -### Augmented QR - -`linear_solver="augmented_qr"` directly factors the whitened augmented system - -$$ -\begin{bmatrix}JS\\\sqrt{\lambda}I\end{bmatrix}z -\approx -\begin{bmatrix}-r\\0\end{bmatrix}, -\qquad s=Sz. -$$ - -It never forms a Gram matrix and remains full column rank for finite \(J\) when -\(\lambda>0\), including when \(J\) is rank deficient. Its factorization width -is the parameter count \(n\), so it is intended for small systems such as DAE -algebraic roots. In the package's usual \(m\ll n\) regime, `qr` performs the -same damped solve after reducing to residual dimension and is substantially -cheaper when its full-row-rank assumption holds. - -### LSMR - -`linear_solver="lsmr"` solves that same whitened augmented system iteratively by -LSMR bidiagonalization, using only \(J\)/\(J^\top\) matvecs — the matrix-free -sibling of `augmented_qr`. Because it works on \(B = JS\) directly rather than -on a Gram/normal system whose condition number is the *square* of -\(\operatorname{cond}(B)\), it keeps the step accurate at small \(\lambda\) -where the squared solves hit their `eps·cond` floor. It requires the metric's -`inv_sqrt`/`inv_sqrt_transpose` and accepts an optional -`whitened_preconditioner` (a `WhitenedPreconditioner` parameter-space -right-preconditioner `R⁻¹`) that clusters the LSMR spectrum when the whitened -operator is itself ill-conditioned. The damping row rides inside the -preconditioned operator, so the *posed* subproblem is exactly the -identity-damped whitened subproblem in \(u = R^{-1}z\) for every -\(\lambda>0\): at inner convergence the step is independent of \(R\) -(budget-truncated iterates can still differ across \(R\) — the -preconditioner changes the iteration path, not the subproblem), and the -\(\lambda \to 0\) selection limit is minimum-\(M\)-norm for any \(R\). It is -detailed in the -[utilities guide](utilities.md#matrix-free-lsmr-whitened-subproblem). - -## Minimal Example +- `args` is **solver-inert** auxiliary data: sampled batches, module + graphdefs, anything the solver should thread through untouched. +- `p` is everything you may want a **total derivative of the solution** with + respect to. `solve(...).x` carries a custom implicit AD rule in `p`. ```python -import jax import jax.numpy as jnp - from nlls_gram import LevenbergMarquardt +def residual(x, args, p): + return args["design"] @ x - p["target"] -def residual_fn(x, args): - ts, ys = args - return x["a"] * jnp.exp(x["b"] * ts) - ys - - -ts = jnp.linspace(0.0, 2.0, 20) -ys = 2.0 * jnp.exp(-1.0 * ts) -x = {"a": 1.0, "b": 0.0} - -solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) -lm_state = solver.init(x, (ts, ys)) - - -@jax.jit -def train_step(x, lm_state): - return solver.update(x, lm_state, (ts, ys)) - - -for _ in range(50): - x, lm_state, info = train_step(x, lm_state) - -print(x["a"], x["b"]) +solver = LevenbergMarquardt(residual) +result = solver.solve(jnp.zeros(8), {"design": design}, p={"target": y}, + max_steps=200, atol=1e-8) +result.x, result.status, result.steps ``` -## Solve Loop Callbacks - -`solve` accepts a traceable callback that can stop early, replace `args` and -`user_state` for later iterations, and reset damping and other per-step -hyperparameters mid-solve. See [Callbacks and Cookbook](callbacks.md) for the -callback contract, resettable hyperparameters, and recipes: host loops, -logging, divergence stops, epoch resampling, scheduled inner-solve accuracy, -validation early stopping, wall-clock time limits, and fixed-size history -recording. - -## Performance Notes - -- The solver instance and the callback are static arguments of the internal - jitted loop, keyed by object identity — but solvers compare by - configuration, so equal settings share one compilation. Constructing - `LevenbergMarquardt` inside a jitted function is supported when every - constructor argument is a static Python value (option strings, floats, - hooks; the solver holds no arrays) — never from traced values. What - recompiles is rebuilding the *pieces* per call: define residuals, - callbacks, and hooks once at setup scope; an inline `lambda` at the call - site recompiles every `solve`. -- `max_steps`, `atol`, `gtol`, and `xtol` are traced values: sweeping them - does not recompile (concrete numbers, not tracers). -- `jax.vmap(lambda x0: solver.solve(x0, ...))` works for independent - multi-start and per-sample calibration solves. The batched loop runs until - every lane has stopped, so `status` and `steps` are per-lane results but - runtime is governed by the slowest lane. See - [Callbacks and Cookbook](callbacks.md#batched-multi-start). -- Each `update` costs one residual linearization, one Jacobian - materialization in the dense paths — `jacobian_mode="auto"` assembles it - from the small side, `n_params` JVP columns when tall or square and - `n_residuals` VJP rows when strictly fat, and `"fwd"`/`"rev"` force one - mode (see the - [tuning guide](tuning_guide.md#jacobian-assembly-jacobian_mode)) — and one - candidate residual evaluation; geodesic acceleration adds a - forward-over-forward directional derivative and, only when the ratio gate - passes, one more residual evaluation. -- Dtypes flow from `x` and the residual; keep everything in one dtype to - avoid promotions. - -### Jacobian Caching Across Rejected Steps - -A rejected LM step leaves the parameters unchanged, so the next update's -residual and Jacobian are identical — only the damping changed. With -`cache_jacobian=True` (the default) the solver carries `(resid, Jt)` in -`LMState` and a -rejected step's successor skips the residual evaluation and the -Jacobian assembly passes, re-solving only the small damped system (roughly -2x faster per rejected step; more when the residual is expensive relative to -the Gram assembly). The flag only affects the dense Gram/normal forms — -`gram_cholesky`, `normal_cholesky`, and `auto`, which resolves to one of -them; the carried `(n_params, n_residuals)` \(J^\top\) buffer serves both -factorizations. The matrix-free solvers never materialize a Jacobian, so it -is ignored for them. +## Minimum-norm interpolation ```python -solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) -lm_state = solver.init(x0, args) # x0 required to size the cache -``` - -Caveats: - -- The cache is valid only while `x`, `args`, and `p` are all unchanged. - Inside `solve`, invalidation is automatic: an accepted step invalidates it, - and so does any callback action that actually changes the values of `x` or - `args` — the comparison is by value, so the `jnp.where` recipe pattern that - returns unchanged values every step keeps the cache, and epoch resampling - needs no extra care. The one hazard is a **manual `update()` loop** that - changes `args` or `p` between steps (minibatching): the solver cannot see - the swap and a stale cache fails silently, with steps taken against the old - Jacobian — leave the cache off there, or reset with - `dataclasses.replace(lm_state, jacobian_valid=jnp.asarray(False))`. -- The cache adds an `(n_params, n_residuals)` buffer to `LMState` for the - whole solve — relevant on GPU memory budgets. -- Callbacks that rebuild the lm_state must preserve the cache fields — use - `dataclasses.replace(ctx.lm_state, damping=...)`, not a bare - `LMState(damping)`. -- When rejections never happen the cache costs essentially nothing at run - time, which is why it is on by default; pass `cache_jacobian=False` for - manual minibatch loops (the hazard above) or when the buffer does not fit - GPU memory. - -## Implicit Differentiation - -`solve` has a custom implicit JVP/VJP with respect to the external parameter -pytree `p`: derivatives of `result.x` (and, with `has_aux=True`, of -`result.aux`) are defined by the residual equation at the returned solution -rather than by differentiating through the LM iterations. See -[Implicit Differentiation](implicit_ad.md) for the math, the role of the -metric in selecting the minimum-norm tangent, the explicit direct, SVD, QR, -and matrix-free `ad_solver` methods, and worked examples. - -## Geodesic Acceleration - -Geodesic acceleration is on by default (`geodesic_acceleration=False` -disables it). The solver computes the second-order residual directional term -with JAX forward-over-forward JVPs; the same metric-damped linear solve -computes the acceleration. - -With a custom metric, the acceptance ratio uses the metric norm: - -$$ -\frac{2\|a\|_M}{\|v\|_M + \epsilon}. -$$ - -Therefore `metric.norm` is required whenever geodesic acceleration is combined -with a custom metric. - -## Dtypes and Pytrees - -Dtypes flow from `x` and the residual: every internal scalar (damping, -damping factors, tolerances, metric quantities) is cast to the residual dtype, -so a float32 problem computes purely in float32 and a float64 problem purely -in float64 — no example needs explicit dtypes beyond its data. Enable x64 -before creating arrays if the problem should run in float64: - -```python -import jax - -jax.config.update("jax_enable_x64", True) -``` - -`init(x0, args, p=...)` mirrors `update`'s data arguments: it evaluates the -residual once and types the lm_state (and any Jacobian cache buffers) from the -actual problem, so there is no dtype argument to get wrong — a float32 -problem stays float32 even with x64 enabled. `solve` likewise recasts the -damping and tolerances to the residual dtype internally. - -### Precision Knobs - -Two constructor knobs promote a targeted slice of a float32 program to -float64 without touching the model. Both accept `None` (the default) or -`jnp.float64`, and both require x64 support to be enabled — they make -float64 available to one pipeline; they never demote explicitly-float64 -data. - -- **`linear_solve_dtype=jnp.float64`** promotes the dense linear-solve - pipelines: the `gram_cholesky`/`normal_cholesky` forward factorizations - *and* the assembled direct/SVD/QR implicit-AD methods (the implicit solve inherits the knob, - so the undamped implicit system — the most conditioning-sensitive solve - in the library — is never silently less precise than the damped forward - one). The recipe: \(J^\top\) (or \(B^\top\)) is cast wide *before* the - metric application, the assembly, factorization, and triangular solves - run in float64, and only the returned step or tangent is cast back to the - residual dtype. The model, residual, and Jacobian VJP passes stay - float32. Forming a Gram or normal matrix squares - \(\operatorname{cond}(JS)\), which is exactly what makes those paths - float32-fragile for stiff systems (e.g. a metric weight injecting a - \(1/\varepsilon\) spike into \(P\)) — this knob is the targeted fix. It - requires a solver that has a dense pipeline to promote: forward - `auto`/`gram_cholesky`/`normal_cholesky`, or an assembled `ad_solver` - (`direct`, `svd`, `qr`, or `augmented_qr`). -- **`metric_solve_dtype=jnp.float64`** sets the dtype the resolved metric - callbacks *compute in*: the solver wraps the metric — a fixed `metric` or - a `metric_factory`'s built one, after `build` — so each callback upcasts its - input, computes wide, and - restores the caller's dtype. `None` leaves the metric computing in - whatever dtype the consuming solve hands it (float64 under - `linear_solve_dtype`, the residual dtype otherwise). Kernel Gram - factorizations are routinely the worst-conditioned piece of the whole - pipeline, so this knob often earns `jnp.float64` even in - otherwise-float32 programs — see the - [Tuning Guide](tuning_guide.md#float64-a-la-carte). It requires a custom - metric or metric factory to wrap. - -See the [Tuning Guide](tuning_guide.md#float64-a-la-carte) for measured -costs and for choosing between the knobs and full x64. - -`update` optimizes exactly the `x` pytree you pass. With Flax NNX, pass only -the trainable state to the solver and merge it with frozen state inside -`residual_fn`; the solver itself remains NNX-agnostic. - -## Benchmarks and GPU Checks - -Optional pytest-benchmark checks live outside the default test suite: - -```bash -uv run --group benchmark pytest benchmarks --benchmark-only -``` - -For the larger interpolation profile: - -```bash -uv run --group benchmark --group gpu pytest \ - benchmarks/test_large_interpolation_benchmark.py --benchmark-only -``` - -For the repeated state-space (Matérn) metric applies and setup (sequential vs -parallel vs dense, n up to 1e5): +import jax.numpy as jnp +from nlls_gram import RidgeLevenbergMarquardt, RepeatedFactorMetric, ridge_continuation -```bash -uv run --group benchmark --group gpu pytest \ - benchmarks/test_quasiseparable_benchmark.py --benchmark-only -``` +# W = blockdiag(K, K) for a kernel Gram matrix K: the RKHS seminorm over two +# coefficient blocks. The constructor takes the FACTOR. +metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=2) -On CUDA machines, the optional GPU tests (including the state-space metric -check) are: +solver = RidgeLevenbergMarquardt(collocation_residual, metric=metric, ridge=1e-4) -```bash -uv run --group gpu pytest tests/test_gpu.py +# Anneal the ridge toward the interpolating limit on stationarity. +callback, user_state = ridge_continuation(ridge_floor=1e-10) +result = solver.solve(x0, callback=callback, user_state=user_state, + gtol=1e-8, atol=1e-8) ``` -## Optimistix - -For a broader JAX nonlinear solver library, see -[Optimistix](https://github.com/patrick-kidger/optimistix). It provides general -least-squares, root-finding, and minimization abstractions. `nlls_gram` is -narrower and focuses on underdetermined LM with explicit parameter-space metrics. - -## API Reference - -::: nlls_gram.LevenbergMarquardt - -::: nlls_gram.GramMetric - -::: nlls_gram.MetricFactory - -::: nlls_gram.metric_from_cholesky - -::: nlls_gram.metric_from_diagonal - -::: nlls_gram.repeated_shifted_dense_metric - -::: nlls_gram.repeated_shifted_state_space_metric - -::: nlls_gram.matern_state_space - -::: nlls_gram.sherman_morrison_preconditioner - -::: nlls_gram.woodbury_preconditioner - -::: nlls_gram.LMState - -::: nlls_gram.LMHyperparams - -::: nlls_gram.LMInfo - -::: nlls_gram.LMStatus - -::: nlls_gram.LMSolveAction - -::: nlls_gram.LMSolveContext - -::: nlls_gram.LMSolveResult - -::: nlls_gram.MultiStart - -::: nlls_gram.MultiStartInfo +The metric covers the leading `metric.size` coordinates; anything past that is +a **free block**, unpenalized by the ridge solver. Calibrate `gtol` as roughly +`1e-3 * ridge * sqrt(q(x*))`, using the reported +`info.penalty_grad_norm = sqrt(penalty_value)`. + +## Linear solvers + +The same typed configs serve both solvers, in both the forward and the +implicit-AD role. A knob that exists for only one method is a field on that +method, so it cannot be passed with another. + +| config | system | dimension | when | +|---|---|---|---| +| `Cholesky()` | dense, auto gram/normal | \(\min(m, n)\) | the default | +| `QR()` | damping-row QR of \([\tilde J;\sqrt\lambda I]\) | \(n\) | tiny damping or ridge; rank-safe | +| `CG(precond)` | matrix-free normal | \(n\) | \(n \lesssim m\), no dense \(J\) | +| `GramCG(precond)` | matrix-free dual | \(m\) | \(m \ll n\), no dense \(J\) | +| `SVD()` | pseudoinverse | — | `ad_solver` only: rank-deficient tangents | + +For \(\lambda > 0\) the gram and normal forms compute the *same* step (the +push-through identity), so the choice is about cost, not semantics. A +`preconditioner` is required for the Krylov configs — +`IdentityPreconditioner()` is the explicit opt-out. + +`ad_solver=None` (the default) matches the forward family, falling back to +`Cholesky()` where the forward config's undamped operator would be singular. + +## Where to go next + +- [Ridge LM](ridge_lm.md) — the objective, whitening, ridge continuation, stopping +- [Metric LM](metric_lm.md) — the damping geometry and its minimum-norm limit +- [Metrics and preconditioners](metrics.md) — the two hook types +- [Callbacks](callbacks.md) — the solve loop and its cookbook +- [Implicit differentiation](implicit_ad.md) — the AD contract +- [Tuning](tuning_guide.md) — picking a solver and a schedule +- [API](api.md) diff --git a/docs/llms.txt b/docs/llms.txt deleted file mode 100644 index 7ae0b3f..0000000 --- a/docs/llms.txt +++ /dev/null @@ -1,15 +0,0 @@ -# nlls_gram - -> Levenberg-Marquardt nonlinear least squares for JAX pytrees, aimed at interpolation problems (zero-residual roots where minimum-norm selection matters, wide or tall). Two solvers share one init/update/solve protocol: RidgeLevenbergMarquardt minimizes ||r||^2 + ridge*||x_m||_W^2 for a positive-definite Metric W on the metric block x_m of x = [x_m; x_f] (free block x_f unpenalized, n_f = len(x) - metric.size inferred at init) with the ridge weight as annealable traced state (ridge_continuation), putting the minimum-seminorm/min-RKHS-norm selection in the objective (nonlinear Tikhonov). The metric is supplied through factor callbacks for W = F'F (factor_apply/factor_solve/factor_solve_transpose/norm, each receiving a MetricContext with the live solver state; IdentityMetric is plain ridge, RepeatedFactorMetric the kernel workhorse taking F = jnp.linalg.cholesky(K, upper=True)) and the solver runs entirely in the whitened variable y = F_bar x with constant penalty rows [I | 0] — spectral floor at the ridge, Cholesky()-path accuracy at deep ridge, lambda-free factorization so continuation composes. Typed solver configs Cholesky()/QR()/CG(preconditioner, ...) with ad_solver Cholesky()/CG(...); the CG preconditioner is a typed Preconditioner subclass (apply(v, damping, ctx); IdentityPreconditioner() opts out; BlockEigenPreconditioner applies damping-analytic block-eigenbasis state carried in the residual args and rebuilt adaptively from solve callbacks via block_eigen_state), required in both roles. GN-implicit AD posed on y; conjunctive gtol+atol stopping in the whitened geometry (steps in the W-norm, gradients in the dual W^{-1}-norm; info.penalty_grad_norm = sqrt(penalty_value), so gtol ~ 1e-3*ridge*sqrt(q)); runs at the residual dtype, QR() the extreme-conditioning fix. LevenbergMarquardt is metric-damped LM where selection comes from the damping geometry (its GramMetric is a separate contract). Per-step update(), a jitted solve() loop with resettable hyperparameters and callbacks, implicit differentiation with respect to external parameters p, and pluggable parameter-space metrics (kernel/RKHS). Metric-LM linear solvers: a shape-adaptive dense default (linear_solver="auto" resolves to gram_cholesky when n > m, else normal_cholesky), qr/augmented_qr, and matrix-free gram_cg/normal_cg/lsmr; jacobian_mode="auto"/"fwd"/"rev" assembles the dense Jacobian from the small side. Implicit differentiation has explicit methods: direct, svd, qr, augmented_qr, gram_cg, normal_cg, and regularized_normal_cg. ad_solver="auto" selects direct for square systems, the matching CG space for nonsquare CG systems, and svd otherwise. Targeted float64 promotion via linear_solve_dtype (metric-LM assembled pipelines) and metric_solve_dtype (metric callbacks). - -## Docs - -- [Ridge LM — the ridge objective on the metric/free block split, selection theorem, the whitened change of variables y = F_bar x (W = F'F, augmented stack [J~; sqrt(ridge)[I 0]]), continuation schedule, the two-phase stopping picture and the whitened gtol calibration recipe (gtol ~ 1e-3*ridge*sqrt(q); noise-floor regime), the Metric interface (factor ops + MetricContext, exact-factor and identity-hashing contracts, free-block guidance), typed Cholesky()/QR()/CG(...) solver table with typed Preconditioners, GN-implicit AD contract, migration from the metric formulation](https://highdimensionaleconlab.github.io/nlls_gram/ridge_lm/) -- [Tuning guide — read first for solver selection and hyperparameter heuristics](https://highdimensionaleconlab.github.io/nlls_gram/tuning_guide/) -- [Main docs — API contracts, math, linear solvers, performance notes](https://highdimensionaleconlab.github.io/nlls_gram/) -- [Callbacks and cookbook — solve-loop callback contract, resettable hyperparameters, recipes](https://highdimensionaleconlab.github.io/nlls_gram/callbacks/) -- [Multi-start — retry failed solves from fresh draws or race starts in parallel under vmap; draw/accept hooks, key schedule, winner-only implicit AD](https://highdimensionaleconlab.github.io/nlls_gram/multi_start/) -- [Metrics — Metric callback contract, cholesky helper, dense and matrix-free examples, and the iterate-aware MetricFactory (prepare/build) that rebuilds the metric from the current iterate and residual aux each accepted step](https://highdimensionaleconlab.github.io/nlls_gram/metrics/) -- [Utilities — dense, diagonal, repeated-shifted dense, and repeated-shifted state-space metric constructors; the Matérn state-space producer; Sherman-Morrison, Woodbury, identity, and randomized Nyström (FTU) preconditioners serving the CG hooks; the normal-space preconditioner contract for linear_solver="normal_cg" (SPD approximation of (B'B + damping I)^-1 that must preserve range(B') on rank-deficient problems); the iterate-adaptive PreconditionerFactory (gram_cg-only) that rebuilds the dual preconditioner from the current iterate each step; the dual-only padded-residual helper; matrix-free LSMR (linear_solver="lsmr") for the whitened damped subproblem when the squared Gram/normal operators are ill-conditioned at small damping, with an optional WhitenedPreconditioner parameter-space right-preconditioner that clusters the LSMR spectrum without changing the damped subproblem; and Krylov recycling (RecycleConfig / deflated_pcg, gram_cg-only) that carries a harvested deflation basis across LM steps](https://highdimensionaleconlab.github.io/nlls_gram/utilities/) -- [Implicit differentiation — JVP and automatically transposed VJP with respect to p; MAX_STEPS is usable by default with an opt-in strict policy; zero failed-solve derivatives from a JVP-safe initial point; shape-first auto dispatch; direct square solves; SVD pseudoinverse; loud unregularized QR; explicit augmented-QR and regularized-normal-CG ridges; matrix-free Gram/normal CG; no default regularization; aux outputs](https://highdimensionaleconlab.github.io/nlls_gram/implicit_ad/) -- [Metric Gauss-Newton — minimum-norm math and kernel metric choices](https://highdimensionaleconlab.github.io/nlls_gram/gauss_newton/) diff --git a/docs/metric_lm.md b/docs/metric_lm.md new file mode 100644 index 0000000..87f84cb --- /dev/null +++ b/docs/metric_lm.md @@ -0,0 +1,84 @@ +# Metric LM + +`LevenbergMarquardt` minimizes \(\|r(x)\|^2\) with the metric weighting the +**trust region** rather than the objective: + +$$ +\min_s \tfrac12\|r + Js\|^2 + \tfrac{\lambda}{2}\|s\|_W^2 , +\qquad +s(\lambda) = -(J^\top J + \lambda W)^{-1}J^\top r . +$$ + +## The minimum-norm limit + +At an interpolating root \(J\) is rank deficient, so \(J^\top J\) is singular +and the \(\lambda \to 0\) limit is a pseudoinverse rather than an inverse. +Writing \(W = F^\top F\) and \(B = JF^{-1}\), the step in the whitened +variable is \(u(\lambda) = -(B^\top B + \lambda I)^{-1}B^\top r\), whose limit +is \(-B^{+}r\) — the **minimum-Euclidean-norm** solution in \(u\), hence the +**minimum-\(W\)-norm** correction in \(s = F^{-1}u\): + +$$ +\lim_{\lambda \to 0} s(\lambda) += -F^{-1}(JF^{-1})^{+}\,r += \arg\min\{\|s\|_W : Js = -r\ \text{in the least-squares sense}\} . +$$ + +The limit holds at every shape and rank, so tall problems that are still +deficient along some directions (redundant rows, collinear columns) keep the +selection. Damping interpolates between two metric methods: large \(\lambda\) +gives a \(W^{-1}\)-scaled gradient step, small \(\lambda\) the metric +Gauss-Newton step above. + +**This selects the correction, not the iterate.** The returned root is +\(x_0 + \sum_k s_k\), so it is the *path* that carries the geometry. When you +want the interpolant itself to be minimum-seminorm, the selection belongs in +the objective — use [`RidgeLevenbergMarquardt`](ridge_lm.md). + +## Choosing the metric + +Under a kernel model \(f(t) = \sum_j \alpha_j k(t, c_j)\), the RKHS norm is +\(\alpha^\top K \alpha\) with \(K\) the Gram matrix over centers, so +`W = K` and the factor is `jnp.linalg.cholesky(K, upper=True)`. A +positive-*semi*definite \(K\) needs a shift to be invertible: +`RepeatedFactorMetric.from_gram(K, repeats=r, epsilon=1e-8)` factors +\(K + \varepsilon I\) once and repeats it. + +Parameters the metric should not weight (a scalar coefficient, a bias) go past +`metric.size` into the **free block**, whose damping weight is +`Metric.free_scale` (1.0 by default). The default `metric=None` is Euclidean +damping over the whole vector. + +## Stopping + +Disjunctive — any one rule fires `CONVERGED`: + +- `atol`: \(\|r\| <\) atol, the equations are solved; +- `gtol`: `info.grad_norm` \(= \|F^{-\top}J^\top r\| <\) gtol, stationarity in + the dual \(W^{-1}\)-norm; +- `xtol`: an accepted step's whitened norm \(\|u\| <\) xtol. + +Setting one to `0` disables it. For an interpolation problem `atol` is usually +the one you want. + +## Rank deficiency and implicit AD + +The implicit rule differentiates the *undamped* Gauss-Newton system, which is +singular on exactly the side the problem is deficient in. Each config is +therefore offered only where its operator is invertible, and says so loudly +otherwise: + +| `ad_solver` | needs | notes | +|---|---|---| +| `None` | — | matches the forward family, falling back to `Cholesky()` | +| `Cholesky()` | full rank in the small side | factors whichever of \(BB^\top\), \(B^\top B\) is smaller | +| `SVD()` | nothing | spectral filter; the rule for padded zero residuals | +| `CG(precond)` | \(n \le m\) | `penalty=` regularizes it for \(n > m\), at an \(O(\text{penalty})\) bias | +| `GramCG(precond)` | \(m \le n\) | | + +The **padded zero residual** pattern — appending identically-zero rows so +compiled shapes stay stable across problem instances — makes the undamped dual +singular by construction. `ad_solver=SVD()` computes the minimum-metric-norm +tangent there, which equals the unpadded one. + +See [Implicit differentiation](implicit_ad.md) for the rule itself. diff --git a/docs/metrics.md b/docs/metrics.md index 0afff61..04326d3 100644 --- a/docs/metrics.md +++ b/docs/metrics.md @@ -1,226 +1,104 @@ -# Gram Metrics (`LevenbergMarquardt`) - -These are the **damping metrics** of the classic -[`LevenbergMarquardt`](gauss_newton.md) solver, kept under the `GramMetric` -name. The positive-definite `Metric` of -[`RidgeLevenbergMarquardt`](ridge_lm.md) — factor callbacks for -\(W = F^\top F\) on the metric block — is a different contract, documented -on the [Ridge LM page](ridge_lm.md#the-metric-interface). - -## The GramMetric Object - -A custom metric is passed as a single `metric=GramMetric(...)` argument. The -`GramMetric` dataclass holds up to four callbacks that operate on the flattened -parameter vector produced internally by `ravel_pytree`. Let \(P=M^{-1}\), and -let \(S\) satisfy \(SS^\top=M^{-1}\). - -| Field | Meaning | -| --- | --- | -| `solve(x)` | \(M^{-1}x = Px\) | -| `norm(x)` | \(\sqrt{x^\top Mx}\) | -| `inv_sqrt(x)` | \(Sx\) | -| `inv_sqrt_transpose(x)` | \(S^\top x\) | - -Fields left as `None` (and `metric=None` itself) default to the identity -metric. A fixed `GramMetric` closes over its data once, at construction; for a -metric that depends on the current iterate or on residual aux outputs, see -[Iterate-Dependent Metrics](#iterate-dependent-metrics-metricfactory) below. -Construct a fixed metric once at problem-setup scope and reuse it. Rebuilding -an equivalent closure creates new callable identities in the solver's static -JIT key and therefore retraces; a persistent compilation cache can reuse the -executable but does not remove that Python tracing work. - -Shape requirements: - -- `solve` must support vectors `(n_params,)` and matrices `(n_params, k)`. -- `inv_sqrt` is applied to vectors `(n_params,)` only (every whitened forward - path and the metric-aware AD methods use it that way); the whitened Jacobian is assembled - with `inv_sqrt_transpose`, below. -- `inv_sqrt_transpose` must support matrices `(n_params, n_residuals)` for - the dense whitened forward forms (`normal_cholesky`, `qr`, - `augmented_qr`) and the SVD/QR AD methods; the matrix-free forms - (`normal_cg`, `lsmr`) apply it to vectors only. -- `norm` only needs to support vectors `(n_params,)`. - -Validation rules — which callbacks a custom metric must supply depends on -the *form* the solver works in: - -| form | requires | -| --- | --- | -| Gram forward: `gram_cholesky`, `gram_cg` | `solve` | -| whitened forward: `normal_cholesky`, `normal_cg`, `qr`, `augmented_qr`, `lsmr` | `inv_sqrt` + `inv_sqrt_transpose` | -| AD: `svd`, `qr`, `augmented_qr`, `normal_cg`, `regularized_normal_cg` | `inv_sqrt` + `inv_sqrt_transpose` | -| AD: `gram_cg` | `solve`, or the pair (falls back to \(P = SS^\top\)) | -| AD: `direct` | no metric callback (the square root tangent is unique) | -| geodesic acceleration + custom metric | `norm` | - -- Concrete forward solver names validate eagerly at construction; a forward - `"auto"` defers its check to trace time, when the concrete shapes resolve - the form — the same precedent as a `metric_factory`, whose built metric - is validated when `build` first runs. AD `"auto"` also defers its metric - check: square systems resolve to `direct` and need no metric callback; - nonsquare systems may require whitening. A solve-only metric can therefore - use `direct` on a square system or `gram_cg` more generally. -- If geodesic acceleration is enabled (the default) and a custom metric is - supplied, `metric.norm` is required — supply it or pass - `geodesic_acceleration=False`. -- The solver does not infer `norm`, `inv_sqrt`, or `inv_sqrt_transpose` from - `solve`. -- Every callback must accept and preserve the dtype it is handed. Normally - that is the residual dtype; with `linear_solve_dtype=jnp.float64` the - dense pipelines hand the callbacks float64 inputs and expect float64 back - (jnp-composed callbacks satisfy this automatically through standard - promotion). `metric_solve_dtype=jnp.float64` instead makes the solver - wrap the resolved metric so its callbacks *compute* in float64 whatever - dtype they are handed — see the - [precision knobs](index.md#precision-knobs). - -`norm` is separate because `solve` applies \(M^{-1}\), while the norm needs -\(M\): - -$$ -\|x\|_M = \sqrt{x^\top Mx}. -$$ - -Recovering that norm from a black-box \(M^{-1}\) solve would require another -inverse operation. Likewise, a square-root factor \(S\) is not generally -recoverable from an arbitrary solve callback. - -## Cholesky GramMetric Helper - -For a dense metric \(M=LL^\top\) with \(L\) lower triangular (the form -returned by `jnp.linalg.cholesky`), use: +# Metrics and preconditioners -```python -import jax.numpy as jnp - -from nlls_gram import metric_from_cholesky +The two hook types both solvers take. They look similar and mean opposite +things: -L = jnp.linalg.cholesky(metric_matrix) -metric = metric_from_cholesky(L) -``` +- a **`Metric`** defines the subproblem, so it must be **exact**; +- a **`Preconditioner`** only changes the CG iteration path, so it may + approximate freely. -The helper returns a `GramMetric` with all four callbacks filled in. The diagonal -and repeated shifted kernel constructors, plus the preconditioner helpers, -are collected in [Utilities](utilities.md). +## `Metric` -## GramMetric Example +A positive-definite \(W\) given through callbacks for an invertible factor +\(F\) with \(W = F^\top F\). The solver runs in the whitened variable and +never materializes either. ```python -import jax.numpy as jnp +class Metric: + size: int # the metric block: the leading coordinates of x + free_scale = 1.0 # damping weight on everything past it + + def factor_apply(v, ctx): ... # F v + def factor_solve(v, ctx): ... # F^-1 v + def factor_solve_transpose(v, ctx): ... # F^-T v + def norm(v, ctx): ... # ||F v||, defaulted +``` -from nlls_gram import LevenbergMarquardt, metric_from_cholesky +Ops act on metric-block vectors, or matrices whose *leading* axis is `size` +(columns are batched). Shipped implementations: +| | \(W\) | +|---|---| +| `IdentityMetric(size)` | \(I\) | +| `CholeskyMetric(L)` | \(LL^\top\) | +| `DiagonalMetric(weights)` | \(\operatorname{diag}(w)\) | +| `RepeatedFactorMetric(F, repeats=r)` | \(\operatorname{blockdiag}(F^\top F, \ldots)\) | +| `RepeatedFactorMetric.from_gram(K, repeats=r, epsilon=e)` | \(\operatorname{blockdiag}(K + eI, \ldots)\) | -def residual_fn(theta, args): - matrix, target = args - return matrix @ theta - target +`RepeatedFactorMetric` shares one triangular solve across every repeated block +by packing them into the columns of a single right-hand side, so no repeated +factor or full block diagonal is ever formed. +## `Preconditioner` -metric_matrix = jnp.array([[2.0, 0.2], [0.2, 1.0]]) -L = jnp.linalg.cholesky(metric_matrix) +An SPD approximation of the damped inverse, for the Krylov configs. -solver = LevenbergMarquardt( - residual_fn, - init_damping=1e-2, - metric=metric_from_cholesky(L), -) +```python +class Preconditioner: + def apply(v, damping, ctx): ... # ~ (operator + damping I)^-1 v ``` -## Iterate-Dependent Metrics (MetricFactory) - -A fixed `GramMetric` freezes its data at construction. `MetricFactory` instead -rebuilds the metric from the live solve, through a value-hashable -`(prepare, build)` pair passed as `metric_factory=` (pass at most one of -`metric` or `metric_factory`): - -- `prepare(x, args, p, aux) -> state` builds a fixed-shape pytree of arrays - from the current iterate `x` (the user pytree, not the raveled vector), - the residual `args`, `p`, and the residual aux evaluated at the same - linearization point (`None` when `has_aux=False`). It runs once per - accepted step inside the jitted loop; after a rejected step `x` did not - move, so the carried state is reused. Expensive setup — Gram assembly, a - dense Cholesky — belongs here, where it is cached. -- `build(state) -> GramMetric` assembles the metric from the prepared state, - once per `update` and before the inner iterative loops, so factorization or - structured setup runs once per step rather than per CG/LSMR iteration. Any - `GramMetric`-returning builder works directly. - -The canonical use is a factor the residual passes back through its aux -output — the residual computes it primally, the Jacobian never -differentiates it, and the metric consumes it: +Which space `v` lives in is named by the config: `CG` is parameter space, +`GramCG` residual space. `IdentityPreconditioner()` is the explicit opt-out — +running Krylov methods without a preconditioning decision should be a visible +choice, not a default. + +| | approximates | +|---|---| +| `IdentityPreconditioner()` | \(I\) | +| `BlockEigenPreconditioner(blocks_fn, permutation)` | a block-diagonal eigenbasis, analytic in both ridge and damping | +| `NystromPreconditioner(matvec, n, rank, key)` | a randomized rank-\(k\) sketch (Frangella-Tropp-Udell) | +| `ShermanMorrisonPreconditioner(solve, u, weight)` | \(A + wuu^\top\) from a solve with \(A\) | +| `WoodburyPreconditioner(solve, U, weights)` | the rank-\(k\) generalization | +| `PaddedPreconditioner(base, n_real)` | a base extended over exactly-zero padded rows | + +**Range preservation.** On rank-deficient problems the minimum-norm selection +rests on the CG iterates staying in \(\operatorname{range}(B^\top)\). +Unpreconditioned CG from zero does, since the right-hand side starts there and +the operator maps the subspace to itself. A preconditioner \(C\) enters the +Krylov space through its images, so unless +\(C(\operatorname{range}(B^\top)) \subseteq \operatorname{range}(B^\top)\) the +iterates leak into the null space and the step silently stops being the +minimum-norm one — the CG residual still converges, so nothing fails loudly. +Safe: the identity, polynomials in the operator, an exact \((B^\top B + \tau +I)^{-1}\) at fixed \(\tau > 0\). On full-column-rank problems the condition is +vacuous. + +## Iterate-dependent state + +Both types take the same optional pair when their numbers must track the +iterate: ```python -import jax.numpy as jnp - -from nlls_gram import LevenbergMarquardt, MetricFactory, metric_from_cholesky - - -def residual(x, args, p): - value = economic_residual(x, args, p) - gram = kernel_gram(x["points"], p["kernel"]) - L = jnp.linalg.cholesky(gram + p["eps"] * jnp.eye(gram.shape[0])) - return value, {"L": L} - - -solver = LevenbergMarquardt( - residual, - has_aux=True, - metric_factory=MetricFactory( - prepare=lambda x, args, p, aux: aux["L"], - build=metric_from_cholesky, - ), -) +def prepare(self, theta, ctx): ... # -> traced pytree, or None (the default) +def rebuild(self, ctx): ... # -> traced bool, True by default ``` -`prepare` can equally compute from the iterate directly (no `has_aux` -needed). For example, a moving state-space Matérn metric can rebuild its -single structured factor from an ordered coordinate `t`: +The output rides on the solver state and comes back as `ctx.metric_state` / +`ctx.preconditioner_state`. It is rebuilt on accepted steps and reused across +rejected ones (where `x` did not move), runs inside the jitted loop as traced +ops, and is **frozen at the solution** under implicit AD. Its pytree structure +must not change between rebuilds. Override `rebuild` to decline a refresh — +for a preconditioner that is always safe and often much cheaper. -```python -import jax.numpy as jnp - -from nlls_gram import ( - MetricFactory, - matern_state_space, - repeated_shifted_state_space_metric, -) - -factory = MetricFactory( - prepare=lambda x, args, p, aux: jnp.sort(x["t"]), - build=lambda t: repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma, ell, nu=1.5), - repeats=3, - zero_pad_size=2, - epsilon=1e-8, - ), -) -``` +Setup that does *not* depend on the iterate belongs in `__init__`, where it is +paid once. + +## Compilation -Rules and semantics: - -- The built `GramMetric` obeys the same per-solver callback requirements and - shape contract as a fixed custom metric; validation runs when `build` - first executes (at trace time), not at construction. -- The metric defines the subproblem, so `build`'s callbacks must stay exact - (unlike a preconditioner, which may approximate). -- Within one `update`, the velocity, geodesic-acceleration, and norm - applications all use the same pre-step state. -- A `solve` callback that replaces `x` or `args` invalidates the carried - state, and multi-start draws never inherit another start's state. -- With `has_aux=True`, `jax.linearize(..., has_aux=True)` keeps aux primal: - an aux-only factorization costs one primal evaluation per linearization - and contributes nothing to the Jacobian's JVP/VJP passes — no - `stop_gradient` is needed. -- Under implicit differentiation of `solve` with respect to `p`, the metric - is frozen at the returned solution: `prepare`/`build` run once at - `(result.x, result.args, result.p, result.aux)` and the state-dependence - is not differentiated. The freeze is a first-order statement — higher-order - AD through a factory-built metric's state dependence is unsupported in every - AD rule (dense and cg-resolved alike apply the metric through opaque solve - wrappers), so take higher-order derivatives of `solve` only with a fixed - metric. See - [Implicit differentiation](implicit_ad.md#iterate-dependent-metrics-are-frozen-per-solve). -- Like every jit-static hook, define the `(prepare, build)` pair once at - setup scope; a fresh closure per call keys a new compilation. +The solver is a jit **static** argument, so its hooks enter the compile cache +key. Types holding arrays (every metric above, most preconditioners) hash by +identity: **build them once at setup scope and reuse them**, or every +construction keys a fresh compilation of the whole solve loop. Stateless +value-equal types (`IdentityPreconditioner`) are free to construct inline. +`tests/test_compilation.py` pins this. diff --git a/docs/ridge_lm.md b/docs/ridge_lm.md index d333c2f..e5c32fe 100644 --- a/docs/ridge_lm.md +++ b/docs/ridge_lm.md @@ -491,47 +491,6 @@ frozen-projector AD rules make. Failed statuses return exact zero tangents and evaluate the masked tangent program at stop-gradient copies of the original inputs and the *initial* ridge. -## Migration from the metric formulation - -```python -# before (metric LM): selection via the algorithm's damping geometry, -# epsilon-shifted so the metric stays invertible -metric = repeated_shifted_dense_metric(K, repeats=3, zero_pad_size=d, epsilon=1e-7) -solver = LevenbergMarquardt(residual_fn, metric=metric, - linear_solve_dtype=jnp.float64, - metric_solve_dtype=jnp.float64) -result = solver.solve(theta_0, max_steps=400, atol=2e-8) - -# after (ridge LM): selection in the objective, no epsilon anywhere; -# the metric takes the factor directly (gtol ~ 1e-3 * ridge * sqrt(q)) -metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=3) -solver = RidgeLevenbergMarquardt(residual_fn, metric=metric, - ridge=1e-8) # or None for the dtype default -result = solver.solve(theta_0, max_steps=400, gtol=1e-8, atol=2e-8) - -# optional homotopy if a fixed ridge converges slowly -cb, us0 = ridge_continuation(ridge_floor=1e-8, decrease=0.1) -result = solver.solve(theta_0, max_steps=400, gtol=1e-8, atol=2e-8, - callback=cb, user_state=us0) -``` - -Porting notes: - -- **`info.loss` includes the penalty.** Code that means equation error must - read `info.resid_loss`. -- **Residual-only `atol` stopping must add a `gtol` or `xtol`** — the - conjunctive contract makes this loud, not silent; the whitened geometry - makes the `gtol` choice a one-line calibration - (`1e-3 * ridge * sqrt(q)`) instead of a guess. -- **No dtype-promotion knobs**: the solve runs at the residual dtype - (`QR()` is the extreme-conditioning fix); the metric solver's - `linear_solve_dtype`/`metric_solve_dtype` have no ridge analog. -- Forward `CG` users pass the preconditioner as a required config - field — `CG(IdentityPreconditioner())` at minimum — deliberately - stricter than the metric solver's optional preconditioner hooks. -- Multi-start ranking uses the ridge objective at each lane's own final - ridge — comparable across lanes when they share a continuation schedule. - ## API reference ::: nlls_gram.Metric diff --git a/docs/tuning_guide.md b/docs/tuning_guide.md index 78ffefb..61b08f0 100644 --- a/docs/tuning_guide.md +++ b/docs/tuning_guide.md @@ -1,383 +1,86 @@ -# Tuning Guide +# Tuning -Decision-oriented heuristics for choosing solvers and hyperparameters — -written for humans and AI assistants alike. Contracts and formulas live in -the [main docs](index.md); the math is in -[Metric Gauss-Newton](gauss_newton.md). Throughout, `m` is the residual count -and `n` the parameter count; the package targets `m << n`. +## Picking a solver -## Starting Point +Start with `RidgeLevenbergMarquardt` when the interpolant is the deliverable +and `LevenbergMarquardt` when the root is a means to an end. Defaults — +`Cholesky()`, `geodesic_acceleration=True`, `cache_jacobian=True` — are the +right first try for both. -```python -solver = LevenbergMarquardt(residual_fn) -result = solver.solve(x0, args, max_steps=500, atol=..., gtol=...) -``` - -- **`linear_solver="auto"` (the default) picks the smaller dense - factorization from the problem shape** — the `m × m` residual-space Gram - system when `n > m`, the `n × n` whitened normal system otherwise. The two - produce the same step, so the default is a cost decision, never a - semantics decision. -- **Geodesic acceleration is on by default** — it costs one extra - directional derivative per step (plus one residual evaluation when the - acceptance gate passes), the accept/reject test makes it safe, and on - curved residuals it substantially cuts step counts. Near-linear problems - gain little — `geodesic_acceleration=False` if the extra evaluation - matters. With a custom metric it requires `metric.norm`. -- **The Jacobian cache is on by default** (rejected steps ~2x cheaper) at - the cost of an `(n_params, n_residuals)` state buffer. Pass - `cache_jacobian=False` for manual `update()` loops that swap `args`/`p` - between steps (stale-cache hazard) or when the buffer strains GPU memory. -- Set `atol`/`gtol` rather than relying on `max_steps`: a converged solve - that runs to `max_steps` wastes exactly the steps you didn't bound. - -## Solver Selection - -Shape first. The Gram and normal forms are the same method assembled in -different spaces — the `m × m` residual-space dual `J P J' + damping I` -versus the `n × n` whitened normal system `B'B + damping I` (`B = J S`) — -and they produce identical steps at any positive damping. So the first -question is only which of `m` and `n` is smaller, and `auto` (the default) -answers it: `gram_cholesky` when `n > m` strictly, else `normal_cholesky`, -resolved at trace time from the concrete shapes. The rule reads shapes, not -numerical rank — and it does not need to: rank-deficient problems -(redundant rows, collinear columns — tall interpolation problems always -have some) are handled by every form except `qr`, with the -minimum-`M`-norm small-damping selection intact. The flip also never -changes derivative semantics: AD dispatch uses the traced system shape and an -explicit `ad_solver`, not the primal factorization. The default uses `direct` -for square systems and `svd` for other non-CG systems. - -| situation | use | -| --- | --- | -| dense factorization affordable on the smaller of `m`, `n` | `auto` (default) — `gram_cholesky` if `n > m`, else `normal_cholesky` | -| Jacobian too big to materialize, `n > m` | `gram_cg` | -| Jacobian too big to materialize, `m ≥ n` | `normal_cg` | -| matrix-free and ill-conditioned at small damping | `lsmr` | -| ill-conditioned metric, moderate `m`, full-row-rank `J` | `qr` | -| small system, rank-deficient `J`, direct factorization wanted | `augmented_qr` | +Change the linear solver when a specific symptom appears: -- **Cross-shape use is legitimate — the hooks decide.** The forms compute - the same step, so picking against the shape rule is purely a cost/hook - trade. `dual_preconditioner`, `preconditioner_factory`, and `recycle` are - `gram_cg`-only (they live in residual space); a strong dual - preconditioner or a carried deflation basis can justify `gram_cg` on a - squarish problem. `normal_cg` is the way to precondition in *parameter* - space, and the whitened forms swap `metric.solve` for - `metric.inv_sqrt`/`inv_sqrt_transpose` — pick the form whose callbacks - your metric can supply exactly. -- **`iterative_maxiter` budgets a different Krylov per form**: an - `m`-dimensional space under `gram_cg`, an `n`-dimensional one under - `normal_cg`. Re-tune it when switching forms; a budget tuned for a small - dual can be far too small for a large parameter space. -- **`normal_cg`'s preconditioner has a structural requirement**: it must map - `range(B')` into itself, or the minimum-norm selection is silently lost on - rank-deficient problems — an arbitrary SPD approximation of the inverse - does not qualify. `identity_preconditioner()` always does. See the - [normal-space preconditioner](utilities.md#the-normal-space-preconditioner-normal_cg). -- **Avoid `qr` when massively overparameterized.** It does not use a - Gram/normal form: it factors the whitened `n × m` matrix, so cost scales - with `n` (measured 8-16x slower than `gram_cholesky` at `n=8192, m=1024`), - and it requires full row rank — rank-deficient Jacobians produce - non-finite steps. Its advantage is conditioning (it avoids squaring the - condition number); reach for it only when that is the binding constraint. -- **Use `augmented_qr` for small systems when rank robustness matters.** It - directly factors `[J S; sqrt(damping) I]`, whose damping block guarantees - full column rank, but its width is the parameter count. That is attractive - for DAE algebraic roots and expensive when `n` is large. -- **Use `lsmr` as the matrix-free sibling of `augmented_qr`.** It solves the - same whitened damped subproblem `min_u ||r + B u||² + damping ||u||²` - (`B = J S`, `S = metric.inv_sqrt`, step `s = S u`) by - [LSMR](https://web.stanford.edu/group/SOL/software/lsmr/) bidiagonalization - using only `J`/`Jᵀ` matvecs — no materialized Jacobian, no QR. Its payoff - over the CG forms is conditioning: both Gram and normal operators carry - the **square** of the whitened operator's condition number, so at small - damping (`~1e10` in the motivating case) `eps·cond` puts an accuracy floor - on the step that even dense direct solves hit, and CG truncation - concentrates in the slow, selection-critical eigendirections. `lsmr` works - at `cond(B) ~ sqrt` of that, restoring certifiable endgame accuracy. Reach - for it when a matrix-free solve is required *and* the system is - ill-conditioned near the solution; when it is well-conditioned (or a good - preconditioner exists), the CG forms are cheaper per step. `lsmr` requires - the metric's `inv_sqrt`/`inv_sqrt_transpose` (the identity metric supplies - them). When the whitened operator itself is badly conditioned (`cond(B)` - still large — e.g. `~1e8`, where plain LSMR needs thousands of endgame - iterations), pass a `whitened_preconditioner` (a `WhitenedPreconditioner`): - a parameter-space right-preconditioner `R⁻¹` running LSMR on `B R⁻¹` to - cluster the spectrum and cut the endgame count to the tens (a - Schur-complement factor is canonical). The damping row rides inside the - preconditioned operator, so the posed subproblem is exactly the `I`-damped - one in `u = R⁻¹ z`: `R` changes the iteration path, never the step being - solved for (a budget-truncated iterate can still depend on `R`; a - converged one cannot), and the `damping → 0` selection limit is - minimum-`M`-norm for any `R`. Stopping - maps the same `iterative_tol`/`iterative_atol`/`iterative_maxiter` hooks - (relative/absolute bound on the normal-equations residual, measured on the - preconditioned operator, callback-schedulable). Differentiating a forward - `lsmr` `solve(...).x` uses `direct` for a square system and `svd` otherwise - (`ad_solver="auto"`); pass - `ad_solver="normal_cg"` (no preconditioner needed) or `"gram_cg"` - with an `ad_solver_preconditioner` for a fully matrix-free derivative. -- The CG forms return an *approximate* step under their iteration budget. - That is usually fine — LM's accept/reject absorbs inexactness — but see - the scheduling pattern below. With the default `ad_solver="auto"`, - differentiating a nonsquare forward `gram_cg`/`normal_cg` `solve(...).x` - uses the matching matrix-free CG rule instead of materializing \(J^\top\). - A square system resolves to `direct` first. +| symptom | try | +|---|---| +| \(n\) in the thousands, dense \(J\) too big to form | `GramCG(precond)` when \(m \ll n\), else `CG(precond)` | +| step accuracy degrades as ridge or damping shrinks | `QR()` — it works at \(\operatorname{cond}(A)\), not \(\operatorname{cond}(A)^2\) | +| non-finite step on a rank-deficient Jacobian | `QR()` (rank-safe) or `Cholesky()` | +| tangent is NaN or wrong under implicit AD | `ad_solver=SVD()` | -## Jacobian Assembly (`jacobian_mode`) +`Cholesky()` picks the smaller of the \(m \times m\) dual and the \(n \times +n\) normal system by shape. Forcing `form=` is a cost decision only — for +\(\lambda > 0\) both give the same step. -The dense forward solvers (`auto`, `gram_cholesky`, `normal_cholesky`, -`qr`, `augmented_qr`) and the direct/SVD/QR AD methods materialize the Jacobian; -`jacobian_mode` controls from which side. `"auto"` (the default) vmaps the -identity basis over the **small** dimension: `n` forward-mode JVP columns -when the system is tall or square (`n <= m`), `m` reverse-mode VJP rows -only when strictly fat (`n > m`), with the square tie going to the cheaper -JVP passes. That choice is about compile-time memory and pass cost, never -semantics — an `m x m` residual-space basis over a tall system was a -compile-time memory blowup. `"fwd"`/`"rev"` force one mode (e.g. a residual -whose primitives lack a transpose rule needs `"fwd"`). The matrix-free -solvers never materialize `J` and ignore the setting; a *forced* mode in a -configuration where nothing dense could consume it — a matrix-free forward -solver with a CG-resolved `ad_solver` — is rejected at construction rather -than silently ignored. +## Inner-solve budget -## Float64 à la Carte +The Krylov configs default to `tol=None` (a dtype default: `1e-10` in float64, +`1e-6` in float32). A cheap fixed budget early and an exact solve late is +usually better than either alone: -The Gram and normal forward forms square the condition number (they factor -`J P J'` or `B'B`; the SVD and QR AD methods work from `B` at -`cond(B)`, but classifying singular values near the rank cutoff still -benefits from precision). If that system is ill-conditioned or implicit -derivatives must be accurate, reach for float64 — it fixes more numerical -trouble than any damping adjustment. Three grades, from narrowest to -widest: - -- **`metric_solve_dtype=jnp.float64`** promotes only the resolved metric - callbacks (fixed or factory-built). Kernel Gram factorizations are routinely - the worst-conditioned - piece of the whole pipeline, so this knob often earns float64 even in - otherwise-float32 programs — it is the right first move when the metric, - not the solver algebra, is the fragile part. -- **`linear_solve_dtype=jnp.float64`** promotes the dense linear-solve - pipelines: the `gram_cholesky`/`normal_cholesky` forward factorizations - and the assembled direct/SVD/QR AD methods, while the model stays float32 — measured - ~1.4x per `gram_cholesky` update at `m=100, n=2000` for a *trivial* - residual (an upper bound: real residual and Jacobian costs dominate and - stay float32), recovering the float64 answer to ~1e-6 on a 1e-7-spike - metric where plain float32 is ~5% wrong. -- **`jax_enable_x64`** globally remains the full fix when the model itself - needs it — and is still required for either knob: it is what makes - float64 arrays available (explicitly float32 data stays float32). +```python +CG(precond, tol=0.0, atol=0.0, maxiter=8) # cheap, fixed +``` -Choosing between the grades: the knobs' win is proportional to how much of -the step is model evaluation (residual + the `m` VJP Jacobian passes, which -stay float32) versus promoted algebra; when the promoted algebra IS the -step — trivial residuals, dense-metric-dominated updates — the knobs cost -about the same wall time as full x64 and their remaining win is halved -model memory and the unchanged float32 contract. Neither knob changes the -model evaluation dtype. For the solver's CG paths, the remedies remain -preconditioning and, when the attainable-residual floor binds, full x64. +then raise `iterative_maxiter` from a callback as the loss falls — see +[Callbacks](callbacks.md). The budget is traced state, so changing it costs no +recompilation. ## Damping -**Convergence is usually insensitive to the damping parameters — do not tune -them first.** The accept/reject loop self-corrects `init_damping` within a -few steps. Try them when you see specific signatures: - -- Many early rejections → raise `init_damping` (start nearer gradient - descent). -- Long rejection storms in float32 → set `max_damping` (~`1e6`) so damping - cannot overflow. -- Literal damping underflow → the default `min_damping=None` already resolves - to the residual dtype's smallest positive normal value. This representation - floor prevents flush-to-zero but does not keep the damping numerically active - in an ill-conditioned system. A standard scale-aware floor is on the order of - `eps * operator_scale`; pass that larger absolute `min_damping` explicitly. -- Accept/reject oscillation → bring `damping_decrease`/`damping_increase` - closer to 1 (e.g. 0.7 / 2.0) for smoother adaptation. -- All steps accepted but progress is slow → lower `init_damping` or decrease - faster (`damping_decrease=0.3`). - -## Schedule Accuracy, Cheap → Exact - -Inexact steps are cheap experiments early; near the solution, step quality -limits the convergence rate (and small damping makes the inner system harder -exactly then). Three patterns, in order of preference: - -1. **Relative `iterative_tol`** (e.g. `1e-2`) with a generous - `iterative_maxiter` cap: inner accuracy tightens automatically as the - residual shrinks. No scheduling code. -2. **Grow the CG budget in a callback** when the loss crosses a threshold — - single solve call, so implicit AD applies; see the - [cookbook recipe](callbacks.md#scheduled-inner-solve-accuracy). All of - `LMHyperparams` is resettable this way. -3. **Stage two solvers**: a coarse CG-form solve, then a dense endgame - (`auto`) warm-started with `result.x` and `result.lm_state`. The implicit - derivative is unaffected (it is defined at the returned solution only). - -Forward iterative tolerances and AD tolerances are separate. The -CG-based AD rules use `ad_solver_tol=None` by default, which means `1e-6` in -float32 and `1e-10` in float64; these defaults target derivative accuracy, not -cheap forward steps. Pass `ad_solver="svd"` -when you want the robust assembled pseudoinverse -under a matrix-free forward solver, or tune `ad_solver_tol`, `ad_solver_atol`, -`ad_solver_maxiter`, and `ad_solver_preconditioner(v)` for a matrix-free -derivative. - -Before scheduling accuracy, check whether a structural `dual_preconditioner` -removes the problem: when the dual operator's conditioning grows with problem -size (metric solves inject \(M^{-1}\) into it), a spectrally equivalent -preconditioner can pin the required budget at a small constant (in a -kernel-collocation case study, a flat `iterative_maxiter` of 2–20 across two -orders of magnitude in problem size) where the unpreconditioned budget grows -with refinement. See [Utilities](utilities.md#shermanmorrison-dual-preconditioner). -When no structural preconditioner is available — identity-metric -neural-network duals (empirical NTK Grams) are the canonical case — reach -for the randomized -[`nystrom_preconditioner`](utilities.md#nystrom-preconditioner-for-neural-network-least-squares): -its sketch-and-shift construction targets exactly the fast-decaying spectra -those duals show, and it reads the live damping, so one construction serves -the whole solve. - -Those helpers are all *frozen* at one linearization point. When the dual -operator rotates enough as LM drifts `x` that a preconditioner built at `x0` -decays into an ineffective approximation — the inner CG stalls or breaks down -several steps in, while rebuilding from the current iterate would keep it -converging — pass a -[`PreconditionerFactory(prepare, apply)`](utilities.md#iterate-adaptive-preconditioner-factory) -instead of `dual_preconditioner`. Its `prepare(x, args, p, aux)` rebuilds the -preconditioner state from the current iterate inside the jitted loop (once per -accepted step; a rejected step reuses the carried state), so keep `prepare` -cheap. It composes with recycling and seeds the implicit derivative's -preconditioner from the state at the solution. - -## Recycling and Deflation Across Steps - -When a frozen first-level `dual_preconditioner` plateaus above the accuracy bar -— it clusters most of the dual spectrum but leaves a handful of slow modes that -the fixed budget cannot resolve — carry a **deflation basis** across LM steps. -Pass `recycle=RecycleConfig(rank=k)` (requires `linear_solver="gram_cg"`). The -first-level `P` is unchanged; a second-level basis `U` is harvested from each -step's CG iterations (an eigCG-style thick restart) and recycled into the next -step's two-level preconditioner `M_defl(r) = P(r) + U E^{-1}(U'r)`, plus a -deflated, warm-started initial guess, at zero rebuild cost. Across a sequence of -slowly drifting shifted duals the carried basis adapts the *effective* -preconditioner every step, closing the terminal gap a frozen `P` cannot. - -- The additive scheme lifts each deflated eigenvalue `λ → λ + 1`, so it - *clusters* (and speeds CG) when the slow modes are small outliers near 0 and - `P` normalizes the bulk near 1 — the classic deflation regime. It is a strict - win precisely when a few isolated modes dominate the residual budget. -- **Prefer a damping-independent first-level `P`** (Sherman-Morrison, Woodbury, - cholesky-metric — all ignore λ). Eigenvector deflation is shift-invariant for - the unpreconditioned operator; under a λ-dependent `P` (nystrom, pad) the - preconditioned Ritz vectors drift with λ, weakening cross-step reuse (still - helpful, just approximate). -- `RecycleConfig.rank` (`k`) and `window` (`w`, default `max(2·rank, rank+4)`) - are **static compile knobs** — one program per value. `window` is the primary - memory knob (a transient `(m, w)` harvest buffer); keep it small. -- Recycling **composes** with the `iterative_maxiter` schedule above: the - carried basis shrinks the budget each step needs, and the traced schedule - (still resettable in a callback) then grows it toward the endgame. `warm_start` - (on by default) reuses the previous dual solution as the initial guess. -- Recycling never changes the converged root or the implicit p-derivative (both - are defined at the solution); it only accelerates the forward inner solves, and - the harvest is `stop_gradient`'d. - -## What Is Free to Sweep - -- **Free (traced, no recompile):** `max_steps`, `atol`/`gtol`/`xtol`, the - array-valued `LMHyperparams` fields (same dtype; a knob compiled out as - `None` cannot be switched on), and the *values* of `x0`/`args`/`p`. - The one exception is `max_steps` with `save_steps=True`: the history - buffer's shape depends on it, so each distinct value then retraces. -- **Recompiles per value (static):** `linear_solver`, `jacobian_mode`, - `ad_solver`, the `ad_solver_*` accuracy knobs, `linear_solve_dtype`, - `metric_solve_dtype`, `geodesic_acceleration`, `cache_jacobian`, - `has_aux`, the `GramMetric` callbacks, `metric_factory`, `dual_preconditioner`, - `preconditioner_factory`, `normal_preconditioner`, - `whitened_preconditioner`, `ad_solver_preconditioner`, `recycle` (the - `RecycleConfig`, whose `rank`/`window` size the carried basis), and the - callback function identity. - Solvers themselves compare by configuration, so a freshly constructed - solver with equal settings (around the same residual, metric, and - preconditioner objects) reuses the compiled loop — rebuilding the solver - per seed in an ensemble loop is free. What still forces a recompile is - rebuilding the *pieces* per call: an inline `lambda` residual or callback - at the call site, or a metric/preconditioner reconstructed around fresh - arrays (unhashable objects key by identity). Define those once at setup - scope. +`init_damping=1e-3` with `damping_decrease=0.5` / `damping_increase=4.0` is +the standard schedule. Reach for the others only on evidence: -For crude hyperparameter search: sweep `init_damping` on a log scale by -replacing the damping in an `init()` state — -`dataclasses.replace(solver.init(x0, args), damping=jnp.asarray(d))`, traced -and recompile-free — and treat the static list as an outer loop of at most a -few compilations. +- `min_damping` — lower it (e.g. `1e-12`) when the minimum-norm limit is the + point and the default floor is truncating the endgame; +- `max_damping` — cap it when a bad region sends damping to infinity and the + solver stalls instead of failing; +- `geodesic_acceptance_ratio` — lower it when the second-order correction is + being accepted on steps where it overshoots. -When sweeping `p` (or running continuation/homotopy), warm-start each solve -with the previous `result.x` — traced, recompile-free, and usually collapses -the step count. +## The ridge schedule -## Failure Signatures +For `RidgeLevenbergMarquardt`, a fixed ridge leaves an \(O(\text{ridge})\) +bias. `ridge_continuation(ridge_floor=...)` anneals toward the interpolating +limit, advancing a level whenever the current one is stationary. -| symptom | likely cause | remedy | -| --- | --- | --- | -| `status == NONFINITE` at step 0 | bad initial point or data | check `residual_fn(x0, ...)` directly | -| `qr` gives non-finite steps; other solvers fine | rank-deficient Jacobian | any other solver: the damped Gram/normal forms (`auto`), or `augmented_qr` / `lsmr` | -| `MAX_STEPS` but loss small and flat | settled without a stopping rule | keep the default usable fixed-step result, or set `gtol`/`xtol` for a `CONVERGED` diagnostic | -| damping grows without bound (float32 `inf`) | rejection storm | `max_damping`, or check residual scaling | -| every `solve` call recompiles | residual/callback/metric object rebuilt per call (solvers compare by configuration, but their pieces key by identity) | define the pieces once at setup scope | -| implicit `jax.jvp`/`vjp` wrong or zero | `p` not in the residual signature, or perturbing `args` | move perturbed quantities into `p` | -| NaN or no progress with a state-space Matérn metric | the shift is too small for the resolved grid | increase the positive `epsilon`, which is folded into the structured factorization exactly | +Calibrate `gtol` as roughly `1e-3 * ridge * sqrt(q(x*))` — the reported +`info.penalty_grad_norm` is exactly `sqrt(penalty_value)`, so a pilot run +gives you `q(x*)` to an order of magnitude. Choose `atol` **between** the +ridge-floor residual and the last intermediate level's residual (they differ +by roughly `1/decrease`), so the solve can only stop at the floor. -## The Metric +If the anneal freezes: widen `decrease` (e.g. `0.01`) first, since larger +jumps keep the per-level references generous; `stall_rtol ~ 0.99` is the +escape hatch when it does not. -In underdetermined problems the metric is not a preconditioner — it selects -*which* solution and *which* implicit derivative you get (minimum-`M`-norm). -For kernel parameterizations use `M = K` (coefficients) or `M = K^{-1}` -(function values); see the [kernel table](gauss_newton.md#choosing-the-metric-with-kernels). -If results look right but derivatives look wrong, check the metric before -anything else. +## Free to sweep without recompiling -For repeated kernel blocks plus free scalar parameters, use -`repeated_shifted_dense_metric` or `repeated_shifted_state_space_metric` for +Traced, so changing them reuses the compiled loop: `atol`/`gtol`/`xtol`, the +damping and ridge values, `p`, `args`, `max_steps` (without `save_steps`), and +every `LMHyperparams` field. -\[ -\operatorname{blockdiag}(K,\ldots,K,0_s)+\varepsilon I. -\] +Static, so changing them compiles a new program: the residual, the metric and +preconditioner objects, the linear-solver config, `has_aux`, +`cache_jacobian`, `geodesic_acceleration`, the callback, and any shape. -See [Repeated Shifted Kernel Metrics](utilities.md#repeated-shifted-kernel-metrics). -Choosing `epsilon`: the selected solution and its implicit derivative are -biased \(O(\varepsilon)\) away from the pure seminorm limit, while the metric -inverse is bounded by \(1/\varepsilon\) and the zero-tail dual spike has weight -proportional to \(1/\varepsilon\). Smaller shifts therefore improve seminorm -selection at the price of conditioning. Use float64 or a larger shift when the -metric solve reaches its attainable precision floor. +Build metrics and preconditioners **once at setup scope** — they hold arrays, +so they hash by identity and a rebuild keys a fresh compilation. -Choose the representation explicitly. When the model already holds a dense -kernel Gram, `repeated_shifted_dense_metric` is normally fastest at the -paper-sized grids: it factors \(K+\varepsilon I\) once and batches all repeated -blocks. For a sufficiently large ordered one-dimensional state-space kernel, -`repeated_shifted_state_space_metric` avoids dense \(K\) storage and uses -`matern_state_space` for Matérn-1/2, 3/2, and 5/2. There is no automatic -dense/state-space dispatch; benchmark the full solve rather than only a metric -callback. +## Failure signatures -On GPU the scan choice dominates everything (measured on an NVIDIA L40S, -n=1e5, float32): sequential applies take ~3.1–3.6 **seconds** per -solve+norm pair — a kernel launch per scan step — while the associative -(`parallel=True`) applies take ~0.5–0.9 **ms**, a ~3,000–7,000x gap. In -float64 the `parallel=None` default picks the parallel path off-CPU -automatically; in float32 it conservatively stays sequential (the parallel -substitutions have no contraction guarantee), so **on GPU in float32 pass -`parallel=True` explicitly** after checking finiteness on your grid — on -the L40S stress grids all four applies stayed finite and matched the -sequential path to ~1e-7 (well-conditioned) / ~5e-4 (stiff, -conditioning-amplified). On CPU the sequential default is right: at n=1e5 -the applies cost ~2.5–4.3 ms and even beat the GPU for the sequential -variant. One caveat: the one-time Cholesky *setup* is a sequential scan — -~0.9 s at n=1e5 on the L40S versus ~2–3 ms on CPU — so when the metric is -rebuilt from traced `sigma`/`ell` inside `jax.grad`/`vmap` sweeps at large -`n` on GPU, setup dominates the step. Reuse a constructed metric across -solves whenever the hyperparameters are fixed; parallel setup is tracked -as a follow-up issue. +| you see | likely | +|---|---| +| `NONFINITE` at step 0 | `x0` is outside the residual's domain | +| status `MAX_STEPS`, loss flat | damping stuck high; check `info.damping` | +| `CONVERGED` but the residual is large | `atol` fired on the wrong scale, or `gtol` alone stopped a ridge level | +| tangent finite but wrong | the `ad_solver`'s operator is singular for this shape — see [Metric LM](metric_lm.md#rank-deficiency-and-implicit-ad) | +| every solve recompiles | a metric, preconditioner, or callback rebuilt per call | diff --git a/docs/utilities.md b/docs/utilities.md deleted file mode 100644 index 40f41eb..0000000 --- a/docs/utilities.md +++ /dev/null @@ -1,570 +0,0 @@ -# GramMetric and Preconditioner Utilities - -The library keeps its metric constructors focused on dense, diagonal, and the -repeated shifted kernel geometry used by kernel least-squares models. For any -other geometry, construct a [`GramMetric`](metrics.md) directly. Iterative solver -preconditioners remain separate: they can approximate an operator without -changing the nonlinear least-squares problem, whereas a metric defines the -problem itself. Everything on this page serves the classic -`LevenbergMarquardt` hooks; the ridge solver's typed `Preconditioner` -subclasses (`IdentityPreconditioner`, the adaptive -`BlockEigenPreconditioner` + `block_eigen_state`) are documented on the -[Ridge LM page](ridge_lm.md#preconditioners). - -| Helper | Builds | Storage | -| --- | --- | --- | -| `metric_from_cholesky(L)` | dense `GramMetric` from \(M = LL^\top\) | \(O(n^2)\) | -| `metric_from_diagonal(weights)` | `GramMetric` from \(M = \operatorname{diag}(w)\) | \(O(n)\) | -| `repeated_shifted_dense_metric(K, ...)` | repeated dense kernel blocks plus a common shift | \(O(n^2)+O(1)\) | -| `repeated_shifted_state_space_metric(t, ...)` | the same geometry for an implicit state-space kernel Gram | \(O(nq^2)+O(1)\) | -| `matern_state_space(sigma, ell, nu)` | state-space inputs for Matérn-1/2, 3/2, or 5/2 | \(q=1,2,3\) | -| `sherman_morrison_preconditioner(solve, u, weight)` | `dual_preconditioner` for \(B = A + w\,uu^\top\) | one `solve` | -| `woodbury_preconditioner(solve, U, weights)` | `dual_preconditioner` for \(B = A + U\operatorname{diag}(w)U^\top\) | one `solve` + \(k \times k\) | -| `identity_preconditioner()` | the explicit "no preconditioner" choice | free | -| `nystrom_preconditioner(matvec, n, rank, key)` | randomized Nyström `dual_preconditioner` | two \((n, \text{rank})\) GEMVs | -| `pad_dual_preconditioner(base, n_real)` | extends a `dual_preconditioner` to a zero-padded residual | base + \(O(k)\) | - -## Dense and Diagonal Metrics - -For a dense positive-definite metric \(M=LL^\top\), pass the lower Cholesky -factor. A diagonal metric takes its positive weights directly: - -```python -import jax.numpy as jnp - -from nlls_gram import metric_from_cholesky, metric_from_diagonal - -dense_metric = metric_from_cholesky(jnp.linalg.cholesky(M)) -diagonal_metric = metric_from_diagonal(jnp.array([2.0, 1.0, 0.5])) -``` - -Both constructors provide `solve`, `norm`, `inv_sqrt`, and -`inv_sqrt_transpose`, including matrix right-hand sides where the callback -contract permits them. - -## Repeated Shifted Kernel Metrics - -Both repeated constructors implement exactly - -\[ -M = \operatorname{blockdiag}(\underbrace{K,\ldots,K}_{r},0_s) - + \varepsilon I - = \operatorname{blockdiag}(K+\varepsilon I_n,\ldots, - K+\varepsilon I_n,\varepsilon I_s). -\] - -The flattened parameter vector must contain the `r` kernel-coefficient blocks -first and the `s` zero-block coordinates last. The keyword arguments -`repeats`, `zero_pad_size`, and `epsilon` are mandatory: `repeats` is a -positive integer, `zero_pad_size` is a nonnegative integer (use `0` when no -tail is present), and `epsilon` is a positive scalar. The shift is part of the -metric, including on the trailing zero block. A nonpositive Python scalar is -rejected eagerly; a nonpositive traced or device scalar is mapped to `NaN` so -the solve fails loudly without a host synchronization. - -The constructors provide all four metric callbacks and therefore work with -both Gram and whitened linear solvers. They do not choose a representation -automatically: call the dense or state-space constructor explicitly. - -### Dense Repeated Metric - -```python -from nlls_gram import repeated_shifted_dense_metric - -metric = repeated_shifted_dense_metric( - K, - repeats=5, - zero_pad_size=3, - epsilon=1e-8, -) -``` - -For a positive-semidefinite `K`, `repeated_shifted_dense_metric` factors -\(K+\varepsilon I_n\) once. It stores -one \(n\times n\) Cholesky factor and the scalar shift, not `repeats` copies, -a full block diagonal, or a padding vector. Each callback reshapes the -repeated blocks into columns and applies the shared factor once to that batch; -in particular, `solve` performs two triangular solves total rather than two -per block. Matrix inputs add their right-hand sides to the same packed column -dimension. The tail uses scalar division or scaling by `epsilon`. - -Persistent storage is \(O(n^2)+O(1)\), independent of `repeats` and -`zero_pad_size`. Work still scales with the number of parameter coordinates, -as it must, but avoids factoring or loading a massive sparse-in-content dense -matrix. This is the preferred constructor when a dense `K` already exists and -for the small-to-moderate kernel grids where dense BLAS is fastest. - -### State-Space Repeated Metric - -For a stationary kernel with a finite-dimensional state-space representation, -the same geometry can be applied without constructing a dense \(K\): - -```python -from nlls_gram import ( - matern_state_space, - repeated_shifted_state_space_metric, -) - -metric = repeated_shifted_state_space_metric( - t, - *matern_state_space(sigma=1.0, ell=10.0, nu=1.5), - repeats=5, - zero_pad_size=3, - epsilon=1e-8, -) -``` - -Here `t` is the strictly increasing one-dimensional coordinate on which the -state-space kernel is evaluated; it need not represent calendar time. Ordering -is semantically required; non-increasing traced or device coordinates map the -metric shift to `NaN` so the solve fails loudly without a host synchronization. -The remaining positional inputs are the observation vector `h`, stationary -covariance `Pinf`, and callable `transition(dt)`. For Matérn-1/2, 3/2, and 5/2, -`matern_state_space` returns those objects with latent state dimension -\(q=1,2,3\), respectively. - -The constructor folds `epsilon` into the diagonal before a structured -Cholesky factorization. It stores one quasiseparable factor and applies all -repeated blocks as batched right-hand sides through forward or reverse scans. -The metric norm evaluates \(\lVert L^\top x\rVert\) in one reverse scan. No -dense \(K\), repeated factor, full block diagonal, or padding vector is -formed. Persistent storage is \(O(nq^2)+O(1)\), independent of `repeats` and -`zero_pad_size`, and each apply costs \(O(nq^2b)\) for `b` packed right-hand -side columns (for a vector input, `b == repeats`). - -`parallel=None` selects from the process default backend: associative scans -only for float64 off CPU and sequential scans otherwise. Pass `True` or -`False` when arrays use nondefault device placement or to force a path after -checking numerical agreement on the target grid. State-space structure does -not imply that it is faster at small `n`: benchmark the end-to-end solve, and -prefer `repeated_shifted_dense_metric` when a dense Gram is already needed by -the model. There is deliberately no automatic dense/state-space dispatch. - -## Sherman–Morrison Dual Preconditioner - -With `linear_solver="gram_cg"`, the `dual_preconditioner(v, damping)` argument -supplies an approximation of \((J M^{-1} J^\top + \lambda I)^{-1} v\) on -residual-space vectors. It never changes the subproblem being solved: at -inner convergence the step is identical, and a budget-truncated step still -lies in \(\operatorname{range}(M^{-1}J^\top)\), so the minimum-metric-norm -selection for underdetermined residuals is unchanged and an approximate -preconditioner is safe — even though `metric.solve` must stay exact. - -A metric weight \(m\) on a scalar parameter injects an exactly known rank-1 -spike into the dual operator. For the kernel-collocation family, a Jacobian -column \(-c\,u\) for that parameter contributes \((c^2/m)\,uu^\top\), and - -```python -from nlls_gram import sherman_morrison_preconditioner - -dual_preconditioner = sherman_morrison_preconditioner( - alpha_metric.solve, jnp.ones(n), c**2 / m_0 -) -``` - -builds \(B^{-1}\) for \(B = K + (c^2/m_0)\,\mathbf{1}\mathbf{1}^\top\) from -one kernel solve plus a rank-1 correction (\(B\), not \(P\): the docs reserve -\(P\) for \(M^{-1}\)). Under the unified shifted metric the scalar-block -weight is \(\varepsilon\), so the spike weight is \(c^2/\varepsilon\) — it -grows as \(\varepsilon\) shrinks, making the preconditioner more -load-bearing, not less. For \(k\) scalar parameters at once, -`woodbury_preconditioner(solve, U, weights)` is the rank-\(k\) -generalization (\(B = A + U\operatorname{diag}(w)U^\top\), one matrix -solve plus a \(k \times k\) Cholesky, reducing exactly to Sherman-Morrison -at \(k = 1\)). Such structural preconditioners -can be spectrally equivalent to the dual operator uniformly in \(n\), -keeping the inner CG budget constant where the unpreconditioned budget grows -with refinement — see the [Tuning Guide](tuning_guide.md). - -## Identity Preconditioner - -`linear_solver="gram_cg"` requires a `dual_preconditioner`, -`linear_solver="normal_cg"` a `normal_preconditioner`, and a -`gram_cg`-resolved AD solve an `ad_solver_preconditioner` — running -Krylov methods unpreconditioned should be a decision, not a default. -`identity_preconditioner()` is that decision made explicit and greppable: - -```python -from nlls_gram import identity_preconditioner - -solver = LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - dual_preconditioner=identity_preconditioner(), - ad_solver_preconditioner=identity_preconditioner(), -) -``` - -The returned callable accepts both hook signatures — `(v, damping)` and -`(v)` — so one helper serves all three arguments (and it trivially satisfies -the `normal_preconditioner` range-preservation requirement below). - -## The Normal-Space Preconditioner (`normal_cg`) - -`linear_solver="normal_cg"` requires a `normal_preconditioner(v, damping)`: -a jit-traceable, linear, SPD **parameter-space** approximation of -\((B^\top B + \lambda I_n)^{-1} v\) with \(B = JS\) -(`identity_preconditioner()` is the explicit opt-out). Like every -preconditioner it may approximate freely as far as *convergence* is -concerned — at inner convergence the step is unchanged. But it carries one -structural requirement with no Gram-side analogue: - -**Range preservation.** On rank-deficient problems the minimum-\(M\)-norm -selection rests on the CG iterates staying in -\(\operatorname{range}(B^\top)\): the right-hand side \(-B^\top r\) starts -there, the operator \(B^\top B + \lambda I\) maps the subspace to itself, so -unpreconditioned CG from zero never acquires a null-space component — the -converged step and every budget-truncated step stay selection-clean. A -preconditioner \(C\) enters the Krylov space through its images, so unless - -$$ -C\bigl(\operatorname{range}(B^\top)\bigr) \subseteq \operatorname{range}(B^\top), -$$ - -the iterates leak into the null space of \(B\) and the computed step -silently stops being the minimum-norm one — the CG residual still converges, -so nothing fails loudly. An arbitrary SPD approximation of the inverse does -**not** have this property, and rank deficiency is the package's home turf -(tall interpolation problems always carry redundant rows or collinear -columns). Safe constructions: the identity; polynomials in the operator -itself; an exact \((B^\top B + \tau I)^{-1}\) at a fixed shift -\(\tau > 0\); any \(C\) -that commutes with the orthogonal projector onto -\(\operatorname{range}(B^\top)\). On full-column-rank problems -(\(\operatorname{rank} B = n\)) the condition is vacuous and any SPD \(C\) -is safe. - -`dual_preconditioner`, `preconditioner_factory`, and `recycle` remain -`gram_cg`-only — they live in residual space and cannot serve the -parameter-space system. A `normal_cg`-resolved *implicit* solve needs no -preconditioner at all (its right-hand side lies in -\(\operatorname{range}(B^\top)\), so unpreconditioned CG already selects -the minimum-norm tangent); an optional `ad_solver_preconditioner` supplied -there acts in the same parameter space under the same range-preservation -requirement at `damping = 0` — see -[Implicit AD](implicit_ad.md#the-ad-solver-preconditioner). - -## Nyström Preconditioner for Neural-Network Least Squares - -When no structural preconditioner is available — typically neural-network -least squares under the identity metric, where the dual operator is the -\(m \times m\) empirical NTK Gram \(JJ^\top\) with fast spectral decay — -`nystrom_preconditioner(matvec, n, rank, key)` builds the randomized Nyström -preconditioner of -[Frangella, Tropp, and Udell](https://arxiv.org/abs/2110.02820): sketch the -PSD operator with a thin-QR'd Gaussian test matrix (`rank` operator -applications plus one \(O(n\,\text{rank}^2)\) factorization, once at -construction), recover the rank-`rank` approximation -\(\hat A = U\Lambda U^\top\), and apply - -$$ -v \mapsto U\frac{U^\top v}{\Lambda + \lambda} -+ \frac{v - UU^\top v}{\rho + \lambda}, -$$ - -with \(\rho\) the smallest retained eigenvalue and \(\lambda\) the **live** -LM damping — this is the one shipped helper that uses the `damping` -argument, so a single construction serves every damping value. The -unresolved complement is balanced at \(\rho + \lambda\) rather than -\(\lambda\); that balance carries the FTU condition-number guarantee for -fast-decaying spectra. `matvec` must apply a symmetric PSD operator and -accept `(n, k)` matrices (the `GramMetric.solve` shape contract). Like every -preconditioner it is frozen at construction, so for a nonlinear residual it -approximates the dual at the linearization point it was built from — -staleness across LM steps is safe (preconditioner error never moves the -converged root), and refresh cadence is a tuning knob. - -The NTK matvec assembles matrix-free from the residual at the initial -parameters via `jax.linearize` and `jax.linear_transpose` (this mirrors the -`test_cg_nystrom_mlp_ntk_example` test, which doubles as the runnable -example): - -```python -import jax -import jax.numpy as jnp -from jax.flatten_util import ravel_pytree - -from nlls_gram import ( - LevenbergMarquardt, - identity_preconditioner, - nystrom_preconditioner, -) - -# residual: m collocation residuals of a pure-jax MLP, n_params >> m -theta0, unravel = ravel_pytree(x0) -_, jvp_fn = jax.linearize(lambda th: residual(unravel(th)), theta0) -transpose_fn = jax.linear_transpose(jvp_fn, theta0) - - -def ntk_matvec(V): # (m, k) -> J (J' V), frozen at x0 - return jax.vmap( - lambda col: jvp_fn(transpose_fn(col)[0]), in_axes=1, out_axes=1 - )(V) - - -solver = LevenbergMarquardt( - residual, - linear_solver="gram_cg", - iterative_tol=1e-6, - iterative_maxiter=20, - dual_preconditioner=nystrom_preconditioner( - ntk_matvec, m, rank, jax.random.PRNGKey(0) - ), - ad_solver_preconditioner=identity_preconditioner(), -) -``` - -Passed as `ad_solver_preconditioner` the helper applies its undamped -(zero-damping) inverse, which is valid only when the retained spectrum is -strictly positive. - -## Iterate-Adaptive Preconditioner Factory - -Every helper above is *frozen*: built once, at one linearization point. That is -safe when the dual operator \(J M^{-1} J^\top + \lambda I\) stays spectrally -close as LM drifts \(x\). When it does not — the Jacobian rotates enough that a -preconditioner built at \(x_0\) decays into an ineffective approximation once -\(x\) moves, and the inner CG stalls or breaks down — pass a -`PreconditionerFactory(prepare, apply)` instead of `dual_preconditioner` (pass -exactly one of the two for `linear_solver="gram_cg"`; like both dual hooks it -is `gram_cg`-only). Its `prepare(x, args, p, aux)` -rebuilds the preconditioner state from the **current** iterate, inside the -jitted loop as traced ops with no recompiles: - -```python -from nlls_gram import LevenbergMarquardt, PreconditionerFactory - -def prepare(x, args, p, aux): - # model-structured build from the CURRENT iterate x (the user pytree, - # not the raveled theta); return any fixed-shape pytree of arrays - d = jnp.exp(A @ x) - return d * d # e.g. the exact current dual diagonal - -def apply(state, v, damping): - return v / (state + damping) # SPD, linear in v - -solver = LevenbergMarquardt( - residual_fn, - linear_solver="gram_cg", - preconditioner_factory=PreconditionerFactory(prepare, apply), - iterative_maxiter=..., -) -``` - -- `prepare(x, args, p, aux) -> state` receives the **user pytree** `x` (model - structure intact), the residual `args`, `p`, and the residual aux evaluated - at the same linearization point (`None` when `has_aux=False`) — the same - signature as `MetricFactory.prepare` — and returns a fixed-shape pytree of - arrays. -- `apply(state, v, damping) -> vector` is the per-iteration apply: an SPD, - linear-in-`v` approximation of \((J M^{-1} J^\top + \lambda I)^{-1} v\). It - must stay well-defined at `damping = 0`, because a `gram_cg`-resolved - implicit derivative reuses it (undamped) at the converged solution unless - an explicit `ad_solver_preconditioner` overrides it. - -`prepare` runs **once per accepted step**: after a rejected step \(x\) did not -move, so the carried state is reused and only the live `damping` changes. That -makes the build cost proportional to progress, not to iteration count — but for -an expensive `prepare` it is still one build per accepted step, so keep it -cheap (a diagonal, a small factorization) or fold the heavy work into `args`. -The factory **composes with `recycle`**: deflation runs unchanged on top of the -rebuilt first level (`M_defl(r) = \text{apply}(r) + U E^{-1} U^\top r`). It is -value-hashable on `(prepare, apply)`, so equal pairs share one compiled solve -loop — define them once at setup scope. - -## Padded Zero Residuals (Fixed Residual Shape) - -Some JAX workflows keep a fixed residual shape across problem instances by -appending residual entries that are identically zero: - -```python -def residual_padded(x): - r = residual(x) - return jnp.concatenate((r, jnp.zeros(pad, r.dtype))) -``` - -The padded rows have zero Jacobian rows, so the residual-space dual operator -becomes exactly block diagonal — -\(\operatorname{blockdiag}(J P J^\top + \lambda I,\; \lambda I)\) — and the -solvers behave as follows: - -- **The dense forms are unchanged mathematically.** Under `gram_cholesky` - the padded block decouples exactly and the step matches the unpadded step - (regression-tested for both the plain and geodesic-accelerated updates); - under the normal forms the zero rows contribute nothing to \(B^\top B\) - or \(B^\top r\), so the system is literally identical to the unpadded - one. One shape effect to know: padding raises \(m\), which can flip - `auto`'s shape rule from `gram_cholesky` to `normal_cholesky` — the step - is the same either way. Large padding costs the larger materialized - residual dimension (and, for the Gram form, its dense dual factor). -- **`gram_cg`**: a shape-fixed `dual_preconditioner` (a dense solve, - `nystrom_preconditioner`, or a Sherman-Morrison/Woodbury built at the - unpadded size) fails on the padded residual space and must be wrapped; - `pad_dual_preconditioner(base_preconditioner, n_real)` applies the base - callback on the first `n_real` coordinates and the exact - \(1/\lambda\) inverse on the padded block: - - ```python - from nlls_gram import pad_dual_preconditioner - - dual_preconditioner = pad_dual_preconditioner(base_preconditioner, n_real) - ``` - - A shape-generic base (`identity_preconditioner()`) stays valid unwrapped — - it just forgoes the exact padded-block inverse. Do **not** zero the padded - block instead: that makes the preconditioner singular rather than SPD, - even though it can appear to work when exactly-zero padding never excites - those coordinates. -- **`qr` does not survive padding**: the padded zero rows make the Jacobian - rank-deficient, which the QR path's triangular solves cannot handle — the - step is non-finite. Every other solver handles padding: the damped - Gram/normal forms directly, `augmented_qr` / `lsmr` through the damping - block that stays full column rank for \(\lambda>0\). -- **Implicit AD**: the padded rows make the *undamped* implicit systems - singular *but consistent* — their `p`-derivative rows are identically - zero too — which is exactly the singular-but-consistent regime of - [the implicit rules](implicit_ad.md#rank-deficiency-and-the-ridge). The - `svd` computes the minimum-metric-norm tangent through its spectral-filter - pseudoinverse, and a `normal_cg` AD solve computes it with no ridge in exact - arithmetic — on its default unridged path, with the inner CG run to - convergence, and either unpreconditioned or with a range-preserving - `ad_solver_preconditioner`. `regularized_normal_cg` is the separate biased - method; the loud rank guard belongs to `qr`, not `normal_cg`. A - `gram_cg`-resolved AD solve is the - fragile choice here — run-to-tolerance CG on the singular padded dual — - and `pad_dual_preconditioner` divides the padded block by the live - damping, so it is rejected at construction when passed as an - `ad_solver_preconditioner`. The minimum-metric-norm derivative equals the - unpadded derivative (padding only appends redundant equations), so when - in doubt differentiate the unpadded formulation. - -## Matrix-Free LSMR (Whitened Subproblem) - -`linear_solver="lsmr"` solves the whitened damped LM subproblem -`min_u ||r + B u||² + damping ||u||²` (`B = J S`, `S = metric.inv_sqrt`, -`S Sᵀ = M⁻¹`, step `s = S u`) with [LSMR](https://web.stanford.edu/group/SOL/software/lsmr/) -Golub-Kahan bidiagonalization, using only `J`/`Jᵀ` matvecs — the matrix-free -counterpart of `augmented_qr`. It exists for the same reason `qr`/`augmented_qr` -do: the Gram and normal operators (`J M⁻¹ Jᵀ + damping I`, `BᵀB + damping I`) -carry the *square* of the whitened operator's condition number, so at small -damping their steps bottom out at an `eps·cond` floor (which dense direct -solves hit too) with the error concentrated in the slow, selection-critical -directions. LSMR works at `cond(B) ~ sqrt`, restoring endgame accuracy. See -the [tuning guide](tuning_guide.md#solver-selection) for when to prefer it -over the CG forms. - -- **Stopping** maps the standard hooks: the normal-equations residual - `||Bᵀ(B u + r) + damping·u|| = |zetabar|` (LSMR's exact monotone quantity) is - driven below `iterative_tol · ||Bᵀr|| + iterative_atol`, capped by - `iterative_maxiter` (all traced, so a callback can reschedule them). With - `iterative_maxiter=None` a `min(m, n)`-scaled fallback cap applies. -- **Metric** it needs `metric.inv_sqrt` and `metric.inv_sqrt_transpose` (the - default identity metric supplies both); it does not use `metric.solve`. -- **Preconditioning** its hook is `whitened_preconditioner` (a - `WhitenedPreconditioner`), a parameter-space **right-preconditioner** - applying `R⁻¹`/`R⁻ᵀ` via `solve(v, damping)`/`solve_transpose(w, damping)`. - The solver runs LSMR on the augmented preconditioned operator - - z → [B(solve(z)); sqrt(damping)·solve(z)] - w → solve_transpose(Bᵀ w[:m]) + sqrt(damping)·solve_transpose(w[m:]) - - and un-preconditions the final iterate, `u = R⁻¹ z`. Because the damping - row is `sqrt(damping)·R⁻¹z` — not `sqrt(damping)·z` — the least-squares - problem in `z` is exactly `min ||B u + r||² + damping ||u||²` over - `u = R⁻¹ z`: **every `damping > 0` *posed* subproblem is the - identity-damped whitened subproblem**, so at inner convergence the step - is identical to plain LSMR's and the `damping → 0` selection limit is the - minimum-metric-norm step for *any* `R`. `R` changes the iteration path, - not the subproblem — a budget-truncated (unconverged) iterate can still - depend on `R`. A good `R` (a Schur-complement factor of the parameter-space normal - operator is canonical) clusters the spectrum of `B R⁻¹` and cuts the - endgame iteration count by orders of magnitude — an ill-conditioned - whitened operator can need thousands of plain iterations versus tens - preconditioned. Stopping (`iterative_tol`/`iterative_atol`) is measured on - the preconditioned operator. The half-solves receive the live `damping` - like `dual_preconditioner(v, damping)`. `None` (default) runs plain LSMR. - `dual_preconditioner`, `preconditioner_factory`, and `recycle` remain - `gram_cg`-only and are rejected loudly for `lsmr`. -- **Differentiation**: reverse-AD through `update` works (the whitened - solution is wrapped in `lax.custom_linear_solve` on the SPD preconditioned - normal operator `R⁻ᵀ(BᵀB + damping I)R⁻¹`). Differentiating a forward - `solve(...).x` uses `direct` for a square system and `svd` otherwise - (`ad_solver="auto"`); set - `ad_solver="normal_cg"` (no preconditioner needed) or - `"gram_cg"` with an `ad_solver_preconditioner` for a fully matrix-free - derivative. - -The standalone [`lsmr`](#nlls_gram.lsmr) function (operator/transpose matvecs, -`b`, `damp`) is exposed too, returning `(x, LSMRState)` with iteration count and -final normal-equations residual. - -## Krylov Recycling / Deflation - -`recycle=RecycleConfig(rank=k)` on a `gram_cg` solver carries a deflation basis -across LM steps: each step harvests an eigCG-style basis from its CG iterations -and recycles it into the next step's two-level additive preconditioner -`M_defl(r) = P(r) + U E^{-1}(U'r)` (first-level `P` = the frozen -`dual_preconditioner`, or the `preconditioner_factory`'s current iterate-built -`apply` when one is used) plus a deflated warm start. See the -[tuning guide](tuning_guide.md#recycling-and-deflation-across-steps) for when it -pays off and how to configure `rank`/`window`. - -The building blocks are also exposed for standalone matrix-free solves: - -- [`deflated_pcg`](#nlls_gram.deflated_pcg) — two-level deflated PCG with the - harvest; returns `(solution, HarvestState)`. -- [`build_coarse_operator`](#nlls_gram.build_coarse_operator) — precompute - `W = A U` and the ridged Cholesky factor of `E = U'A U` (built once per step, - reused across right-hand sides). -- `RecycleState` rides `LMState.recycle`; its `iterations` / `residual_norm` - fields report the last velocity solve's diagnostics. - -The `E`-ridge is a trace-scaled shift with a dtype-keyed absolute floor -(`1e-12` float64, `1e-6` float32, floored at `tiny/eps`), so the coarse -Cholesky stays finite even for a zero or rank-deficient `U`; it lives only -inside a preconditioner and never moves the converged root. The harvest -reorthonormalizes its window (`reorthogonalize=True`, the robust default) so the -emitted basis is orthonormal; a genuinely non-finite operator still propagates -loudly rather than being clamped. - -## API - -::: nlls_gram.RecycleConfig - -::: nlls_gram.RecycleState - -::: nlls_gram.deflated_pcg - -::: nlls_gram.HarvestState - -::: nlls_gram.build_coarse_operator - -::: nlls_gram.recycled_cg - -::: nlls_gram.lsmr - -::: nlls_gram.LSMRState - -::: nlls_gram.WhitenedPreconditioner - -::: nlls_gram.metric_from_cholesky - -::: nlls_gram.metric_from_diagonal - -::: nlls_gram.repeated_shifted_dense_metric - -::: nlls_gram.repeated_shifted_state_space_metric - -::: nlls_gram.matern_state_space - -::: nlls_gram.sherman_morrison_preconditioner - -::: nlls_gram.woodbury_preconditioner - -::: nlls_gram.identity_preconditioner - -::: nlls_gram.nystrom_preconditioner - -::: nlls_gram.PreconditionerFactory - -::: nlls_gram.pad_dual_preconditioner diff --git a/mkdocs.yml b/mkdocs.yml index bdbd72b..ca2f4c4 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -44,10 +44,10 @@ extra_javascript: nav: - Home: index.md - Ridge LM: ridge_lm.md - - Callbacks and Cookbook: callbacks.md + - Metric LM: metric_lm.md + - Metrics and Preconditioners: metrics.md + - Callbacks: callbacks.md - Multi-Start: multi_start.md - - Gram Metrics: metrics.md - - Utilities: utilities.md - Implicit Differentiation: implicit_ad.md - - Tuning Guide: tuning_guide.md - - Metric Gauss-Newton: gauss_newton.md + - Tuning: tuning_guide.md + - API: api.md diff --git a/pyproject.toml b/pyproject.toml index 99f65fc..868a701 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "hatchling.build" [project] name = "nlls-gram" -version = "2.6.0" +version = "2.7.0" description = "Metric-aware Levenberg-Marquardt nonlinear least-squares for JAX" readme = "README.md" license = "MIT" diff --git a/uv.lock b/uv.lock index 31002bb..2aff017 100644 --- a/uv.lock +++ b/uv.lock @@ -726,7 +726,7 @@ wheels = [ [[package]] name = "nlls-gram" -version = "2.6.0" +version = "2.7.0" source = { editable = "." } dependencies = [ { name = "jax" }, From 49376abd0994cf9c0f7edb49b8c3f21015cf7985 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 01:46:59 -0700 Subject: [PATCH 07/22] chore: rename the metric benchmark, drop stale name references Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- ...ted_shifted_metric_benchmark.py => test_metric_benchmark.py} | 0 benchmarks/test_ridge_lm_benchmark.py | 2 +- src/nlls_gram/experimental/quasiseparable.py | 2 +- 3 files changed, 2 insertions(+), 2 deletions(-) rename benchmarks/{test_repeated_shifted_metric_benchmark.py => test_metric_benchmark.py} (100%) diff --git a/benchmarks/test_repeated_shifted_metric_benchmark.py b/benchmarks/test_metric_benchmark.py similarity index 100% rename from benchmarks/test_repeated_shifted_metric_benchmark.py rename to benchmarks/test_metric_benchmark.py diff --git a/benchmarks/test_ridge_lm_benchmark.py b/benchmarks/test_ridge_lm_benchmark.py index 75d03d2..7f3b78e 100644 --- a/benchmarks/test_ridge_lm_benchmark.py +++ b/benchmarks/test_ridge_lm_benchmark.py @@ -1,7 +1,7 @@ """Per-update step cost: ridge LM (cholesky/qr/cg) vs metric LM at the kernel-driver problem sizes (p = repeats * n + free parameters, m residuals). The residual is a fixed random affine map so the benchmark isolates the -solver's linear algebra, matching test_repeated_shifted_metric_benchmark's +solver's linear algebra, matching test_metric_benchmark.py's kernel geometry. """ diff --git a/src/nlls_gram/experimental/quasiseparable.py b/src/nlls_gram/experimental/quasiseparable.py index 97a3a29..3166001 100644 --- a/src/nlls_gram/experimental/quasiseparable.py +++ b/src/nlls_gram/experimental/quasiseparable.py @@ -52,7 +52,7 @@ def matern_state_space(sigma, ell, nu): Nugget-free Matern-3/2 and 5/2 Grams on fine grids are extremely ill-conditioned. Pass a positive ``epsilon`` to - ``repeated_shifted_state_space_metric``; the shift is folded into its + ``StateSpaceMetric``; the shift is folded into its structured factorization exactly. """ From 1ae43b29f6947da9bf70e8ee261ef6589f4c1fee Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 02:05:23 -0700 Subject: [PATCH 08/22] fix: reject solver configs in roles they cannot fill, and three AD bugs From an external review. Five real bugs, all reproduced before fixing: 1. The ridge solver accepted GramCG, whose dual operator never sees the penalty rows -- it returned the UNPENALIZED step (1.0 where the ridge step is 0.5) with no complaint. It only rejected Cholesky(form="gram"). 2. The normal-CG implicit VJP's push-through transpose reused the parameter-space preconditioner for its two dual solves, handing an m-vector to a hook expecting n. Those solves are now unpreconditioned, which is what residual space requires here. 3. ad_solver=QR() was accepted and silently ran dense Cholesky; the ridge solver treated QR/SVD/GramCG as normal CG; forward SVD() failed only later inside update. 4. Both init methods built the hook context WITHOUT lm_state, so a metric or preconditioner prepare() reading ctx.lm_state.damping -- documented as available -- crashed on the first call. 5. BlockEigenPreconditioner unconditionally read ctx.lm_state.ridge, which is None under LevenbergMarquardt, so it could not serve the metric solver at all. (3) is fixed structurally rather than case by case: each config declares supports_forward / supports_ad / supports_penalty, and one shared _validate_configuration in the base rejects the combination at construction. Cholesky.form and jacobian_mode now reject unknown values instead of falling through to a different algorithm, and the metrics validate free_scale > 0 and size >= 0 (a non-positive free_scale makes the whitening noninvertible). Also from the review: _cold_state and _block_sizes were still duplicated between the solvers and move to the base; LMState.recycle and LevenbergMarquardt.ridge were dead after their features were removed; the ridge module and LMInfo docstrings still described blockdiag(F, I) and metric-LM grad_norm as ||J'r||, both stale since whitening became shared. Tests: the reject-step cache test was silently SKIPPING (its fixture no longer produced a rejected step) and now exercises the path; the padded-SVD test checked only the primal, where ad_solver affects only the tangent; added coverage for role rejection, free_scale's effect on step and tangent, and a tall normal-CG VJP with a dimension-specific preconditioner (which is what catches bug 2). 165 passed, 12 skipped. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/linear_solvers.py | 46 +++++++++++++-- src/nlls_gram/lm_core.py | 66 +++++++++++++++++++++ src/nlls_gram/lm_types.py | 15 +++-- src/nlls_gram/metric_lm.py | 46 ++++----------- src/nlls_gram/metrics.py | 15 +++++ src/nlls_gram/preconditioners.py | 58 ++++++++++--------- src/nlls_gram/ridge_lm.py | 43 ++------------ tests/test_failed_implicit_ad.py | 2 +- tests/test_metric_lm.py | 98 ++++++++++++++++++++++++++------ tests/test_multi_start.py | 3 +- tests/test_ridge_lm.py | 13 +++++ 11 files changed, 269 insertions(+), 136 deletions(-) diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index 4ecc537..abdb42a 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -179,10 +179,25 @@ class StepSolver(NamedTuple): class LinearSolver: - """Base class for the typed configs. ``materializes_jacobian`` drives the - dense ``J'`` assembly and its reject-step reuse.""" + """Base class for the typed configs. + + The class attributes declare which roles a config can fill, so an + unsupported combination is rejected at construction rather than silently + resolving to a different algorithm: + + - ``materializes_jacobian`` drives the dense ``J'`` assembly and its + reject-step reuse; + - ``supports_forward`` / ``supports_ad``: the ``linear_solver`` and + ``ad_solver`` roles; + - ``supports_penalty``: whether the config can carry + :class:`~nlls_gram.RidgeLevenbergMarquardt`'s penalty rows. The dual + operator never sees them, so the Gram forms cannot. + """ materializes_jacobian = True + supports_forward = True + supports_ad = True + supports_penalty = True def new_cache(self, m, n, n_m, dtype, penalized): """The reject-step cache pytree at ``init``, or ``None``.""" @@ -214,6 +229,17 @@ class Cholesky(LinearSolver): form: str = "auto" + def __post_init__(self): + if self.form not in ("auto", "gram", "normal"): + raise ValueError( + f"Cholesky.form must be 'auto', 'gram', or 'normal'; got {self.form!r}" + ) + + @property + def supports_penalty(self): + # form="auto" resolves to normal under a penalized subproblem. + return self.form != "gram" + def _resolved_form(self, m, n, penalized): # The ridge solver's penalty rows have no dual analogue -- the dual # operator J~J~' never sees them -- so a penalized subproblem is @@ -292,8 +318,14 @@ class QR(LinearSolver): damping rows, and those rows keep the system full rank for any ``damping > 0``, so a rank-deficient Jacobian is handled rather than producing a non-finite step. No knobs. + + Forward only: the implicit-AD system is undamped, so the damping rows that + make this path well posed vanish there. Use ``SVD()`` for a rank-deficient + tangent. """ + supports_ad = False + def new_cache(self, m, n, n_m, dtype, penalized): rows = min(m + n_m, n + 1) if penalized else min(m, n + 1) return QRCache( @@ -489,11 +521,12 @@ class GramCG(_KrylovConfig): ``preconditioner`` acts on residual-space vectors -- an SPD approximation of ``(J~J~' + damping I)^{-1}`` -- which is the only difference from :class:`CG`'s contract, and the reason the two are separate configs rather - than one with a flag. Only the ridge solver has penalty rows, and they - have no dual analogue, so this config serves - :class:`~nlls_gram.LevenbergMarquardt` alone. + than one with a flag. The ridge penalty rows have no dual analogue, so + this config serves :class:`~nlls_gram.LevenbergMarquardt` alone. """ + supports_penalty = False + preconditioner: Preconditioner tol: float | None = None atol: float = 0.0 @@ -543,5 +576,8 @@ class SVD(LinearSolver): dense fallback rather than the default. """ + supports_forward = False + supports_penalty = False + def prepare(self, sub): raise NotImplementedError("SVD is an ad_solver, not a forward solver") diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 02f1116..3e46782 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -55,6 +55,57 @@ def __eq__(self, other): def __hash__(self): return self._static_hash + def _validate_configuration(self, linear_solver, ad_solver, penalized): + """Reject a config in a role it cannot fill, at construction. + + Without this an unsupported combination resolves to a DIFFERENT + algorithm -- ``ad_solver=QR()`` quietly running dense Cholesky, or the + ridge solver handing its penalized subproblem to a dual form that + never sees the penalty rows. + """ + role = [(linear_solver, "linear_solver", "supports_forward")] + if ad_solver is not None: + role.append((ad_solver, "ad_solver", "supports_ad")) + for config, keyword, attribute in role: + if not getattr(config, attribute): + raise ValueError( + f"{config!r} cannot serve as {keyword}: it does not " + f"implement that role" + ) + if penalized and not config.supports_penalty: + raise ValueError( + f"{config!r} cannot serve as {keyword} for the ridge " + "objective: its operator never sees the penalty rows" + ) + if self.jacobian_mode not in ("auto", "fwd", "rev"): + raise ValueError(f"unknown jacobian_mode: {self.jacobian_mode}") + + def _block_sizes(self, theta_size): + # The free-block size is inferred from the flattened iterate: the + # metric covers the leading metric.size coordinates, the rest is free. + n_m = self.metric.size + if n_m > theta_size: + raise ValueError( + f"the metric covers {n_m} leading coordinates but x flattens " + f"to only {theta_size}; the free block is len(x) - metric.size " + "and must be nonnegative" + ) + return n_m, theta_size - n_m + + def _cold_state(self, lm_state): + # Drawn multi-start lanes must not reuse caches or hook state built at + # another (x, args); damping, ridge, and hyper stay inherited from the + # caller's initial state. + updates = {} + for flag in ("jacobian_valid", "metric_valid", "precond_valid"): + if getattr(lm_state, flag) is not None: + updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) + if lm_state.solver_cache is not None: + updates["solver_cache"] = jax.tree.map( + jnp.zeros_like, lm_state.solver_cache + ) + return dataclasses.replace(lm_state, **updates) if updates else lm_state + def _resolve_jacobian_mode(self, m, n): # "auto" vmaps the identity basis of the SMALL side: n forward-mode # columns when the system is tall or square (n <= m), m reverse-mode @@ -166,6 +217,21 @@ def _extended_solve_transpose(self, v, ctx): axis=0, ) + def _init_hook_state(self, theta, lm_state, args, p): + """The metric's and preconditioner's state at ``x0``, valid there, so + the first update reuses it. The flags stay absent when the hooks are + stateless.""" + ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) + valid = jnp.asarray(True, dtype=jnp.bool_) + hooks = {} + if self._metric_prepares: + hooks["metric_state"] = self.metric.prepare(theta, ctx) + hooks["metric_valid"] = valid + if self._precond_prepares: + hooks["precond"] = self.preconditioner.prepare(theta, ctx) + hooks["precond_valid"] = valid + return hooks + def _hook_state(self, theta, lm_state, args, p): """The metric's and preconditioner's prepared state for this step: reused while still valid (a rejected step left ``x`` in place, or the diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py index ce080f6..aee4d89 100644 --- a/src/nlls_gram/lm_types.py +++ b/src/nlls_gram/lm_types.py @@ -159,7 +159,6 @@ class LMState: metric_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. precond: the preconditioner's ``prepare`` output at the current ``x``. precond_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. - recycle: Krylov recycling state. """ damping: jax.Array @@ -174,7 +173,6 @@ class LMState: metric_valid: jax.Array | None = None precond: Any = None precond_valid: jax.Array | None = None - recycle: Any = None @jax.tree_util.register_dataclass @@ -192,11 +190,12 @@ class LMInfo: ``RidgeLevenbergMarquardt`` -- ridge code that means equation error must read ``resid_loss``. - The ridge solver runs in the whitened variable ``y = F_bar x``, so its + BOTH solvers run in the whitened variable ``y = F_bar x``, so ``grad_norm``, ``step_norm``, and ``penalty_grad_norm`` are Euclidean in ``y``: steps measured in the W-norm, gradients in the dual W^{-1}-norm. - Objective values are unaffected -- whitening is a linear bijection of the - same objective. + With the default Euclidean metric they are the plain quantities. Objective + values are unaffected -- whitening is a linear bijection of the same + objective. Attributes: loss: objective at the retained iterate, ``min(loss_old, @@ -209,9 +208,9 @@ class LMInfo: used_geodesic: ``()`` bool, whether the geodesic correction entered the accepted step. acceleration_ratio: ``()`` acceleration-to-velocity norm ratio. - grad_norm: ``()`` stationarity residual at the pre-step ``x``: - ``||J' r||`` for the metric solver, and the whitened - ``||F_bar^{-T} J'r + ridge [y_m; 0]||`` for the ridge solver. + grad_norm: ``()`` whitened stationarity residual at the pre-step + ``x``: ``||F_bar^{-T} J'r||``, plus ``ridge [y_m; 0]`` for the + ridge solver. step_norm: ``()`` norm of the candidate step, reported even when the step is rejected. ridge: ``()`` the ridge weight used this step (ridge solver only). diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index 21f3d07..977da39 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -119,7 +119,6 @@ def __init__( self.residual_fn = canonical_residual self.residual_arity = residual_arity self.metric = _EuclideanMetric() if metric is None else metric - self.ridge = None self.init_damping = init_damping self.damping_decrease = damping_decrease self.damping_increase = damping_increase @@ -128,6 +127,7 @@ def __init__( self.linear_solver = linear_solver self.jacobian_mode = jacobian_mode self.ad_solver = ad_solver + self._validate_configuration(linear_solver, ad_solver, penalized=False) krylov = isinstance(linear_solver, (CG, GramCG)) if krylov: self.preconditioner = linear_solver.preconditioner @@ -198,16 +198,6 @@ def __init__( ) self._static_hash = hash(self._static_key) - def _block_sizes(self, theta_size): - # The Euclidean default has size 0, so the whole vector is free block. - n_m = self.metric.size - if n_m > theta_size: - raise ValueError( - f"the metric covers {n_m} leading coordinates but x flattens " - f"to only {theta_size}" - ) - return n_m, theta_size - n_m - def init(self, x0, args=None, *, p=None): """Build the initial :class:`~nlls_gram.LMState` at ``x0``. @@ -222,15 +212,7 @@ def init(self, x0, args=None, *, p=None): dtype = residual.dtype min_damping = _damping_floor(self.min_damping, dtype) damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) - hooks = {} - ctx = SolverContext(x=theta, args=args, p=p) - valid = jnp.asarray(True, dtype=jnp.bool_) - if self._metric_prepares: - hooks["metric_state"] = self.metric.prepare(theta, ctx) - hooks["metric_valid"] = valid - if self._precond_prepares: - hooks["precond"] = self.preconditioner.prepare(theta, ctx) - hooks["precond_valid"] = valid + hooks = self._init_hook_state(theta, LMState(damping), args, p) if not self.cache_jacobian: return LMState(damping, **hooks) return LMState( @@ -485,19 +467,6 @@ def _cast_state(self, lm_state, dtype): hyper=_cast_hyper(lm_state.hyper, dtype), ) - def _cold_state(self, lm_state): - # Drawn multi-start lanes must not reuse caches or hook state built at - # another (x, args); damping and hyper stay inherited. - updates = {} - for flag in ("jacobian_valid", "metric_valid", "precond_valid"): - if getattr(lm_state, flag) is not None: - updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) - if lm_state.solver_cache is not None: - updates["solver_cache"] = jax.tree.map( - jnp.zeros_like, lm_state.solver_cache - ) - return dataclasses.replace(lm_state, **updates) if updates else lm_state - def _ranking_objective(self, result, p, callback): # Without a callback info.loss already reports the objective at the # retained iterate; a callback can replace x/args after the last @@ -639,14 +608,14 @@ def Bt(w): def apply_M(v): return self.ad_solver_preconditioner.apply(v, zero_damping, ctx) - def cg(matvec, rhs): + def cg(matvec, rhs, preconditioner=apply_M): solution, _ = jsp_sparse_linalg.cg( matvec, rhs, tol=self._ad_cg_tol(dtype), atol=jnp.asarray(self.ad_solver_atol, dtype=dtype), maxiter=self.ad_solver_maxiter, - M=apply_M, + M=preconditioner, ) return solution @@ -689,7 +658,12 @@ def transpose_solve(_, c): return Bt(dual_solve(dual_solve(B(c)))) def dual_solve(y): - return cg(lambda w: B(Bt(w)), y) + # UNPRECONDITIONED: this solve is posed on residual-space + # m-vectors, while self.ad_solver_preconditioner is the + # parameter-space one CG's own operator takes. Handing it an + # m-vector is a shape error at best and a wrong tangent at + # worst. + return cg(lambda w: B(Bt(w)), y, preconditioner=None) rhs = -Bt(residual_p_dot) return jax.lax.custom_linear_solve( diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index e482c49..b13259b 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -118,6 +118,13 @@ def norm(self, v, ctx): return jnp.linalg.norm(self.factor_apply(v, ctx)) +def _check_free_scale(free_scale): + # F_bar = blockdiag(F, sqrt(free_scale) I), so a non-positive scale makes + # the whitening noninvertible or complex. + if free_scale <= 0: + raise ValueError("free_scale must be positive") + + def _check_leading_size(v, size): if v.shape[0] != size: raise ValueError( @@ -137,6 +144,11 @@ class IdentityMetric(Metric): size: int free_scale: float = 1.0 + def __post_init__(self): + if self.size < 0: + raise ValueError("size must be nonnegative") + _check_free_scale(self.free_scale) + def factor_apply(self, v, ctx): _check_leading_size(v, self.size) return v @@ -172,6 +184,7 @@ def __post_init__(self): L = jnp.asarray(self.L) if L.ndim != 2 or L.shape[0] != L.shape[1] or L.shape[0] == 0: raise ValueError("L must be a nonempty square matrix") + _check_free_scale(self.free_scale) object.__setattr__(self, "L", L) object.__setattr__(self, "size", L.shape[0]) @@ -204,6 +217,7 @@ def __post_init__(self): weights = jnp.asarray(self.weights) if weights.ndim != 1: raise ValueError("weights must be 1-D") + _check_free_scale(self.free_scale) object.__setattr__(self, "weights", weights) object.__setattr__(self, "size", weights.shape[0]) @@ -253,6 +267,7 @@ def __post_init__(self): raise TypeError("F must have a real floating-point dtype") if self.repeats < 1: raise ValueError("repeats must be a positive integer") + _check_free_scale(self.free_scale) object.__setattr__(self, "F", F.astype(dtype)) object.__setattr__(self, "size", self.repeats * F.shape[0]) diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index 5dca700..f37d666 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -1,16 +1,13 @@ -"""Preconditioner types and helpers for the package's Krylov paths. - -:class:`Preconditioner` (with :class:`IdentityPreconditioner`) is the typed -hook of :class:`~nlls_gram.RidgeLevenbergMarquardt`'s ``CG`` config: an SPD -approximation of the damped whitened normal inverse, receiving the live -solver state through a :class:`~nlls_gram.SolverContext`. - -The remaining helpers serve ``LevenbergMarquardt``'s string-named solver -menu: a ``dual_preconditioner(v, damping)`` callback supplies an -approximation of ``(J M^{-1} J' + damping I)^{-1} v`` on residual-space -vectors for ``linear_solver="gram_cg"``. Unlike ``metric.solve`` -- which -defines the converged root and must stay exact -- a preconditioner never -changes the subproblem being solved, so approximations are safe. +"""Preconditioners for the Krylov configs of both solvers. + +``apply(v, damping, ctx)`` returns an SPD approximation of the damped +operator's inverse. Which space ``v`` lives in is named by the config that +consumes it: :class:`~nlls_gram.CG` is parameter space, +:class:`~nlls_gram.GramCG` residual space. + +Unlike a :class:`~nlls_gram.Metric` -- which defines the converged root and +must stay exact -- a preconditioner only changes the CG iteration path, so +approximations and staleness are safe. """ from dataclasses import dataclass, field @@ -24,20 +21,18 @@ class Preconditioner: """SPD preconditioner for ``RidgeLevenbergMarquardt``'s CG paths. - ``apply(v, damping, ctx)`` returns an SPD approximation of - ``(J~'J~ + ridge E + damping I)^{-1} v`` on whitened parameter-space - vectors. In the forward role (``linear_solver=CG(...)``) it sits in CG's - ``M`` slot with the live damping; in the AD role (``ad_solver=CG(...)``) - the implicit-AD system is undamped and ``damping`` is zero. ``ctx`` is - the same :class:`~nlls_gram.SolverContext` the metric factor ops receive - (the flat iterate, the live ``LMState``, ``args``, ``p``), so a - preconditioner can key off the solver state. A preconditioner changes - the CG iteration path, never the subproblem being solved, so - approximations are safe. - - Implement a custom preconditioner as a small dataclass (``eq=False`` - identity hashing when it holds arrays -- construct once at setup scope - and reuse, since the instance enters the solver's compile-cache key):: + ``apply(v, damping, ctx)`` returns an SPD approximation of the damped + operator's inverse -- ``(J~'J~ + ridge E + damping I)^{-1}`` in parameter + space under :class:`~nlls_gram.CG`, ``(J~J~' + damping I)^{-1}`` in + residual space under :class:`~nlls_gram.GramCG`. In the forward role it + sits in CG's ``M`` slot with the live damping; in the ``ad_solver`` role + the implicit system is undamped and ``damping`` is zero. ``ctx`` is the + same :class:`~nlls_gram.SolverContext` the metric factor ops receive, so a + preconditioner can key off the solver state. + + Implement a custom one as a small dataclass (``eq=False`` identity hashing + when it holds arrays -- construct once at setup scope and reuse, since the + instance enters the solver's compile-cache key):: @dataclass(frozen=True, eq=False) class JacobiPreconditioner(Preconditioner): @@ -145,7 +140,14 @@ def prepare(self, theta, ctx): def apply(self, v, damping, ctx): state = ctx.preconditioner_state - ridge = jnp.asarray(ctx.lm_state.ridge, dtype=v.dtype) + # LevenbergMarquardt carries no ridge, so its metric-block families + # shift by the damping alone. + carried = ctx.lm_state.ridge + ridge = ( + jnp.zeros((), v.dtype) + if carried is None + else jnp.asarray(carried, dtype=v.dtype) + ) permuted = v[state["permutation"]] pieces = [] offset = 0 diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 9cc356f..288f662 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -13,7 +13,8 @@ iteratively regularized Gauss-Newton method (Bakushinskii 1992; Blaschke-Neubauer-Scherzer 1997; Kaltenbacher-Neubauer-Scherzer 2008). Numerically the solver runs entirely in the whitened variable -``y = F_bar x`` (``W = F'F``, ``F_bar = blockdiag(F, I)``): stock Euclidean +``y = F_bar x`` (``W = F'F``, ``F_bar = blockdiag(F, sqrt(free_scale) I)``): +stock Euclidean LM on the augmented residual ``[r; sqrt(ridge) y_m]`` (Marquardt 1963; More 1978) with geodesic acceleration (Transtrum-Sethna 2012); the ``qr`` path uses corrected semi-normal equations (Bjorck 1987; Bjorck 1996 Sec. 6.6.5). @@ -417,12 +418,6 @@ def __init__( raise ValueError("min_damping must be positive and at most init_damping") if max_damping is not None and max_damping < init_damping: raise ValueError("max_damping must be at least init_damping") - if getattr(linear_solver, "form", "normal") == "gram": - raise ValueError( - "Cholesky(form='gram') factors the dual J~J~', which never " - "sees the ridge penalty rows; the ridge objective needs the " - "normal form" - ) self.residual_fn = canonical_residual self.residual_arity = residual_arity self.metric = metric @@ -435,6 +430,7 @@ def __init__( self.linear_solver = linear_solver self.jacobian_mode = jacobian_mode self.ad_solver = ad_solver + self._validate_configuration(linear_solver, ad_solver, penalized=True) # The configs' numeric fields fold into the traced LMHyperparams carry # at init exactly as the flat constructor args used to; the config # instances themselves sit in the value-based static key, so @@ -551,17 +547,7 @@ def init(self, x0, args=None, *, p=None): min_damping = _damping_floor(self.min_damping, dtype) damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) ridge = self._resolve_ridge(dtype) - # Hook state is built at x0 and VALID there, so the first update - # reuses it; the flags stay None when the hooks are stateless. - hooks = {} - ctx = SolverContext(x=theta, args=args, p=p) - valid = jnp.asarray(True, dtype=jnp.bool_) - if self._metric_prepares: - hooks["metric_state"] = self.metric.prepare(theta, ctx) - hooks["metric_valid"] = valid - if self._precond_prepares: - hooks["precond"] = self.preconditioner.prepare(theta, ctx) - hooks["precond_valid"] = valid + hooks = self._init_hook_state(theta, LMState(damping, ridge), args, p) if not self.cache_jacobian: return LMState(damping, ridge, **hooks) p_dim = theta.size @@ -965,27 +951,6 @@ def _cast_state(self, lm_state, dtype): ) return dataclasses.replace(lm_state, **updates) - def _cold_state(self, lm_state): - # Drawn multi-start lanes must not reuse caches built at another - # (x, args); damping, hyper, and ridge stay inherited from the - # caller's initial state (never reset to constructor defaults -- - # parallel lane 0 uses the cold state while sequential attempt 0 uses - # the original, and ridge=None cannot be resolved without the - # residual dtype anyway). - updates = {} - if lm_state.jacobian_valid is not None: - updates["jacobian_valid"] = jnp.zeros_like(lm_state.jacobian_valid) - if lm_state.solver_cache is not None: - updates["solver_cache"] = jax.tree.map( - jnp.zeros_like, lm_state.solver_cache - ) - for flag in ("metric_valid", "precond_valid"): - if getattr(lm_state, flag) is not None: - updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) - if not updates: - return lm_state - return dataclasses.replace(lm_state, **updates) - def _ranking_objective(self, result, p, callback): # Multi-start selection ranks by the ridge objective at each lane's # OWN final ridge (comparable across lanes when they share a diff --git a/tests/test_failed_implicit_ad.py b/tests/test_failed_implicit_ad.py index ae9a538..ab4e475 100644 --- a/tests/test_failed_implicit_ad.py +++ b/tests/test_failed_implicit_ad.py @@ -223,7 +223,7 @@ def residual(x, _, p): solver = LevenbergMarquardt( residual, - ad_solver="svd", + ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) diff --git a/tests/test_metric_lm.py b/tests/test_metric_lm.py index e70139e..ac6d7f2 100644 --- a/tests/test_metric_lm.py +++ b/tests/test_metric_lm.py @@ -7,6 +7,8 @@ test_multi_start.py. """ +import dataclasses + import jax import jax.numpy as jnp import numpy as np @@ -207,28 +209,36 @@ def test_geodesic_correction_matches_its_closed_form(name): ) -def test_rejected_step_leaves_x_and_reuses_the_cached_jacobian(): - calls = [] - - def counting_residual(x): - calls.append(None) - return quadratic_residual(x) - - # A tiny max_damping forces the first step to overshoot and be rejected. +def test_rejected_step_leaves_x_and_marks_the_cache_reusable(): + # A wildly overshooting Gauss-Newton step from tiny damping on a curved + # residual: the trial point is worse, so the step is rejected, x is + # unchanged, and the Jacobian cache is marked valid for the retry. solver = LevenbergMarquardt( - counting_residual, init_damping=1e-8, geodesic_acceleration=False + lambda x: jnp.array([jnp.exp(x[0]) - 1.0, x[1]]), + init_damping=1e-10, + geodesic_acceleration=False, ) - x0 = jnp.asarray([8.0, 8.0], jnp.float32) + x0 = jnp.asarray([-6.0, 0.0], jnp.float32) state = solver.init(x0) - x1, state1, info1 = solver.update(x0, state) - if bool(info1.accepted): - pytest.skip("fixture no longer produces a rejected first step") + x1, state1, info = solver.update(x0, state) + assert not bool(info.accepted) np.testing.assert_array_equal(np.asarray(x1), np.asarray(x0)) assert bool(state1.jacobian_valid) - before = len(calls) - solver.update(x1, state1) - # The reused cache costs one trial evaluation, not a fresh linearization. - assert len(calls) - before <= 2 + # The retry reuses that cache and reaches the same place as a solver told + # to recompute, so reuse is an optimization and not a semantic change. + fresh = LevenbergMarquardt( + lambda x: jnp.array([jnp.exp(x[0]) - 1.0, x[1]]), + init_damping=1e-10, + geodesic_acceleration=False, + cache_jacobian=False, + ) + cached_next = solver.update(x1, state1)[0] + fresh_next = fresh.update( + x1, dataclasses.replace(fresh.init(x0), damping=state1.damping) + )[0] + np.testing.assert_allclose( + np.asarray(cached_next), np.asarray(fresh_next), rtol=1e-6, atol=1e-7 + ) def test_solve_and_manual_update_loop_agree(): @@ -372,6 +382,17 @@ def padded(x, args, p): np.testing.assert_allclose( np.asarray(padded_result.x), np.asarray(unpadded.x), rtol=2e-3, atol=2e-4 ) + # The point of SVD() here is the TANGENT: padding makes the undamped dual + # singular, and the spectral filter recovers the unpadded tangent anyway. + p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} + padded_solver = LevenbergMarquardt(padded, ad_solver=SVD(), min_damping=1e-12) + tangent = jax.jvp( + lambda pv: padded_solver.solve(jnp.zeros(N), p=pv, max_steps=200, atol=1e-6).x, + (p,), + (p_dot,), + )[1] + expected = min_norm_solution(np.eye(N), np.asarray(p_dot["b"], np.float64)) + np.testing.assert_allclose(np.asarray(tangent), expected, rtol=2e-3, atol=2e-4) def test_has_aux_reports_pre_step_aux_and_a_final_value(): @@ -388,7 +409,8 @@ def residual(x): ) -def test_equal_configs_share_one_compilation(): +def test_solver_identity_is_value_based(): + # The jitted loop keys on this; test_compilation.py checks what it buys. def build(): return LevenbergMarquardt( linear_residual, linear_solver=Cholesky(), init_damping=1e-3 @@ -396,3 +418,43 @@ def build(): assert build() == build() and hash(build()) == hash(build()) assert build() != LevenbergMarquardt(linear_residual, linear_solver=QR()) + + +@pytest.mark.parametrize( + "kwargs,message", + [ + (dict(linear_solver=SVD()), "linear_solver"), + (dict(ad_solver=QR()), "ad_solver"), + ], +) +def test_a_config_in_a_role_it_cannot_fill_is_rejected(kwargs, message): + # Without this the combination silently resolves to a DIFFERENT algorithm. + with pytest.raises(ValueError, match=message): + LevenbergMarquardt(linear_residual, **kwargs) + + +def test_free_scale_changes_the_step_and_its_tangent(): + # free_scale is the free block's damping weight, so it must move both the + # forward step and the implicit tangent -- not be quietly ignored. + def residual(x, args, p): + return A @ x - p["b"] + + p = {"b": B} + p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} + solutions, tangents = [], [] + for free_scale in (1.0, 100.0): + metric = RepeatedFactorMetric( + jnp.linalg.cholesky(jnp.asarray(W_NP[:4, :4], jnp.float32), upper=True), + free_scale=free_scale, + ) + solver = LevenbergMarquardt(residual, metric=metric, min_damping=1e-12) + run = lambda pv: ( + solver.solve( # noqa: B023 + jnp.zeros(N), p=pv, max_steps=200, atol=1e-6 + ).x + ) + solutions.append(np.asarray(run(p))) + tangents.append(np.asarray(jax.jvp(run, (p,), (p_dot,))[1])) + # A heavier free block is pulled toward zero relative to the metric block. + assert np.linalg.norm(solutions[1][4:]) < np.linalg.norm(solutions[0][4:]) + assert np.linalg.norm(tangents[1] - tangents[0]) > 1e-3 diff --git a/tests/test_multi_start.py b/tests/test_multi_start.py index ca91796..1388825 100644 --- a/tests/test_multi_start.py +++ b/tests/test_multi_start.py @@ -5,6 +5,7 @@ import pytest from nlls_gram import ( + SVD, LevenbergMarquardt, LMSolveAction, LMStatus, @@ -696,7 +697,7 @@ def fresh(_): new_args = jax.lax.cond(ctx.step == 1, fresh, lambda _: ctx.args, None) return LMSolveAction(args=new_args) - solver = LevenbergMarquardt(residual, init_damping=1e-2, ad_solver="svd") + solver = LevenbergMarquardt(residual, init_damping=1e-2, ad_solver=SVD()) args0 = {"data": jnp.array([1.0, -2.0, 0.5]), "key": jax.random.key(22)} x0 = jnp.array([jnp.nan, jnp.nan, jnp.nan]) # forces one retry p = jnp.asarray(2.0) diff --git a/tests/test_ridge_lm.py b/tests/test_ridge_lm.py index 6f594d2..b86822a 100644 --- a/tests/test_ridge_lm.py +++ b/tests/test_ridge_lm.py @@ -9,8 +9,10 @@ from nlls_gram import ( CG, QR, + SVD, Cholesky, CholeskyCache, + GramCG, IdentityMetric, IdentityPreconditioner, LMState, @@ -267,6 +269,17 @@ def test_constructor_and_state_validation(): # An uncapped zero-tolerance CG loop has no stopping rule. with pytest.raises(ValueError, match="maxiter"): CG(IdentityPreconditioner(), tol=0.0) + # The dual operator never sees the penalty rows, so a Gram form would + # silently solve the UNPENALIZED subproblem. + for gram in (Cholesky(form="gram"), GramCG(IdentityPreconditioner(), maxiter=8)): + with pytest.raises(ValueError, match="penalty rows"): + RidgeLevenbergMarquardt(linear_residual, metric=metric, linear_solver=gram) + # QR has no AD rule (the implicit system is undamped, where its damping + # rows vanish); SVD has no forward rule. + with pytest.raises(ValueError, match="ad_solver"): + RidgeLevenbergMarquardt(linear_residual, metric=metric, ad_solver=QR()) + with pytest.raises(ValueError, match="linear_solver"): + RidgeLevenbergMarquardt(linear_residual, metric=metric, linear_solver=SVD()) # The metric must cover no more than the flattened iterate. small = RidgeLevenbergMarquardt( lambda theta: theta[:1], metric=IdentityMetric(3), ridge=1e-3 From 09a1ae9d657dfb2af04387d5c40767f6022fe37e Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 02:11:42 -0700 Subject: [PATCH 09/22] fix: stale hook state after a callback move, and four AD/dtype defects From a second (JAX-focused) review. The serious one: _apply_action invalidated the Jacobian cache when a callback replaced x or args, but not metric_valid or precond_valid. update() sets metric_valid = ~improved, so after a REJECTED step it is True; a callback that then installed a new x left the metric state prepared at the old iterate in place and the next step reused it. The metric defines the subproblem, so that silently solved a different problem in a different geometry. All three validity flags now get the same treatment. Also fixed: - solve() called hyperparams() with no dtype, so CG(tol=None) resolved against the JAX default float. On a float32 problem under enabled x64 that gave tol=1e-10 -- unreachable, since float32 eps is 1.2e-7 -- and every inner CG burned its full maxiter for the whole solve. The sentinel now resolves in _cast_hyper, where the residual dtype is known. - The solve callback was not passed through _hashable_hook, so a callback written to the frozen-dataclass pattern the docs recommend died with a raw "Non-hashable static arguments" error if it held an array. draw and accept already had this. - ad_solver=None under CG(penalty=...) inherited the preconditioner but not the penalty, silently discarding the option -- and leaving the AD solve on the singular operator whose explicit form the guard rejects. - Cholesky's docstring called gram-vs-normal "a cost choice, not a semantics choice". True in exact arithmetic; false in floating point for m > n, where the dual carries m-n structural zero eigenvalues and loses ~1e-2 relative at damping=1e-14 against the normal form's 1e-15. form="auto" never picks gram there, so the default was always safe; the docstring now says which is. Documented rather than changed: only result.x/aux/p carry tangents. info (including info.loss), lm_state, steps, and the histories get exact zero, which jax.grad reports as a silent zero on an otherwise natural bilevel objective. Damping and step norms are path artifacts, not properties of the root, so the contract is right -- it just was not written down. Dead: canonicalize_ad_preconditioner (unreferenced, documents the removed string API). Metric.norm's "must match to floating-point accuracy" contract was vacuous -- neither solver calls it. test_compilation.py was blind to the multi-start drivers' own jit caches; it now counts all three and adds the trap the file was missing: a residual lambda rebuilt per call recompiles every time (3 solves, 3 programs), while a module-level one compiles once. Also pins save_steps making max_steps static, and a stateful preconditioner reused across solver rebuilds. 169 passed, 12 skipped. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/linear_solvers.py | 24 +++++---- src/nlls_gram/lm_core.py | 38 +++++++++++--- src/nlls_gram/lm_types.py | 12 ++++- src/nlls_gram/metric_lm.py | 9 ++-- src/nlls_gram/metrics.py | 7 ++- src/nlls_gram/utilities.py | 38 -------------- tests/test_compilation.py | 88 +++++++++++++++++++++++++++++++-- tests/test_metric_lm.py | 9 ++-- 8 files changed, 154 insertions(+), 71 deletions(-) diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index abdb42a..bfe015e 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -219,12 +219,17 @@ class Cholesky(LinearSolver): ``form="gram"`` factors the ``m x m`` dual ``D = J~ J~'`` instead and takes the step ``u = -J~'(D + damping I)^{-1} r``. For ``damping > 0`` the - two produce the SAME step, by the push-through identity - ``B'(BB' + lam I)^{-1} = (B'B + lam I)^{-1}B'``; they differ only in which - dimension they factor in. ``form="auto"`` (the default) picks the smaller - at trace time -- gram when ``n > m``, normal otherwise -- so it is a cost - choice, not a semantics choice, and it keys on shape alone, never on - numerical rank. + two produce the same step in exact arithmetic, by the push-through + identity ``B'(BB' + lam I)^{-1} = (B'B + lam I)^{-1}B'``. + + In FLOATING POINT they part company when ``m > n``: the dual then carries + ``m - n`` structural zero eigenvalues, so its condition number is + ``sigma_max^2 / damping`` however well conditioned ``J~`` is, and the gram + step loses digits as damping falls (measured ~1e-2 relative at + ``damping=1e-14`` where the normal form holds 1e-15). ``form="auto"`` (the + default) never picks gram there -- it takes gram only when ``n > m``, where + the normal system is the singular one -- so the default is safe and the + choice is a cost one. Forcing ``form="gram"`` on a tall problem is not. """ form: str = "auto" @@ -260,7 +265,7 @@ def new_cache(self, m, n, n_m, dtype, penalized): ) def prepare(self, sub): - n_m, ridge, dtype = sub.n_m, sub.ridge, sub.dtype + n_m, ridge = sub.n_m, sub.ridge # B' = F_bar^{-T} J', shape (n, m). Every form below is built from it. grad = sub.whitened_transpose(sub.Jt @ sub.resid) if sub.penalized: @@ -279,9 +284,8 @@ def assemble(): matrix = sub.cached(assemble) size = sub.m if gram else sub.n - factor = jsp_linalg.cho_factor( - matrix + sub.damping * jnp.eye(size, dtype=dtype) - ) + shift = jnp.arange(size) + factor = jsp_linalg.cho_factor(matrix.at[shift, shift].add(sub.damping)) if gram: # u = -B'(D + damping I)^{-1} c on residual-space right-hand sides. def dual_step(c): diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 3e46782..2ca6b83 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -154,9 +154,14 @@ def hyperparams(self, dtype=None): """``LMHyperparams`` built from the constructor values.""" iterative_tol = self.iterative_tol if iterative_tol is None: - # CG's tol=None: the _ad_cg_tol dtype-default convention. - resolved = jnp.result_type(float) if dtype is None else dtype - iterative_tol = 1e-10 if jnp.finfo(resolved).bits > 32 else 1e-6 + # NaN marks "resolve against the problem dtype"; _cast_hyper does + # it once the residual dtype is known. Resolving here would bake in + # the JAX default float, which is wrong for a float32 problem under + # enabled x64. + if dtype is None: + iterative_tol = jnp.nan + else: + iterative_tol = 1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6 return LMHyperparams( jnp.asarray(self.damping_decrease, dtype=dtype), jnp.asarray(self.damping_increase, dtype=dtype), @@ -354,10 +359,18 @@ def _apply_action(self, action, x, lm_state, args, user_state): if action.user_state is not None: user_state = action.user_state problem_changed = xargs_changed | state_changed - if self.cache_jacobian and (action.x is not None or action.args is not None): - lm_state = dataclasses.replace( - lm_state, jacobian_valid=lm_state.jacobian_valid & ~xargs_changed - ) + if action.x is not None or action.args is not None: + # Everything prepared at the pre-action (x, args) is stale once + # either moves. The metric matters most: it DEFINES the subproblem, + # so reusing a factor built at the old iterate would silently solve + # a different problem in a different geometry. + stale = {} + for flag in ("jacobian_valid", "metric_valid", "precond_valid"): + carried = getattr(lm_state, flag) + if carried is not None: + stale[flag] = carried & ~xargs_changed + if stale: + lm_state = dataclasses.replace(lm_state, **stale) touched = ( action.x is not None or action.args is not None @@ -437,6 +450,16 @@ def solve( tangents for ``result.x`` and ``result.aux``, with the failed lane's linear tangent program evaluated at differentiation-inert copies of the original ``(x0, args, p)``. + + ONLY ``result.x``, ``result.aux``, and ``result.p`` carry tangents. + Everything else -- ``info`` (including ``info.loss``), ``lm_state``, + ``steps``, the histories, and the multi-start diagnostics -- is + differentiation-inert and gets EXACT ZERO, since damping, step norms, + and iteration counts are artifacts of the path rather than properties + of the root. Differentiating a loss therefore means recomputing it + from ``result.x``, not reading ``result.info.loss``:: + + jax.grad(lambda p: objective(solver.solve(x0, p=p).x, p))(p) """ self._check_residual_args(args, p) if max_steps <= 0: @@ -450,6 +473,7 @@ def solve( if not isinstance(xtol, jax.core.Tracer) and xtol < 0: raise ValueError("xtol must be nonnegative") self._validate_tolerances(atol, gtol, xtol) + callback = _hashable_hook(callback) lm_state = self._solve_lm_state(x0, args, p, lm_state) if lm_state.hyper is None: lm_state = dataclasses.replace(lm_state, hyper=self.hyperparams()) diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py index aee4d89..fec3464 100644 --- a/src/nlls_gram/lm_types.py +++ b/src/nlls_gram/lm_types.py @@ -111,6 +111,16 @@ def _damping_floor(min_damping, dtype): def _cast_hyper(hyper, dtype): if hyper is None: return None + # NaN is the "resolve me against the problem dtype" sentinel for CG's + # tol=None: solve() builds the hyperparameters before it has seen a + # residual, and 1e-10 is unreachable in float32, so an unresolved default + # would burn the full CG budget every inner solve. + iterative_tol = jnp.asarray(hyper.iterative_tol, dtype=dtype) + iterative_tol = jnp.where( + jnp.isnan(iterative_tol), + jnp.asarray(1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6, dtype=dtype), + iterative_tol, + ) return LMHyperparams( jnp.asarray(hyper.damping_decrease, dtype=dtype), jnp.asarray(hyper.damping_increase, dtype=dtype), @@ -119,7 +129,7 @@ def _cast_hyper(hyper, dtype): if hyper.max_damping is None else jnp.asarray(hyper.max_damping, dtype=dtype), jnp.asarray(hyper.geodesic_acceptance_ratio, dtype=dtype), - jnp.asarray(hyper.iterative_tol, dtype=dtype), + iterative_tol, jnp.asarray(hyper.iterative_atol, dtype=dtype), None if hyper.iterative_maxiter is None diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index 977da39..da0cf16 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -167,6 +167,8 @@ def __init__( self.ad_solver_preconditioner = ( linear_solver.preconditioner if inherit else None ) + if inherit: + self.ad_solver_penalty = getattr(linear_solver, "penalty", None) self.has_aux = has_aux # Only the dense paths materialize J', and the caches ride the same # reject-reuse lifecycle, so the flag is inert for the matrix-free forms. @@ -620,9 +622,10 @@ def cg(matvec, rhs, preconditioner=apply_M): return solution if isinstance(config, GramCG): - # Dual: (B B') y = (dr/dp) p_dot, then u = -B' y. The right-hand - # side lies in range(B), so unpreconditioned CG from zero keeps the - # iterates selection-clean on rank-deficient problems. + # Dual: (B B') y = (dr/dp) p_dot, then u = -B' y. Selection is + # safe under any preconditioner here -- u = -B'y is invariant to + # the null(B') component of y -- unlike the normal form, where the + # preconditioner must preserve range(B'). def dual_matvec(y): return B(Bt(y)) diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index b13259b..48485fd 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -46,10 +46,9 @@ class Metric: - ``factor_apply(v, ctx)``: ``F v`` - ``factor_solve(v, ctx)``: ``F^{-1} v`` - ``factor_solve_transpose(v, ctx)``: ``F^{-T} v`` - - ``norm(v, ctx)``: ``||v||_W`` (vectors only; the base default is - ``||factor_apply(v)||_2`` and an override must match it to - floating-point accuracy, since the solver compares objective values - built from both forms) + - ``norm(v, ctx)``: ``||v||_W``, defaulted to ``||factor_apply(v)||_2``. + Provided for callers; the solvers measure in the whitened variable and + never call it. Every callback receives a :class:`~nlls_gram.SolverContext` carrying the solver's live state, so an exotic metric can key off the iterate; diff --git a/src/nlls_gram/utilities.py b/src/nlls_gram/utilities.py index b255fd0..2013762 100644 --- a/src/nlls_gram/utilities.py +++ b/src/nlls_gram/utilities.py @@ -185,41 +185,3 @@ def canonical_residual(x, args, p): else: canonical_residual = residual_fn return canonical_residual, residual_arity - - -def canonicalize_ad_preconditioner(ad_solver_preconditioner): - """Normalize an ``ad_solver_preconditioner`` to the 1-arg form the AD - solve calls. A callable already usable as ``(v)``, including helpers - whose damping argument has a default, passes through unchanged. A - callable REQUIRING a second argument (a ``(v, damping)`` helper such - as Sherman-Morrison or Woodbury) is wrapped to be called with an - explicit zero damping, the correct value for the undamped AD system. - Helpers marked ``requires_positive_damping`` are rejected: their - zero-damping apply divides by zero. - """ - if getattr(ad_solver_preconditioner, "requires_positive_damping", False): - raise ValueError( - "this preconditioner divides by the live damping and cannot " - "serve as ad_solver_preconditioner (the AD system is undamped)" - ) - try: - signature = inspect.signature(ad_solver_preconditioner) - except (TypeError, ValueError): - return ad_solver_preconditioner - try: - signature.bind(object()) - except TypeError: - pass - else: - return ad_solver_preconditioner - try: - signature.bind(object(), object()) - except TypeError: - raise ValueError( - "ad_solver_preconditioner must be callable as (v) or (v, damping)" - ) from None - - def canonical_ad_preconditioner(v): - return ad_solver_preconditioner(v, jnp.asarray(0.0, dtype=v.dtype)) - - return canonical_ad_preconditioner diff --git a/tests/test_compilation.py b/tests/test_compilation.py index cc48458..4eea631 100644 --- a/tests/test_compilation.py +++ b/tests/test_compilation.py @@ -18,15 +18,21 @@ from nlls_gram import ( CG, QR, + BlockEigenPreconditioner, Cholesky, CholeskyMetric, DiagonalMetric, IdentityPreconditioner, LevenbergMarquardt, + MultiStart, RepeatedFactorMetric, RidgeLevenbergMarquardt, ridge_continuation, ) +from nlls_gram.multi_start import ( + _multi_start_parallel_jit, + _multi_start_sequential_jit, +) from nlls_gram.solve_loop import _solve_loop_jit N, M = 5, 3 @@ -42,15 +48,22 @@ def make_p(scale=1.0): return {"b": scale * jnp.ones(M, jnp.float32)} +JITTED = (_solve_loop_jit, _multi_start_sequential_jit, _multi_start_parallel_jit) + + @pytest.fixture(autouse=True) def fresh_cache(): - _solve_loop_jit._clear_cache() + for jitted in JITTED: + jitted._clear_cache() yield - _solve_loop_jit._clear_cache() + for jitted in JITTED: + jitted._clear_cache() def compilations(): - return _solve_loop_jit._cache_size() + # The multi-start drivers have their own caches, keyed on draw/accept and + # num_starts as well; counting only the plain loop would miss them. + return sum(jitted._cache_size() for jitted in JITTED) def test_equal_solvers_built_repeatedly_share_one_compilation(): @@ -192,3 +205,72 @@ def jaxpr_text(config): assert "cholesky" not in jaxpr_text( CG(IdentityPreconditioner(), tol=1e-8, maxiter=16) ) + + +def draw_shifted(key, x, args): + return x + 0.1 * jax.random.normal(key, x.shape, x.dtype), args + + +def test_multi_start_reuses_its_driver_compilation(): + solver = LevenbergMarquardt(residual) + for scale in (1.0, 2.0, 3.0): + solver.solve( + jnp.zeros(N), + p=make_p(scale), + multi_start=MultiStart( + key=jax.random.key(0), num_starts=3, draw=draw_shifted + ), + **SOLVE, + ) + # The sequential driver inlines the loop into its own jit, so there is + # one program total -- and reusing an equal MultiStart adds none. + assert compilations() == 1 + + +def test_a_fresh_residual_closure_per_call_recompiles(): + # The commonest real-world trap, and one the package CANNOT fix: the + # residual is a jit static, so a lambda rebuilt per iteration is a new + # program every time. Pinned as a negative control so the guards above + # cannot pass by accident. + for scale in (1.0, 2.0, 3.0): + LevenbergMarquardt(lambda x, args, p: A @ x - p["b"]).solve( + jnp.zeros(N), p=make_p(scale), **SOLVE + ) + assert compilations() == 3 + # A module-level residual reused across calls compiles once. + for jitted in JITTED: + jitted._clear_cache() + for scale in (1.0, 2.0, 3.0): + LevenbergMarquardt(residual).solve(jnp.zeros(N), p=make_p(scale), **SOLVE) + assert compilations() == 1 + + +def test_save_steps_makes_max_steps_static(): + # history_len is a jit static because the buffer shape depends on it -- + # documented, and pinned here so the cost is not a surprise. + solver = LevenbergMarquardt(residual) + for max_steps in (5, 6, 7): + solver.solve(jnp.zeros(N), p=make_p(), max_steps=max_steps, atol=1e-6) + assert compilations() == 1 + for jitted in JITTED: + jitted._clear_cache() + for max_steps in (5, 6, 7): + solver.solve( + jnp.zeros(N), p=make_p(), max_steps=max_steps, atol=1e-6, save_steps=True + ) + assert compilations() == 3 + + +def test_a_stateful_preconditioner_reused_shares_one_compilation(): + # BlockEigenPreconditioner holds a closure and an array, so it hashes by + # identity: reusing the instance must not recompile, and its per-step + # prepare() must not either. + preconditioner = BlockEigenPreconditioner( + lambda theta, ctx: [(jnp.eye(N, dtype=jnp.float32)[None], 0.0)], + jnp.arange(N), + ) + for scale in (1.0, 2.0, 3.0): + LevenbergMarquardt( + residual, linear_solver=CG(preconditioner, tol=1e-8, maxiter=16) + ).solve(jnp.zeros(N), p=make_p(scale), **SOLVE) + assert compilations() == 1 diff --git a/tests/test_metric_lm.py b/tests/test_metric_lm.py index ac6d7f2..175ce80 100644 --- a/tests/test_metric_lm.py +++ b/tests/test_metric_lm.py @@ -448,11 +448,10 @@ def residual(x, args, p): free_scale=free_scale, ) solver = LevenbergMarquardt(residual, metric=metric, min_damping=1e-12) - run = lambda pv: ( - solver.solve( # noqa: B023 - jnp.zeros(N), p=pv, max_steps=200, atol=1e-6 - ).x - ) + + def run(pv, solver=solver): + return solver.solve(jnp.zeros(N), p=pv, max_steps=200, atol=1e-6).x + solutions.append(np.asarray(run(p))) tangents.append(np.asarray(jax.jvp(run, (p,), (p_dot,))[1])) # A heavier free block is pulled toward zero relative to the metric block. From 55891a8fcd7e0f660fbddd902c73c2eaf2d42682 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 08:39:22 -0700 Subject: [PATCH 10/22] refactor: remove RepeatedFactorMetric.from_gram; callers factor the shifted Gram themselves Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- README.md | 2 +- benchmarks/test_metric_benchmark.py | 7 +++++-- benchmarks/test_ridge_lm_benchmark.py | 7 +++++-- docs/metric_lm.md | 4 ++-- docs/metrics.md | 1 - src/nlls_gram/metrics.py | 26 +++----------------------- tests/test_float64_subprocess.py | 6 ++++-- 7 files changed, 20 insertions(+), 33 deletions(-) diff --git a/README.md b/README.md index 9210492..a99b023 100644 --- a/README.md +++ b/README.md @@ -47,7 +47,7 @@ import jax.numpy as jnp from nlls_gram import RidgeLevenbergMarquardt, RepeatedFactorMetric, ridge_continuation # W = blockdiag(K, K): the RKHS seminorm over two coefficient blocks. The -# constructor takes the FACTOR; from_gram(K, ...) shifts and factors a K. +# constructor takes the FACTOR; shift a semidefinite K by epsilon*I first. metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=2) solver = RidgeLevenbergMarquardt(collocation_residual, metric=metric, ridge=1e-4) diff --git a/benchmarks/test_metric_benchmark.py b/benchmarks/test_metric_benchmark.py index bbe20a4..4ed16ff 100644 --- a/benchmarks/test_metric_benchmark.py +++ b/benchmarks/test_metric_benchmark.py @@ -52,8 +52,11 @@ def test_repeated_factor_metric_apply( device = devices[0] t = jax.device_put(jnp.linspace(0.0, 40.0, n), device) K = _matern_gram(t, nu) - metric = RepeatedFactorMetric.from_gram( - K, repeats=repeats, epsilon=EPSILON, free_scale=EPSILON + shifted = K + EPSILON * jnp.eye(K.shape[0], dtype=K.dtype) + metric = RepeatedFactorMetric( + jnp.linalg.cholesky(shifted, upper=True), + repeats=repeats, + free_scale=EPSILON, ) total_size = repeats * n shape = (total_size,) if rhs_columns == 1 else (total_size, rhs_columns) diff --git a/benchmarks/test_ridge_lm_benchmark.py b/benchmarks/test_ridge_lm_benchmark.py index 7f3b78e..72bf1a7 100644 --- a/benchmarks/test_ridge_lm_benchmark.py +++ b/benchmarks/test_ridge_lm_benchmark.py @@ -85,8 +85,11 @@ def test_update_step( device = devices[0] K, residual, x0 = _problem(n, repeats, free_size, m_resid, device) if configuration == "metric": - metric = RepeatedFactorMetric.from_gram( - K, repeats=repeats, epsilon=EPSILON, free_scale=EPSILON + shifted = K + EPSILON * jnp.eye(K.shape[0], dtype=K.dtype) + metric = RepeatedFactorMetric( + jnp.linalg.cholesky(shifted, upper=True), + repeats=repeats, + free_scale=EPSILON, ) solver = LevenbergMarquardt(residual, metric=metric) else: diff --git a/docs/metric_lm.md b/docs/metric_lm.md index 87f84cb..df7b0f4 100644 --- a/docs/metric_lm.md +++ b/docs/metric_lm.md @@ -41,8 +41,8 @@ Under a kernel model \(f(t) = \sum_j \alpha_j k(t, c_j)\), the RKHS norm is \(\alpha^\top K \alpha\) with \(K\) the Gram matrix over centers, so `W = K` and the factor is `jnp.linalg.cholesky(K, upper=True)`. A positive-*semi*definite \(K\) needs a shift to be invertible: -`RepeatedFactorMetric.from_gram(K, repeats=r, epsilon=1e-8)` factors -\(K + \varepsilon I\) once and repeats it. +`RepeatedFactorMetric(jnp.linalg.cholesky(K + 1e-8 * I, upper=True), repeats=r)` +factors \(K + \varepsilon I\) once and repeats it. Parameters the metric should not weight (a scalar coefficient, a bias) go past `metric.size` into the **free block**, whose damping weight is diff --git a/docs/metrics.md b/docs/metrics.md index 04326d3..83fa1c3 100644 --- a/docs/metrics.md +++ b/docs/metrics.md @@ -33,7 +33,6 @@ Ops act on metric-block vectors, or matrices whose *leading* axis is `size` | `CholeskyMetric(L)` | \(LL^\top\) | | `DiagonalMetric(weights)` | \(\operatorname{diag}(w)\) | | `RepeatedFactorMetric(F, repeats=r)` | \(\operatorname{blockdiag}(F^\top F, \ldots)\) | -| `RepeatedFactorMetric.from_gram(K, repeats=r, epsilon=e)` | \(\operatorname{blockdiag}(K + eI, \ldots)\) | `RepeatedFactorMetric` shares one triangular solve across every repeated block by packing them into the columns of a single right-hand side, so no repeated diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index 48485fd..ebed324 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -242,9 +242,9 @@ class RepeatedFactorMetric(Metric): ``jnp.linalg.cholesky(K, upper=True)`` for a positive-definite Gram matrix ``K``, giving the repeated kernel seminorm ``sum_j alpha_j' K alpha_j`` over ``repeats`` coefficient blocks. The constructor takes the FACTOR, not - ``K`` (callers typically already hold it); :meth:`from_gram` shifts and - factors a ``K`` instead. Triangularity and positive definiteness are - assumed, not validated. + ``K`` (callers typically already hold it); a positive-SEMIdefinite ``K`` + needs a shift first: ``jnp.linalg.cholesky(K + epsilon * I, upper=True)``. + Triangularity and positive definiteness are assumed, not validated. All repeated blocks (and all batched columns) share a single triangular product or solve: the ops reshape the metric block into the columns of one @@ -270,26 +270,6 @@ def __post_init__(self): object.__setattr__(self, "F", F.astype(dtype)) object.__setattr__(self, "size", self.repeats * F.shape[0]) - @classmethod - def from_gram(cls, K, *, repeats=1, epsilon, free_scale=1.0): - """Factor ``K + epsilon I`` once and repeat it ``repeats`` times. - - The shift makes a positive-SEMIdefinite kernel Gram matrix invertible. - ``epsilon`` must be positive; non-positive values propagate NaN rather - than silently defining a singular factor. - """ - K = jnp.asarray(K) - if K.ndim != 2 or K.shape[0] != K.shape[1] or K.shape[0] == 0: - raise ValueError("K must be a nonempty square matrix") - epsilon = jnp.asarray(epsilon, dtype=jnp.result_type(K, 1.0)) - epsilon = jnp.where(epsilon > 0.0, epsilon, jnp.nan) - shifted = K + epsilon * jnp.eye(K.shape[0], dtype=K.dtype) - return cls( - jnp.linalg.cholesky(shifted, upper=True), - repeats=repeats, - free_scale=free_scale, - ) - def _map_blocks(self, block_op, v): _check_leading_size(v, self.size) block_size = self.F.shape[0] diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index 25bf3a5..0ed59cc 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -515,8 +515,10 @@ def residual(theta): # Metric-damped LM with a small epsilon shift selects x_dagger + O(eps). # free_scale weights the zero-padded tail, the role epsilon used to play # there; the metric block carries K + epsilon I. -metric = RepeatedFactorMetric.from_gram( - K, repeats=repeats, epsilon=1e-8, free_scale=1e-8 +metric = RepeatedFactorMetric( + jnp.linalg.cholesky(K + 1e-8 * jnp.eye(K.shape[0], dtype=K.dtype), upper=True), + repeats=repeats, + free_scale=1e-8, ) metric_solver = LevenbergMarquardt(residual, metric=metric) metric_result = metric_solver.solve(jnp.zeros(p_dim), max_steps=200, atol=1e-12) From ec330ec6f43d06df06ea40ee1ba141645ebe2cbf Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 08:43:34 -0700 Subject: [PATCH 11/22] docs: drop 'nugget' wording from the quasiseparable docstring Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/experimental/quasiseparable.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/nlls_gram/experimental/quasiseparable.py b/src/nlls_gram/experimental/quasiseparable.py index 3166001..eedeb86 100644 --- a/src/nlls_gram/experimental/quasiseparable.py +++ b/src/nlls_gram/experimental/quasiseparable.py @@ -50,7 +50,7 @@ def matern_state_space(sigma, ell, nu): ``Pinf = diag(1, f^2)``; nu=2.5 has ``h = [sigma, 0, 0]`` and the CAR(3) ``Pinf``/transition transcribed from tinygp v0.3.1. - Nugget-free Matern-3/2 and 5/2 Grams on fine grids are extremely + Unshifted Matern-3/2 and 5/2 Grams on fine grids are extremely ill-conditioned. Pass a positive ``epsilon`` to ``StateSpaceMetric``; the shift is folded into its structured factorization exactly. From 29c1e7203274ab89bfd8fb3b2fbe1134dbc2f18b Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 09:46:04 -0700 Subject: [PATCH 12/22] docs: pytree instance-state design (reviewed; decisions settled) Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/design/pytree_state.md | 511 ++++++++++++++++++++++++++++++++++++ 1 file changed, 511 insertions(+) create mode 100644 docs/design/pytree_state.md diff --git a/docs/design/pytree_state.md b/docs/design/pytree_state.md new file mode 100644 index 0000000..51ba935 --- /dev/null +++ b/docs/design/pytree_state.md @@ -0,0 +1,511 @@ +# Pytree metric/preconditioner state and caller-owned adaptation + +Design proposal for review. Branch `refactor/unify-solver-contracts`, version +stays 2.7.0. Breaking changes are free: all callers are our own repos +(`kernels`, `spooky`), ported in the same effort. No shims, no deprecations. +Revision 2, incorporating the first external review. + +## Problem + +The current contract conflates three things: + +1. **Construction** — how metric/preconditioner numeric state is built + (`prepare(theta, ctx)` on each class, plus the `block_eigen_state` free + function, plus `blocks_fn` closure fields). +2. **Refresh policy** — when it is rebuilt (`rebuild(ctx)` predicates, + `metric_valid`/`precond_valid` reject-reuse flags, the subclass-override + idiom for "rebuild on ridge advance"). +3. **Hashing** — instances hold arrays and closures, so they identity-hash + into the solver's static key, and a rebuilt equal-config instance keys a + fresh compilation of the whole solve loop. + +Symptoms: the kernels driver threads preconditioner state through `args` with +~25 lines of callback plumbing; `rebuild` receives a context without the +carried state it would need to decide; four `LMState` fields and three +`lm_core` methods exist only to shepherd hook state around. + +## Design + +### Instances are pytrees + +Every concrete `Metric` and `Preconditioner` class is registered as a JAX +pytree: array fields are traced leaves, the type plus its static fields are +structure. Instances ride **inside `LMState`** (`lm_state.metric`, +`lm_state.preconditioner`) as nested carried state, so their arrays flow +through the jitted loop, `vmap`, and the implicit-AD rule like any other +state. + +**Rebuild = call the constructor again.** There is no `prepare`, no +`rebuild`, no `remake`. A callback that wants a fresh preconditioner +constructs a new instance of the same type inside the traced callback — pure +traced ops, same treedef, no recompilation. A different type or field +structure is a loud trace-time error. Constructors must canonicalize their +leaf dtypes (`jnp.asarray(..., dtype)`), so a rebuilt instance's leaf avals +match the carried ones inside the user's `lax.cond`. + +`dataclasses.replace` semantics: fine for **metrics** (their `__post_init__` +is validation plus shape derivation, cheap under trace); **preconditioners +are rebuilt by constructor, never `replace`d** — `replace` re-runs +`__init__`, which re-pays the eigendecomposition/sketch, and the +construction-time-only inputs below are not stored to re-supply. Documented +on the base classes. + +### Registration helper (public) + +`jax.tree_util.register_dataclass` unflattens by calling the constructor, +which re-runs `__post_init__` (re-`eigh`, tracer-hostile validation) on +every carry reconstruction — verified against the installed JAX. So the +package ships its own ~20-line helper in `utilities.py`, exported as public +API: + +```python +def register_pytree_dataclass(cls, *, data_fields, meta_fields=()): + """Register a frozen dataclass as a pytree whose unflatten BYPASSES + __init__/__post_init__ (object.__new__ + object.__setattr__). + data_fields are traced leaves; meta_fields are static structure and + must be hashable. Returns cls.""" +``` + +Consequences: + +- Constructors freely compute derived leaves once (`eigh` in + `BlockEigenPreconditioner`, the sketch in `NystromPreconditioner`) and + validate eagerly; unflatten restores fields verbatim. +- Aux data is the tuple of static field values passed through the existing + `_typed_key` type-tagging, so treedefs hash and compare **by value with + jit's strict-type semantics**: two equal-config instances with fresh + arrays have equal treedefs, while `1`, `1.0`, and `True` in a static + field stay distinct (raw tuples would collapse them). +- The helper validates that every dataclass field appears exactly once in + `data_fields` or `meta_fields`, so a forgotten field is a registration + error rather than a silently dropped leaf. +- `tree_map` over an instance rebuilds it without re-running the + constructor, so a transform that changes leaf shapes or breaks a derived + invariant (`permutation` without `inverse_permutation`) produces an + inconsistent instance. Documented: shape-changing or invariant-coupled + mutation goes through the constructor; `tree_map` is for + transform-machinery (vmap batching, tangent zeroing), which preserves + both. +- Each concrete class registers itself (subclassing a registered base does + not register the subclass); the custom-metric and custom-preconditioner + doc recipes lead with the registration call. The solver raises a clear + error at construction when handed an unregistered instance (one that + flattens as a leaf), pointing at the helper. +- `_EuclideanMetric` — the `metric=None` default — is registered too (a + frozen dataclass with no leaves), so the default path passes the same + check. + +Static/leaf split for the shipped classes (construction-time-only inputs are +`dataclasses.InitVar`s — consumed by `__post_init__`, never stored): + +| class | leaves (traced) | static (structure) | InitVar (consumed) | +|---|---|---|---| +| `IdentityMetric` | `free_scale` | `size` | | +| `CholeskyMetric` | `L`, `free_scale` | `size` | | +| `DiagonalMetric` | `weights`, `free_scale` | `size` | | +| `RepeatedFactorMetric` | `F`, `free_scale` | `repeats`, `size` | | +| `IdentityPreconditioner` | — | — | | +| `BlockEigenPreconditioner` | per-family eigenvectors/eigenvalues/ridge_weight, `permutation`, `inverse_permutation` | family count (structure; array shapes live in the leaf avals) | `families` | +| `ShermanMorrisonPreconditioner` | `u`, `weight`, `solve_u`, `denominator` | `solve` | | +| `WoodburyPreconditioner` | `U`, `weights`, `solve_U`, `capacitance_factor` (array only — `cho_factor`'s `lower` bool is passed as a literal in `apply`, never stored as a leaf) | `solve` | | +| `PaddedPreconditioner` | `base` (subtree) | `n_real` | | +| `NystromPreconditioner` | `basis`, `eigenvalues` | `n`, `rank` | `matvec`, `key`, `dtype` | + +`ShermanMorrison`/`Woodbury` call `solve` on **every** `apply` (it is the +action of `A^{-1}`), so it cannot be consumed at construction; it is a +**static field**: a fixed hashable callable whose identity enters the +treedef, and whose closed-over arrays are compile-time constants. These two +classes are setup-scope objects for fixed dual operators, not +callback-refresh targets; rebuilding with the *same* `solve` callable keeps +the treedef. `NystromPreconditioner.matvec` genuinely is construction-only +(its `apply` uses only the stored sketch) and stays an `InitVar`. +`experimental.StateSpaceMetric` gets the same deliberate split when it is +registered: `transition` is construction-only, `parallel` static (its ops +branch on it in Python). + +`free_scale` is a **leaf**: changing it must not recompile. (`_free_scale` +loses its `scale == 1.0` Python short-circuit — a tracer breaks it — and +always divides.) Constructors canonicalize it to a strongly-typed scalar of +the factor's float dtype (default float when the metric holds no arrays), +so an initial Python `1.0` and a callback-rebuilt value have identical +avals. Validation of possibly-traced fields follows the existing +convention: concrete values are validated eagerly, tracers/arrays skip the +sign checks. + +`BlockEigenPreconditioner` drops `blocks_fn` entirely: + +```python +BlockEigenPreconditioner(families, permutation) +# families: sequence of (blocks, ridge_weight) pairs, blocks shaped +# (groups, size, size) — the constructor symmetrizes, eigendecomposes, +# and stores the results as leaves (absorbing today's block_eigen_state, +# which is deleted). +``` + +### Contracts shrink + +```python +class Metric: + size: int # static + free_scale # leaf + def factor_apply(self, v, ctx): ... + def factor_solve(self, v, ctx): ... + def factor_solve_transpose(self, v, ctx): ... + def norm(self, v, ctx): ... # defaulted via factor_apply + +class Preconditioner: + requires_positive_damping = False + def apply(self, v, damping, ctx): ... +``` + +Ops read `self` — the carried instance. Deleted: `Metric.prepare`, +`Metric.rebuild`, `Preconditioner.prepare`, `Preconditioner.rebuild`, +`block_eigen_state`, `SolverContext.metric_state`, +`SolverContext.preconditioner_state`, `LMState.metric_state`, +`LMState.metric_valid`, `LMState.precond`, `LMState.precond_valid`, +`lm_core`'s `_init_hook_state`/`_hook_state`/`_frozen_ctx`, and the +duplicate `_block_sizes` definition in `lm_core.py`. + +`SolverContext` keeps `x`, `lm_state`, `args`, `p` — an exotic metric can +still key off the live iterate, and reaches any carried state through +`ctx.lm_state`. + +### Every traced read goes through the carried instance + +This is the load-bearing rule, and it covers **`linear_solvers.py`** too: +`CG.prepare` and `GramCG.prepare` currently build `apply_M` from +`self.preconditioner` — a jit-static object whose arrays are compile-time +constants. All such sites move to the carried instances +(`sub.ctx.lm_state.preconditioner`; the metric via the ctx the whiten +closures already close over). To make any stray old-style read fail loudly +instead of silently baking one instance's arrays into a shared compile, the +solver's constructor-held attributes are renamed: `self.initial_metric`, +`self.initial_preconditioner`. They exist to seed `init`/`_cold_state`, to +key compilation, and for static reads (`metric.size` — sound either way, +since the treedef contract pins statics). The config fields +(`CG.preconditioner`) keep their names as the initial-instance source but +are never read inside `prepare`. + +The enforcement is a correctness test, not just a convention: two solvers +built around same-treedef, **different-valued** metrics (and +preconditioners) must produce different answers on every linear-solver path +— under the new value-based static key they share one compiled loop, so any +leftover static read reproduces the first solver's geometry and fails this +test. (The old identity-hashed keys made that bug impossible; the new tests +are what make the sharing safe.) + +### LMState + +```python +@dataclass(frozen=True) +class LMState: + damping: jax.Array + ridge: jax.Array | None = None + resid / Jt / jacobian_valid / aux # Jacobian cache, unchanged + hyper: LMHyperparams | None = None + solver_cache: Any = None + metric: Metric | None = None # NEW: the carried instance + preconditioner: Preconditioner | None = None # NEW +``` + +Ownership contract, stated in the docs: **callback-owned** state is +`damping`, `ridge`, `metric`, `preconditioner`, and the `hyper` group +(replaceable as a unit); everything else (`resid`/`Jt`/`jacobian_valid`/ +`aux`/`solver_cache`) is **solver-owned** — preserve it with +`dataclasses.replace(ctx.lm_state, ...)`. No deeper nesting: grouping the +live `damping` with its schedule would mix a solver-written scalar with +callback-owned knobs and force nested replaces in the hot update path. + +`init` and `_cold_state` seed the constructor instances into the state, and +so does the metric solver's minimal-state fast path in `_solve_lm_state` +(today it returns a bare `LMState(damping)`; that would break the carry +structure) — so every state entering the solve loop carries instances. +Inside the loop every traced read goes through the carried instances. +`update` handed a hand-built state with `metric=None` **reads** through +`initial_metric`/`initial_preconditioner` but **passes the `None` +through** to the returned state — injecting an instance would change the +carry structure of a user's own `lax.while_loop` around `update`. With +`prepare` gone, a manual loop that wants an iterate-tracking metric +rebuilds the instance between its own calls. `_cast_state` casts named +scalars only (`damping`, `ridge`, `hyper`, cache ridge) and never touches +instance leaves. + +### All adaptive policy lives in the single per-step callback + +Ridge anneal, preconditioner refresh, metric swap, data re-draw, damping +reset, custom stop — one callback, running where it does today: after the +accept/reject update, before the termination test. (Validated against +spooky's `epoch_callback`, which keeps working unchanged modulo the rename +below.) + +The solver keeps only the reactive, non-policy automation, all as extensions +of the existing `_apply_action` + `problem_changed` machinery: + +1. **Metric mutation is detected automatically by value**, the same rule as + `x`/`args` today: `_apply_action` compares the action's metric leaves + against the carried ones with `_tree_changed`, short-circuiting at trace + time on leaf **identity** — a callback that used + `dataclasses.replace(ctx.lm_state, ridge=...)` hands back the same + tracer objects for the metric subtree, so the untouched-metric case + emits no comparison ops at all (large factors pay the `array_equal` + reduction only on steps that actually rebuild). What a change *means* + differs by solver, because the metric's role differs: + - **`RidgeLevenbergMarquardt`**: the metric defines the objective, so a + change sets `problem_changed` — suppressing that iteration's + convergence test (the step's diagnostics were computed under the old + geometry) — and invalidates the solver caches (`G`/`R` embed the + whitening). + - **`LevenbergMarquardt`**: the metric is damping geometry only; the + objective `||r||^2` did not move, so convergence is **not** + suppressed. The solver caches are still invalidated (the assembled + whitened normal matrix embeds the factor). + - The Jacobian cache is **never** cleared by a metric change: `J = dr/dx` + does not depend on the metric, and whitening is applied fresh from the + cached `Jt` each step. + + Consequence worth stating for the ridge solver: an iterate-dependent + metric rebuilt on *every* accepted step suppresses convergence on every + accepted step, so `xtol` (accepted-only) can never fire and termination + comes from `gtol`/`atol` on rejected steps or from a conditional rebuild + (`lax.cond` on progress). Rebuild-when-it-matters is the documented + pattern. Two more caller obligations replace deleted automation, both + documented: a callback that replaces `x` or `args` and uses a metric + built from them must rebuild the metric **in the same action** (the old + `metric_valid` clearing is gone with the flags); and under multi-start, + drawn lanes inherit the caller's initial instances, so a lane's *first* + step runs under the initial metric — the callback corrects it from step + two (the old per-lane `prepare` re-ran at the drawn point before the + first step). +2. **Preconditioner changes are neither compared nor invalidated.** + Staleness is safe by contract (it only changes the CG iteration path), + so a refresh costs nothing beyond the refresh. +3. **Structure enforcement**: `_apply_action` guards the returned + `metric`/`preconditioner` like it already guards `hyper` — treedef AND + leaf dtype/weak-type must match the carried ones — with an error naming + the field, rather than letting a raw carry mismatch surface downstream. +4. Ridge changes keep their existing detection (`_apply_action_state`). + +### Renames + +`LMSolveAction` → **`LMAction`**, `LMSolveContext` → **`LMContext`**. They +are the callback protocol's types; "solve" in the name was noise. +`LMSolveResult` keeps its name — it is specifically what `solve` returns. +`LMAction` keeps `stop`/`status` (spooky needs them). No aliases. + +### Compilation identity + +The solver's `_static_key` replaces the identity-hashed metric and +preconditioner components with `jax.tree_util.tree_structure(instance)`. +Linear-solver configs containing a preconditioner (`CG`, `GramCG`) are keyed +as (type, scalar knobs, treedef of the preconditioner). Equal-config +instances with fresh arrays therefore share one compiled loop; instances +with different static fields have different treedefs and key different +programs. Leaf *values* stay free to change because they enter the compiled +program as traced carry leaves; leaf *shapes/dtypes* retrace through the +ordinary jit input avals, not through the static key. + +The keying rule is exactly "treedef-hash what is threaded, identity-hash +what is baked": an **explicit `ad_solver=CG(instance)`** keeps +identity-based keying for that instance, because its arrays enter the +tangent program as closed-over constants — treedef keying there would let +two solvers with different AD preconditioner values compare equal and +silently share one baked-in program. + +New `test_compilation.py` pins: + +- a fresh equal-config metric/preconditioner per solve compiles once (the + old tests pinned the weaker reuse-the-same-object property); +- a callback-driven instance swap does not recompile; +- a changed static field does; +- **companion correctness pins** (the other half of the guarantee): two + same-treedef different-valued metrics produce different solutions, and a + callback-swapped preconditioner demonstrably changes the CG iteration + path (tight `maxiter`, exact vs. identity), so cache sharing can never + hide a static-read bug. + +### Implicit AD + +At the solution the converged instances ride in `result.lm_state`, which the +tangent rule already stop-gradients: their leaves are frozen inputs to the +implicit system, replacing `_frozen_ctx`'s prepare-at-solution. The +state-dependence of a callback-refreshed metric is not differentiated. + +One deliberate contract change, stated plainly: `_frozen_ctx` used to +re-run `prepare` **at the returned solution**, whatever the forward refresh +policy had been; the new rule freezes the **carried** instance — the +geometry the solve actually converged under, which may be one refresh +behind the solution point. For a fixed metric (every real caller today) the +two are identical. An iterate-dependent metric that wants the old +at-solution semantics refreshes on every accepted step, making the carried +instance current at convergence. This is documented and pinned by a test +rather than silently absorbed. + +Failed lanes: the tangent program must not read callback-mutated instances +from a failed solve (a swapped metric can be as invalid as a swapped ridge). +`_initial_ad_point` grows the pre-loop instances alongside the pre-loop +ridge it already carries, and `_ad_x_tangent` selects per-lane between the +result instances and the initial ones with the existing `_where_tree` +success mask — structure equality is already enforced, so the select is +well-posed. + +AD-role preconditioning: `ad_solver=None` keeps today's inherit-the-forward +rule, now reading the **carried instance from `result.lm_state`** (the +callback-refreshed one at the solution). `ad_solver=CG(None, tol=..., +maxiter=...)` — `preconditioner=None` is newly legal in the AD role only — +also inherits the carried instance while pinning the AD tolerance and +budget (the kernels driver needs exactly this; with `ad_solver=None` the AD +budget falls back to CG defaults, which is tens of thousands of iterations +at that problem size). An explicit `ad_solver=CG(instance, ...)` uses the +given instance as-is (identity-keyed, see above). `preconditioner=None` +stays invalid in the forward role — opting out of forward preconditioning +remains the explicit `IdentityPreconditioner()`. The +`requires_positive_damping` exclusion is preserved in every AD form: an +inherited forward instance carrying that flag (e.g. `Padded`) falls back to +unpreconditioned, and an explicit one is rejected at construction, exactly +as today. + +### Multi-start + +Sequential and Python modes: drawn lanes start from `_cold_state` of the +caller's initial state, so they inherit the caller's initial instances and +never see another lane's callback mutations. Unchanged. + +Parallel (vmapped) mode: **supported, no guard** — this resolves the open +question differently from the plan's lean. Instance leaves batch under +`vmap` like every other carried array (verified: an unbatched instance in +the initial carry with per-lane `lax.cond` rebuilds returns correctly +batched leaves), so per-lane mutation of leaf *values* is correct by +construction; lanes cannot diverge in structure, shape, or dtype — the same +rule as every other vmapped carry. The old design couldn't batch +identity-hashed closures, but the new one has nothing left to guard. The +real cost is documented instead: under `vmap` a `lax.cond` rebuild lowers +to a select that pays both branches every step — keep refresh logic behind +`lax.cond` for sequential drivers, and expect the rebuild cost per step if +you vmap it. + +### `ridge_continuation` becomes `AnnealRidge`, a shipped convenience callback + +The `ridge_continuation` factory and the `RidgeContinuation` name leave the +API. What ships instead is **`AnnealRidge`** — a frozen-dataclass callable +with today's full semantics and validation (`ridge_floor > 0`, +`0 < decrease < 1`, `grad_rtol > 0`, `stall_rtol` in `[0, 1)`), plus an +`init_state(dtype=None)` method replacing the factory's returned +`user_state0`: + +```python +anneal = AnnealRidge(ridge_floor=1e-10) +result = solver.solve(x0, callback=anneal, + user_state=anneal.init_state(dtype), + gtol=1e-8, atol=1e-8) +``` + +Its **docstring documents the implementation** — the per-level reference in +`user_state`, the `+inf` fresh-level sentinel, the reset-on-advance, the +interplay with convergence suppression — so a driver that needs more than +annealing composes it inside its own callback rather than forking it: + +```python +def driver_callback(ctx): + action = anneal(ctx) + advanced = action.lm_state.ridge < ctx.lm_state.ridge + precond = jax.lax.cond( + advanced, + lambda: BlockEigenPreconditioner( + build_families(ctx.x, ctx.args), PERMUTATION + ), + lambda: ctx.lm_state.preconditioner, + ) + return dataclasses.replace( + action, + lm_state=dataclasses.replace(action.lm_state, preconditioner=precond), + ) +``` + +`lax.cond` branches trace once, so the `eigh` is paid only when the level +advances. The docs call out the anti-pattern explicitly: merging with +`jnp.where` over an unconditional rebuild pays the `eigh` every step — the +old kernels wrapper's actual behavior. The dtype handling keeps today's +contract: the stationarity comparison runs at the ridge dtype (the tracker +is cast in, results cast back to the tracker's dtype), and equal schedules +stay value-hashable so rebuilding one does not recompile the loop. + +Callback hashing contract (documented): a callback is built once per +process — a module-level function, a frozen dataclass callable with +scalar-only fields, or a setup-scope closure the driver constructs once. +What recompiles is rebuilding a *fresh closure per solve call*. Closures +over large arrays (the kernels rebuild needs `K`, `K_tilde`, `F`, physics +constants — more than `ctx` carries) are fine at driver scope: +identity-hashed, one compile per run, and cross-run persistent-cache hits +are keyed on the traced HLO, which closure identity does not enter. + +## Before/after: the external callers + +### kernels `multicountry_growth_kernel.py` (CG path) + +Before (~25 lines): `args = {"preconditioner": build_preconditioner_state(theta_0)}`, +a wrapper callback that calls the continuation, detects `advanced`, rebuilds +the state, `jnp.where`-merges it (paying the eigh every step), and threads it +back through `args`; an explicit `ad_solver=CG(BlockEigenPreconditioner(), ...)` +so the AD solve can find the state in `result.args`. + +After: `multicountry_block_eigen_state` returns the family arrays; the +driver builds `BlockEigenPreconditioner(families(theta_0), permutation)` +once, passes it to `CG(...)`, and uses a driver-scope callback composing +the shipped `AnnealRidge` with the `lax.cond` rebuild closing over the +kernel matrices. +`ad_solver=CG(None, tol=lm_set.cg_tol, maxiter=lm_set.cg_maxiter)` inherits +the refreshed carried instance at the solution while keeping the pinned AD +budget, so the args-threading is deleted. + +### spooky `mv2020_rbc_continuous.py` + +`epoch_callback` (data re-draw + damping reset + custom stop on epoch +boundaries via `lax.cond`) keeps working verbatim modulo +`LMSolveAction` → `LMAction`. It touches neither metric nor preconditioner, +so no invalidation fires beyond the existing args-change rule. + +### Full migration inventory + +- `kernels/multicountry_growth_kernel.py` + `multicountry_growth_preconditioner.py` + (above; the preconditioner module returns families instead of calling + `block_eigen_state`). +- `kernels/open_economy_growth_kernel.py` (`ridge_continuation` → + `AnnealRidge`). +- `kernels/extra/neoclassical_growth_kernel_recursive_adaptive.py` + (`LMSolveAction` rename). +- `kernels/tests/test_python_models.py` → moves to `extra/tests/` (dead + import + one dead-API test deleted). +- `kernels/trade_growth/` → moves to `extra/trade_growth/` wholesale; it + targets a pre-2.7 API and is excluded from the sweep. +- `spooky/mv2020_rbc_continuous.py`, `spooky/mv2020_rbc_discrete.py`, and + the annotated qmd (rename only; ported after kernels). + +## Out of scope (settled elsewhere) + +- **dtype policy**: one consistent dtype inferred from the problem; the + float64-solve promotion knob stays out until a float32 test campaign + motivates it (decision of 2026-07-25). +- No new `DampingSettings` grouping: `hyper` already is the settings group. + +## Test plan (Stage 4) + +- Compilation pins and companion correctness pins listed above. +- Callback swaps metric → ridge solver: that iteration cannot report + `CONVERGED`, solver caches invalidated, Jacobian cache retained; metric + solver: no suppression, caches invalidated. Preconditioner swap → no + invalidation, demonstrably different CG path. Wrong-type/structure swap → + loud `_apply_action` error naming the field. +- Block-eigen constructor numerics vs a dense reference. +- `AnnealRidge` reproduces today's `ridge_continuation` results on the + existing fixtures (including the `stall_rtol` variant), and the + composition recipe from its docstring works as written. +- Failed-lane AD with a callback-mutated metric uses the initial instances + (extends the existing failed-lane ridge tests). +- The untouched-metric identity short-circuit: a callback returning + `dataclasses.replace(ctx.lm_state, ridge=...)` every step adds no + comparison ops for the metric subtree (jaxpr inspection). +- AD-contract pin: the tangent uses the carried (frozen) instances; the + `requires_positive_damping` inherited-AD fallback still applies. +- Prune tests of deleted machinery. +- AD: rerun the reverse/forward tangent suites — the frozen-at-solution + semantics replace `_frozen_ctx`. From c8e11e2b8781f6afae6e217955cb1cf2059d1b1b Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 10:15:34 -0700 Subject: [PATCH 13/22] refactor!: metric and preconditioner instances are pytrees carried in LMState Instances register via register_pytree_dataclass (bypass-unflatten, statics as type-tagged aux), ride in lm_state.metric/preconditioner, and every traced read goes through the carried instance -- rebuild is calling the constructor again inside the solve callback. Compile identity keys on instance structure, so equal-config fresh instances share one loop. Deletes prepare/rebuild, hook-state fields and machinery, block_eigen_state, and the ridge_continuation factory (AnnealRidge, with init_state, replaces it); renames LMSolveAction/LMSolveContext to LMAction/LMContext. A ridge-solver metric change suppresses that step's convergence test and stales the solver caches; the metric solver only stales caches; preconditioner refreshes are free. ad_solver=CG(None, ...) inherits the carried forward preconditioner at the solution with pinned AD knobs; failed lanes differentiate at the pre-loop instances. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/__init__.py | 23 +- .../experimental/state_space_metric.py | 64 ++-- src/nlls_gram/linear_solvers.py | 68 +++- src/nlls_gram/lm_core.py | 245 ++++++------- src/nlls_gram/lm_types.py | 53 +-- src/nlls_gram/metric_lm.py | 153 +++++--- src/nlls_gram/metrics.py | 106 ++++-- src/nlls_gram/preconditioners.py | 347 +++++++++--------- src/nlls_gram/ridge_lm.py | 337 +++++++++-------- src/nlls_gram/solve_loop.py | 6 +- src/nlls_gram/utilities.py | 69 +++- tests/test_compilation.py | 98 ++++- tests/test_failed_implicit_ad.py | 48 ++- tests/test_float64_subprocess.py | 26 +- tests/test_multi_start.py | 6 +- tests/test_ridge_lm.py | 3 + tests/test_ridge_metrics.py | 3 + tests/test_ridge_preconditioners.py | 129 ++++--- tests/test_ridge_solve_features.py | 36 +- 19 files changed, 1101 insertions(+), 719 deletions(-) diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index 849673e..9213446 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -12,7 +12,7 @@ - ``RidgeLevenbergMarquardt`` puts it in the OBJECTIVE, minimizing ``||r(x)||^2 + ridge * ||x_m||_W^2`` for a positive-definite ``Metric`` W on the metric block, with the ridge weight carried as traced state a callback - can anneal (``ridge_continuation``). Classical nonlinear Tikhonov + can anneal (``AnnealRidge``). Classical nonlinear Tikhonov regularization; the minimum-seminorm interpolant is what it converges to. - ``LevenbergMarquardt`` puts it in the DAMPING GEOMETRY, minimizing ``||r(x)||^2`` with the same ``Metric`` weighting the trust region, so the @@ -36,10 +36,10 @@ QRCache, ) from nlls_gram.lm_types import ( + LMAction, + LMContext, LMHyperparams, LMInfo, - LMSolveAction, - LMSolveContext, LMSolveResult, LMState, LMStatus, @@ -62,18 +62,15 @@ Preconditioner, ShermanMorrisonPreconditioner, WoodburyPreconditioner, - block_eigen_state, -) -from nlls_gram.ridge_lm import ( - RidgeContinuation, - RidgeLevenbergMarquardt, - ridge_continuation, ) +from nlls_gram.ridge_lm import AnnealRidge, RidgeLevenbergMarquardt +from nlls_gram.utilities import register_pytree_dataclass __all__ = [ "CG", "QR", "SVD", + "AnnealRidge", "BlockEigenPreconditioner", "Cholesky", "CholeskyCache", @@ -83,10 +80,10 @@ "GramCG", "IdentityMetric", "IdentityPreconditioner", + "LMAction", + "LMContext", "LMHyperparams", "LMInfo", - "LMSolveAction", - "LMSolveContext", "LMSolveResult", "LMState", "LMStatus", @@ -99,11 +96,9 @@ "Preconditioner", "QRCache", "RepeatedFactorMetric", - "RidgeContinuation", "RidgeLevenbergMarquardt", "ShermanMorrisonPreconditioner", "SolverContext", "WoodburyPreconditioner", - "block_eigen_state", - "ridge_continuation", + "register_pytree_dataclass", ] diff --git a/src/nlls_gram/experimental/state_space_metric.py b/src/nlls_gram/experimental/state_space_metric.py index a88d675..6c75c85 100644 --- a/src/nlls_gram/experimental/state_space_metric.py +++ b/src/nlls_gram/experimental/state_space_metric.py @@ -8,14 +8,16 @@ right-hand sides. """ -from dataclasses import dataclass, field +from dataclasses import InitVar, dataclass, field +from typing import Any import jax import jax.numpy as jnp from nlls_gram.experimental import quasiseparable from nlls_gram.experimental.quasiseparable import matern_state_space -from nlls_gram.metrics import Metric, _check_leading_size +from nlls_gram.metrics import Metric, _canonical_free_scale, _check_leading_size +from nlls_gram.utilities import register_pytree_dataclass __all__ = ["StateSpaceMetric", "matern_state_space"] @@ -29,7 +31,8 @@ class StateSpaceMetric(Metric): :func:`matern_state_space` supplies for Matern-1/2, -3/2, and -5/2. ``transition(dt)`` returns the transpose of the textbook state transition for each gap. Non-increasing coordinates propagate NaN rather than quietly - defining a nonstationary factor. + defining a nonstationary factor. All four are consumed at construction; + only the quasiseparable factor generators are stored (as traced leaves). The metric is ``blockdiag(K + epsilon I, ...)`` over ``repeats`` blocks; ``epsilon`` is added before the quasiseparable factorization. Anything @@ -41,28 +44,26 @@ class StateSpaceMetric(Metric): use nondefault device placement. """ - t: jax.Array - h: jax.Array - Pinf: jax.Array - transition: object + t: InitVar[Any] + h: InitVar[Any] + Pinf: InitVar[Any] + transition: InitVar[Any] repeats: int = field(default=1, kw_only=True) - epsilon: float = field(default=1e-8, kw_only=True) - free_scale: float = field(default=1.0, kw_only=True) + epsilon: InitVar[Any] = field(default=1e-8, kw_only=True) + free_scale: Any = field(default=1.0, kw_only=True) parallel: bool | None = field(default=None, kw_only=True) size: int = field(init=False) - _factor: tuple = field(init=False) + factor: tuple = field(init=False) - def __post_init__(self): - t = jnp.asarray(self.t) + def __post_init__(self, t, h, Pinf, transition, epsilon): + t = jnp.asarray(t) if t.ndim != 1 or t.shape[0] == 0: raise ValueError("t must be a nonempty 1-D array") if self.repeats < 1: raise ValueError("repeats must be a positive integer") - d, p, q, A = quasiseparable._state_space_generators( - t, self.h, self.Pinf, self.transition - ) + d, p, q, A = quasiseparable._state_space_generators(t, h, Pinf, transition) dtype = jnp.result_type(d, p, q, A, 1.0) - epsilon = jnp.asarray(self.epsilon, dtype=dtype) + epsilon = jnp.asarray(epsilon, dtype=dtype) # A non-increasing coordinate or a non-positive shift poisons the # factor rather than silently producing a wrong one. epsilon = jnp.where( @@ -74,8 +75,12 @@ def __post_init__(self): if parallel is None: parallel = jax.default_backend() != "cpu" and dtype == jnp.float64 c, w = quasiseparable._cholesky(d, p, q, A) - object.__setattr__(self, "_factor", (c, p, w, A, parallel)) + object.__setattr__(self, "parallel", bool(parallel)) + object.__setattr__(self, "factor", (c, p, w, A)) object.__setattr__(self, "size", self.repeats * t.shape[0]) + object.__setattr__( + self, "free_scale", _canonical_free_scale(self.free_scale, dtype) + ) def _map_blocks(self, block_op, v): _check_leading_size(v, self.size) @@ -89,22 +94,35 @@ def _map_blocks(self, block_op, v): ).reshape((self.size,) + trailing) def factor_apply(self, v, ctx): - c, p, w, A, parallel = self._factor + c, p, w, A = self.factor return self._map_blocks( lambda m: quasiseparable._cholesky_transpose_matvec( - c, p, w, A, m, parallel + c, p, w, A, m, self.parallel ), v, ) def factor_solve(self, v, ctx): - c, p, w, A, parallel = self._factor + c, p, w, A = self.factor return self._map_blocks( - lambda m: quasiseparable._backward_substitution(c, p, w, A, m, parallel), v + lambda m: quasiseparable._backward_substitution( + c, p, w, A, m, self.parallel + ), + v, ) def factor_solve_transpose(self, v, ctx): - c, p, w, A, parallel = self._factor + c, p, w, A = self.factor return self._map_blocks( - lambda m: quasiseparable._forward_substitution(c, p, w, A, m, parallel), v + lambda m: quasiseparable._forward_substitution( + c, p, w, A, m, self.parallel + ), + v, ) + + +register_pytree_dataclass( + StateSpaceMetric, + data_fields=("factor", "free_scale"), + meta_fields=("repeats", "parallel", "size"), +) diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index bfe015e..7bf28a3 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -32,6 +32,7 @@ import jax.scipy.sparse.linalg as jsp_sparse_linalg from nlls_gram.preconditioners import Preconditioner +from nlls_gram.utilities import _IdentityKey __all__ = [ "CG", @@ -44,6 +45,33 @@ ] +def _config_static_key(config, *, baked): + # Compile-key component for a solver config. The Krylov configs hold a + # preconditioner instance whose place in the key depends on how its + # arrays reach the compiled program: threaded through the carried state + # (forward role) -> key by pytree structure, so equal-config fresh + # instances share a compile; baked in as closure constants (explicit + # ad_solver role) -> key by identity, so different values never share + # one. Everything else is a value-hashable dataclass and keys as itself. + if config is None or not isinstance(config, (CG, GramCG)): + return config + precond = config.preconditioner + if precond is None: + precond_key = None + elif baked: + precond_key = _IdentityKey(precond) + else: + precond_key = jax.tree_util.tree_structure(precond) + return ( + type(config), + precond_key, + config.tol, + config.atol, + config.maxiter, + getattr(config, "penalty", None), + ) + + @jax.tree_util.register_dataclass @dataclass(frozen=True) class CholeskyCache: @@ -443,20 +471,24 @@ class CG(_KrylovConfig): ``requires_positive_damping`` are rejected for that role) and ``penalty`` optionally adding a small ridge that stabilizes a rank-deficient tangent. - ``preconditioner`` is REQUIRED -- nobody should run Krylov methods without - a preconditioning decision, so :class:`~nlls_gram.IdentityPreconditioner` - is the explicit opt-out and a custom one is a small subclass implementing - ``apply(v, damping, ctx)``. On rank-deficient problems it must map - ``range(B')`` into itself or the minimum-norm selection is silently lost; - the identity, polynomials in the operator, and exact shifted inverses are - safe, and on full-column-rank problems the condition is vacuous. + ``preconditioner`` is REQUIRED in the forward role -- nobody should run + Krylov methods without a preconditioning decision, so + :class:`~nlls_gram.IdentityPreconditioner` is the explicit opt-out and a + custom one is a small registered dataclass implementing + ``apply(v, damping, ctx)``. In the ``ad_solver`` role, + ``preconditioner=None`` inherits the CARRIED forward instance at the + solution while pinning the AD tolerance and budget. On rank-deficient + problems the preconditioner must map ``range(B')`` into itself or the + minimum-norm selection is silently lost; the identity, polynomials in the + operator, and exact shifted inverses are safe, and on full-column-rank + problems the condition is vacuous. ``tol=None`` resolves to a dtype default (``1e-10`` in float64, ``1e-6`` in float32); ``maxiter`` must be set when both tolerances are explicitly zero, since an uncapped zero-tolerance CG loop has no stopping rule. """ - preconditioner: Preconditioner + preconditioner: Preconditioner | None tol: float | None = None atol: float = 0.0 maxiter: int | None = None @@ -491,8 +523,15 @@ def N_matvec(u): normal = normal + pullback return normal + damping * u + # The CARRIED instance, so a callback refresh reaches the very next + # inner solve; the config's own field only seeds the initial state. + precond = ctx.lm_state.preconditioner + def apply_M(v): - return self.preconditioner.apply(v, damping, ctx) + return precond.apply(v, damping, ctx) + + if precond is None: + apply_M = None def solve_N(_, c): return self._cg(N_matvec, c, sub, apply_M) @@ -531,7 +570,7 @@ class GramCG(_KrylovConfig): supports_penalty = False - preconditioner: Preconditioner + preconditioner: Preconditioner | None tol: float | None = None atol: float = 0.0 maxiter: int | None = None @@ -544,8 +583,15 @@ def dual_matvec(y): damping * y ) + # The CARRIED instance, so a callback refresh reaches the very next + # inner solve; the config's own field only seeds the initial state. + precond = ctx.lm_state.preconditioner + def apply_M(v): - return self.preconditioner.apply(v, damping, ctx) + return precond.apply(v, damping, ctx) + + if precond is None: + apply_M = None def solve_dual(_, c): return self._cg(dual_matvec, c, sub, apply_M) diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 2ca6b83..28522cd 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -14,10 +14,9 @@ from jax.flatten_util import ravel_pytree from nlls_gram.lm_types import ( + LMAction, LMHyperparams, - LMSolveAction, LMStatus, - SolverContext, _damping_floor, ) from nlls_gram.multi_start import ( @@ -29,7 +28,6 @@ _multi_start_python_impl, _multi_start_sequential_jit, ) -from nlls_gram.preconditioners import Preconditioner from nlls_gram.solve_loop import _solve_loop_jit, _solve_python_impl from nlls_gram.utilities import ( _hashable_hook, @@ -44,7 +42,9 @@ class LevenbergMarquardtBase: # Value-based identity: the jitted solve loop marks the solver itself # static, so equal-config solvers built around the same residual share the # compiled loop across instances. Subclasses set _static_key/_static_hash - # in __init__ from their constructor arguments. + # in __init__ from their constructor arguments; metric/preconditioner + # instances key by pytree STRUCTURE (their arrays are threaded through + # the carried state, so equal-config fresh instances share one compile). def __eq__(self, other): if self is other: return True @@ -55,6 +55,18 @@ def __eq__(self, other): def __hash__(self): return self._static_hash + # Whether a callback-replaced metric moves the objective (the ridge + # solver's penalty embeds it) or only the damping geometry. + _metric_defines_objective = False + + def _check_registered_instance(self, instance, keyword): + if instance is not None and jax.tree_util.all_leaves([instance]): + raise TypeError( + f"{keyword} must be a registered pytree ({type(instance).__name__} " + "flattens as a leaf); register the class with " + "nlls_gram.register_pytree_dataclass" + ) + def _validate_configuration(self, linear_solver, ad_solver, penalized): """Reject a config in a role it cannot fill, at construction. @@ -80,26 +92,13 @@ def _validate_configuration(self, linear_solver, ad_solver, penalized): if self.jacobian_mode not in ("auto", "fwd", "rev"): raise ValueError(f"unknown jacobian_mode: {self.jacobian_mode}") - def _block_sizes(self, theta_size): - # The free-block size is inferred from the flattened iterate: the - # metric covers the leading metric.size coordinates, the rest is free. - n_m = self.metric.size - if n_m > theta_size: - raise ValueError( - f"the metric covers {n_m} leading coordinates but x flattens " - f"to only {theta_size}; the free block is len(x) - metric.size " - "and must be nonnegative" - ) - return n_m, theta_size - n_m - def _cold_state(self, lm_state): - # Drawn multi-start lanes must not reuse caches or hook state built at - # another (x, args); damping, ridge, and hyper stay inherited from the - # caller's initial state. + # Drawn multi-start lanes must not reuse caches built at another + # (x, args); damping, ridge, hyper, and the carried instances stay + # inherited from the caller's initial state. updates = {} - for flag in ("jacobian_valid", "metric_valid", "precond_valid"): - if getattr(lm_state, flag) is not None: - updates[flag] = jnp.zeros_like(getattr(lm_state, flag)) + if lm_state.jacobian_valid is not None: + updates["jacobian_valid"] = jnp.zeros_like(lm_state.jacobian_valid) if lm_state.solver_cache is not None: updates["solver_cache"] = jax.tree.map( jnp.zeros_like, lm_state.solver_cache @@ -180,114 +179,64 @@ def hyperparams(self, dtype=None): def _block_sizes(self, theta_size): # The free-block size is inferred from the flattened iterate: the # metric covers the leading metric.size coordinates, the rest is free. - n_f = theta_size - self.metric.size + n_f = theta_size - self.initial_metric.size if n_f < 0: raise ValueError( - f"the metric covers {self.metric.size} leading coordinates " - f"but x flattens to only {theta_size}; the free block is " - "len(x) - metric.size and must be nonnegative" + f"the metric covers {self.initial_metric.size} leading " + f"coordinates but x flattens to only {theta_size}; the free " + "block is len(x) - metric.size and must be nonnegative" ) - return self.metric.size, n_f + return self.initial_metric.size, n_f + + def _resolved_state(self, lm_state): + # A hand-built pre-seeding LMState reads through the constructor + # instances; states from init/solve carry their own. The resolved + # view is ephemeral (ctx only) -- update passes the input fields + # through, so a user's own while_loop carry keeps its structure. + if lm_state.metric is not None: + return lm_state + return dataclasses.replace( + lm_state, + metric=self.initial_metric, + preconditioner=self.initial_preconditioner, + ) # The solver-internal extension F_bar = blockdiag(F, sqrt(free_scale) I): - # the metric's factor op on the metric block, a scalar on the free block. - # Applied to vectors or leading-axis-batched matrices; F_bar itself is - # never materialized, and the free block drops out entirely when it is - # empty or unscaled. - def _free_scale(self, v): - scale = self.metric.free_scale - return v if scale == 1.0 else v / jnp.sqrt(jnp.asarray(scale, v.dtype)) + # the CARRIED metric's factor op on the metric block, a scalar on the + # free block. Applied to vectors or leading-axis-batched matrices; F_bar + # itself is never materialized. free_scale is a traced leaf, so the + # division is unconditional; the Euclidean default's static 1.0 folds + # away at compile time. + def _scaled_free(self, v, metric): + return v / jnp.sqrt(jnp.asarray(metric.free_scale, v.dtype)) def _extended_solve(self, v, ctx): - n_m = self.metric.size + metric = ctx.lm_state.metric + n_m = metric.size if n_m == 0: - return self._free_scale(v) + return self._scaled_free(v, metric) if v.shape[0] == n_m: - return self.metric.factor_solve(v, ctx) + return metric.factor_solve(v, ctx) return jnp.concatenate( - [self.metric.factor_solve(v[:n_m], ctx), self._free_scale(v[n_m:])], axis=0 + [metric.factor_solve(v[:n_m], ctx), self._scaled_free(v[n_m:], metric)], + axis=0, ) def _extended_solve_transpose(self, v, ctx): - n_m = self.metric.size + metric = ctx.lm_state.metric + n_m = metric.size if n_m == 0: - return self._free_scale(v) + return self._scaled_free(v, metric) if v.shape[0] == n_m: - return self.metric.factor_solve_transpose(v, ctx) + return metric.factor_solve_transpose(v, ctx) return jnp.concatenate( [ - self.metric.factor_solve_transpose(v[:n_m], ctx), - self._free_scale(v[n_m:]), + metric.factor_solve_transpose(v[:n_m], ctx), + self._scaled_free(v[n_m:], metric), ], axis=0, ) - def _init_hook_state(self, theta, lm_state, args, p): - """The metric's and preconditioner's state at ``x0``, valid there, so - the first update reuses it. The flags stay absent when the hooks are - stateless.""" - ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) - valid = jnp.asarray(True, dtype=jnp.bool_) - hooks = {} - if self._metric_prepares: - hooks["metric_state"] = self.metric.prepare(theta, ctx) - hooks["metric_valid"] = valid - if self._precond_prepares: - hooks["precond"] = self.preconditioner.prepare(theta, ctx) - hooks["precond_valid"] = valid - return hooks - - def _hook_state(self, theta, lm_state, args, p): - """The metric's and preconditioner's prepared state for this step: - reused while still valid (a rejected step left ``x`` in place, or the - hook declined to rebuild), rebuilt from the live iterate otherwise.""" - bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) - metric_state = precond_state = None - if self._metric_prepares: - metric_state = jax.lax.cond( - lm_state.metric_valid | ~jnp.asarray(self.metric.rebuild(bare)), - lambda _: lm_state.metric_state, - lambda _: self.metric.prepare(theta, bare), - operand=None, - ) - if self._precond_prepares: - precond_state = jax.lax.cond( - lm_state.precond_valid - | ~jnp.asarray(self.preconditioner.rebuild(bare)), - lambda _: lm_state.precond, - lambda _: self.preconditioner.prepare(theta, bare), - operand=None, - ) - return metric_state, precond_state - - def _carried_ctx(self, theta, lm_state, args, p): - return SolverContext( - x=theta, - lm_state=lm_state, - args=args, - p=p, - metric_state=lm_state.metric_state, - preconditioner_state=lm_state.precond, - ) - - def _frozen_ctx(self, theta, lm_state, args, p, preconditioner): - # Under implicit AD the hooks are FROZEN at the returned solution: - # prepare runs once there and the state-dependence is not - # differentiated, the same contract as a fixed metric closing over - # constants. - bare = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) - metric_state = ( - self.metric.prepare(theta, bare) if self._metric_prepares else None - ) - precond_state = None - if preconditioner is not None and ( - type(preconditioner).prepare is not Preconditioner.prepare - ): - precond_state = preconditioner.prepare(theta, bare) - return dataclasses.replace( - bare, metric_state=metric_state, preconditioner_state=precond_state - ) - def _ad_linearization(self, x, args, p, p_dot): theta, unravel = ravel_pytree(x) @@ -308,11 +257,39 @@ def _ad_cg_tol(self, dtype): default_tol = 1e-10 if jnp.finfo(dtype).bits > 32 else 1e-6 return jnp.asarray(default_tol, dtype=dtype) + def _ad_preconditioner(self, lm_state): + # "carried": the forward instance at the solution, callback refreshes + # included; "explicit": the ad_solver's own baked instance. + if self._ad_preconditioner_source == "carried": + return lm_state.preconditioner + if self._ad_preconditioner_source == "explicit": + return self.ad_solver_preconditioner + return None + def _action_or_default(self, action): if action is None: - return LMSolveAction() + return LMAction() return action + def _check_instance_structure(self, new, previous, name): + # Trace-time guard mirroring the hyper contract: a replaced instance + # must be the same registered type with matching static fields and + # leaf shapes/dtypes, or the while-loop carry breaks downstream with + # a raw mismatch error that never names the culprit. + def spec(tree): + leaves, treedef = jax.tree_util.tree_flatten(tree) + return treedef, [ + (jnp.shape(leaf), jnp.result_type(leaf)) for leaf in leaves + ] + + if spec(new) != spec(previous): + raise ValueError( + f"the callback action replaced lm_state.{name} with a " + "different type, structure, or leaf shape/dtype; rebuild the " + "same class with arrays matching the carried instance, and " + "preserve untouched fields with dataclasses.replace(ctx.lm_state, ...)" + ) + def _apply_action(self, action, x, lm_state, args, user_state): action = self._action_or_default(action) # The step's diagnostics and every cache describe the pre-action @@ -321,6 +298,7 @@ def _apply_action(self, action, x, lm_state, args, user_state): # the field every step with unchanged values changes nothing. xargs_changed = jnp.asarray(False) state_changed = jnp.asarray(False) + metric_changed = jnp.asarray(False) if action.x is not None: xargs_changed = xargs_changed | _tree_changed(action.x, x) x = action.x @@ -352,7 +330,20 @@ def _apply_action(self, action, x, lm_state, args, user_state): "of the same dtype — a knob constructed as None cannot be " "enabled mid-solve" ) + self._check_instance_structure(lm_state.metric, previous.metric, "metric") + self._check_instance_structure( + lm_state.preconditioner, previous.preconditioner, "preconditioner" + ) + # A changed metric moves the ridge objective (suppressing this + # step's convergence test) but only re-whitens the metric + # solver's; both stale the whitening-dependent solver caches, + # neither the Jacobian cache -- J = dr/dx does not see the + # metric. Preconditioner changes are deliberately not compared: + # staleness only moves the CG iteration path. + metric_changed = _tree_changed(lm_state.metric, previous.metric) lm_state, state_changed = self._apply_action_state(lm_state, previous) + if self._metric_defines_objective: + state_changed = state_changed | metric_changed if action.args is not None: xargs_changed = xargs_changed | _tree_changed(action.args, args) args = action.args @@ -360,23 +351,20 @@ def _apply_action(self, action, x, lm_state, args, user_state): user_state = action.user_state problem_changed = xargs_changed | state_changed if action.x is not None or action.args is not None: - # Everything prepared at the pre-action (x, args) is stale once - # either moves. The metric matters most: it DEFINES the subproblem, - # so reusing a factor built at the old iterate would silently solve - # a different problem in a different geometry. - stale = {} - for flag in ("jacobian_valid", "metric_valid", "precond_valid"): - carried = getattr(lm_state, flag) - if carried is not None: - stale[flag] = carried & ~xargs_changed - if stale: - lm_state = dataclasses.replace(lm_state, **stale) + # The Jacobian cache describes the pre-action (x, args) and is + # stale once either moves. + if lm_state.jacobian_valid is not None: + lm_state = dataclasses.replace( + lm_state, jacobian_valid=lm_state.jacobian_valid & ~xargs_changed + ) touched = ( action.x is not None or action.args is not None or action.lm_state is not None ) - lm_state = self._invalidate_caches(lm_state, action, touched, problem_changed) + lm_state = self._invalidate_caches( + lm_state, action, touched, problem_changed | metric_changed + ) return action, x, lm_state, args, user_state, problem_changed # Subclass hooks for the callback-action path. The defaults are inert. @@ -386,13 +374,13 @@ def _check_action_state(self, lm_state): def _apply_action_state(self, lm_state, previous): return lm_state, jnp.asarray(False) - def _invalidate_caches(self, lm_state, action, touched, problem_changed): + def _invalidate_caches(self, lm_state, action, touched, caches_stale): if touched and lm_state.solver_cache is not None: cache = lm_state.solver_cache lm_state = dataclasses.replace( lm_state, solver_cache=dataclasses.replace( - cache, valid=cache.valid & ~problem_changed + cache, valid=cache.valid & ~caches_stale ), ) return lm_state @@ -428,8 +416,8 @@ def solve( ``LMStatus.CONVERGED``. How the three combine is the solver's own contract -- see each subclass. - ``callback`` receives an ``LMSolveContext`` after each step and may - return an ``LMSolveAction`` to stop or to override x/lm_state/args/ + ``callback`` receives an ``LMContext`` after each step and may + return an ``LMAction`` to stop or to override x/lm_state/args/ user_state; ``p`` is passed through but cannot be replaced. A callback that installs an invalid ``x`` or ``args`` must also stop with a failed status. @@ -586,7 +574,10 @@ def _solve_lm_state(self, x0, args, p, lm_state): return self.init(x0, args, p=p) if lm_state is None else lm_state def _initial_ad_point(self, x, lm_state, args, p): - return (x, args, p) + # The pre-loop instances ride along: a failed lane's callback may + # have left invalid metric/preconditioner arrays behind, so the + # failed tangent program reads these instead. + return (x, args, p, lm_state.metric, lm_state.preconditioner) def _solve_impl( self, diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py index fec3464..e66f591 100644 --- a/src/nlls_gram/lm_types.py +++ b/src/nlls_gram/lm_types.py @@ -15,10 +15,10 @@ import jax.numpy as jnp __all__ = [ + "LMAction", + "LMContext", "LMHyperparams", "LMInfo", - "LMSolveAction", - "LMSolveContext", "LMSolveResult", "LMState", "LMStatus", @@ -31,29 +31,24 @@ class SolverContext: """What the solver knows at a metric, preconditioner, or linear-solver call site -- the inner algebra's context, as opposed to - :class:`LMSolveContext`, which a per-step user callback receives. + :class:`LMContext`, which a per-step user callback receives. Fields are ``None`` where the call site has nothing to offer: - ``x``: the current FLATTENED iterate (the whole parameter vector, not just the metric block). - - ``lm_state``: the live :class:`LMState` (damping, ridge, caches). In the - implicit-AD rule this is the returned state under ``stop_gradient`` -- - inert conditioning data, like the ridge. + - ``lm_state``: the live :class:`LMState` (damping, ridge, caches, and + the carried metric/preconditioner instances). In the implicit-AD rule + this is the returned state under ``stop_gradient`` -- inert + conditioning data, like the ridge. - ``args`` / ``p``: the residual's auxiliary data and differentiation parameters as passed to ``solve``/``update``. - - ``metric_state`` / ``preconditioner_state``: the output of the metric's - and preconditioner's own ``prepare``, rebuilt from the live iterate on - accepted steps and reused across rejected ones. ``None`` for the - stateless default. """ x: Any = None lm_state: Any = None args: Any = None p: Any = None - metric_state: Any = None - preconditioner_state: Any = None class LMStatus(enum.IntEnum): @@ -62,7 +57,7 @@ class LMStatus(enum.IntEnum): Members are real ints (``IntEnum``): they work as dict keys, compare against status arrays, and ``LMStatus(int(result.status)).name`` recovers the label for logging. Callbacks may return bare members (or any weak - integer value) as ``LMSolveAction.status`` -- the solver canonicalizes to + integer value) as ``LMAction.status`` -- the solver canonicalizes to int32 at the boundary, so no explicit dtype casts are needed. """ @@ -147,13 +142,17 @@ class LMState: callback that rebuilds the state must PRESERVE the fields it does not mean to change -- use ``dataclasses.replace(ctx.lm_state, ...)``. + The callback-owned fields are ``damping``, ``ridge``, ``metric``, + ``preconditioner``, and the ``hyper`` group (replaceable as a unit); + everything else is solver-owned bookkeeping. + Attributes: damping: ``()`` current LM damping. ridge: ``()`` ridge weight, strictly positive, for ``RidgeLevenbergMarquardt``; ``None`` for the metric solver. Replacing it is the supported way to anneal mid-solve (see - ``RidgeContinuation``); the solver treats a ridge change as a - problem change, suppressing that step's convergence test and + ``AnnealRidge``); the solver treats a ridge change as a problem + change, suppressing that step's convergence test and invalidating the ridge-keyed caches. resid: cached residual at the current ``x`` (``cache_jacobian`` dense paths only). @@ -165,10 +164,16 @@ class LMState: ``None`` (``init``'s default) falls back to the constructor values. solver_cache: the linear solver's own reject-step cache, whose pytree structure is fixed by the static ``linear_solver`` config. - metric_state: the metric's ``prepare`` output at the current ``x``. - metric_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. - precond: the preconditioner's ``prepare`` output at the current ``x``. - precond_valid: ``()`` bool, ``jacobian_valid`` reuse semantics. + metric: the carried :class:`~nlls_gram.Metric` instance every factor + op reads. A callback replaces it by constructing a new instance + of the same type with matching leaf shapes and dtypes; the ridge + solver treats a changed metric as a problem change (the metric + defines its objective), the metric solver only invalidates the + whitening-dependent solver caches. + preconditioner: the carried :class:`~nlls_gram.Preconditioner` + instance the Krylov configs read; ``None`` outside them. A + callback refresh is never treated as a problem change -- + staleness only moves the CG iteration path. """ damping: jax.Array @@ -179,10 +184,8 @@ class LMState: aux: Any = None hyper: LMHyperparams | None = None solver_cache: Any = None - metric_state: Any = None - metric_valid: jax.Array | None = None - precond: Any = None - precond_valid: jax.Array | None = None + metric: Any = None + preconditioner: Any = None @jax.tree_util.register_dataclass @@ -256,7 +259,7 @@ class LMInfo: @jax.tree_util.register_dataclass @dataclass(frozen=True) -class LMSolveAction: +class LMAction: """Optional callback action for ``solve``. A field left as ``None`` is unchanged. ``status`` is used only when @@ -275,7 +278,7 @@ class LMSolveAction: @jax.tree_util.register_dataclass @dataclass(frozen=True) -class LMSolveContext: +class LMContext: """Information passed to a ``solve`` callback after each LM update.""" step: jax.Array diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index da0cf16..7f09715 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -15,6 +15,7 @@ """ import dataclasses +from dataclasses import dataclass import jax import jax.numpy as jnp @@ -28,6 +29,7 @@ Cholesky, GramCG, Subproblem, + _config_static_key, ) from nlls_gram.lm_core import LevenbergMarquardtBase from nlls_gram.lm_types import ( @@ -38,22 +40,30 @@ _damping_floor, ) from nlls_gram.metrics import Metric -from nlls_gram.preconditioners import Preconditioner from nlls_gram.utilities import ( _static_key_component, + _where_tree, _zero_tangent_leaf, canonicalize_residual, + register_pytree_dataclass, ) __all__ = ["LevenbergMarquardt"] +@dataclass(frozen=True, eq=False) class _EuclideanMetric(Metric): """The default metric: ``F = I`` over however many coordinates ``x`` - flattens to, resolved at trace time rather than at construction.""" + flattens to. ``size = 0`` puts everything in the free block, and the + static unit ``free_scale`` folds the free-block scaling away.""" - size = 0 # the free block absorbs everything, so F_bar is the identity - free_scale = 1.0 + size: int = 0 + free_scale: float = 1.0 + + +register_pytree_dataclass( + _EuclideanMetric, data_fields=(), meta_fields=("size", "free_scale") +) class LevenbergMarquardt(LevenbergMarquardtBase): @@ -118,7 +128,8 @@ def __init__( raise ValueError("max_damping must be at least init_damping") self.residual_fn = canonical_residual self.residual_arity = residual_arity - self.metric = _EuclideanMetric() if metric is None else metric + self.initial_metric = _EuclideanMetric() if metric is None else metric + self._check_registered_instance(self.initial_metric, "metric") self.init_damping = init_damping self.damping_decrease = damping_decrease self.damping_increase = damping_increase @@ -130,43 +141,71 @@ def __init__( self._validate_configuration(linear_solver, ad_solver, penalized=False) krylov = isinstance(linear_solver, (CG, GramCG)) if krylov: - self.preconditioner = linear_solver.preconditioner + if linear_solver.preconditioner is None: + raise ValueError( + "the forward linear_solver requires a preconditioner; " + "IdentityPreconditioner() is the explicit opt-out " + "(preconditioner=None is legal only in the ad_solver role)" + ) + self._check_registered_instance( + linear_solver.preconditioner, "linear_solver.preconditioner" + ) + self.initial_preconditioner = linear_solver.preconditioner self.iterative_tol = linear_solver.tol self.iterative_atol = linear_solver.atol self.iterative_maxiter = linear_solver.maxiter else: - self.preconditioner = None + self.initial_preconditioner = None self.iterative_tol = 0.0 self.iterative_atol = 0.0 self.iterative_maxiter = 8 if isinstance(ad_solver, (CG, GramCG)): - if ad_solver.preconditioner.requires_positive_damping: - raise ValueError( - "this preconditioner divides by the live damping and cannot " - "serve in ad_solver (the AD system is undamped)" - ) self.ad_solver_tol = ad_solver.tol self.ad_solver_atol = ad_solver.atol self.ad_solver_maxiter = ad_solver.maxiter - self.ad_solver_preconditioner = ad_solver.preconditioner self.ad_solver_penalty = getattr(ad_solver, "penalty", None) + if ad_solver.preconditioner is None: + # preconditioner=None in the AD role inherits the CARRIED + # forward instance at the solution (callback refreshes + # included) while pinning the AD tolerance and budget. + self.ad_solver_preconditioner = None + if self.initial_preconditioner is None: + self._ad_preconditioner_source = "none" + elif self.initial_preconditioner.requires_positive_damping: + raise ValueError( + "ad_solver preconditioner=None inherits the forward " + "preconditioner, but this one divides by the live " + "damping and cannot serve the undamped AD system" + ) + else: + self._ad_preconditioner_source = "carried" + else: + if ad_solver.preconditioner.requires_positive_damping: + raise ValueError( + "this preconditioner divides by the live damping and " + "cannot serve in ad_solver (the AD system is undamped)" + ) + self._check_registered_instance( + ad_solver.preconditioner, "ad_solver.preconditioner" + ) + self.ad_solver_preconditioner = ad_solver.preconditioner + self._ad_preconditioner_source = "explicit" else: self.ad_solver_tol = None self.ad_solver_atol = 0.0 self.ad_solver_maxiter = None self.ad_solver_penalty = None - # ad_solver=None under a matrix-free forward hands that - # preconditioner to the undamped implicit solve: the AD operator IS - # the forward operator at zero damping. Damping-dividing hooks fall - # back to unpreconditioned. + self.ad_solver_preconditioner = None + # ad_solver=None under a matrix-free forward hands the CARRIED + # forward preconditioner to the undamped implicit solve: the AD + # operator IS the forward operator at zero damping. + # Damping-dividing hooks fall back to unpreconditioned. inherit = ( ad_solver is None and krylov and not linear_solver.preconditioner.requires_positive_damping ) - self.ad_solver_preconditioner = ( - linear_solver.preconditioner if inherit else None - ) + self._ad_preconditioner_source = "carried" if inherit else "none" if inherit: self.ad_solver_penalty = getattr(linear_solver, "penalty", None) self.has_aux = has_aux @@ -175,23 +214,23 @@ def __init__( self.cache_jacobian = cache_jacobian and linear_solver.materializes_jacobian self.geodesic_acceleration = geodesic_acceleration self.geodesic_acceptance_ratio = geodesic_acceptance_ratio - self._metric_prepares = type(self.metric).prepare is not Metric.prepare - self._precond_prepares = self.preconditioner is not None and ( - type(self.preconditioner).prepare is not Preconditioner.prepare - ) + # Metric and forward-preconditioner instances key by pytree structure: + # their arrays are threaded through the carried state, so equal-config + # fresh instances share one compiled loop. An explicit AD instance is + # baked into the tangent program as constants, so it keys by identity. self._static_key = tuple( _static_key_component(value) for value in ( residual_fn, - metric, + jax.tree_util.tree_structure(self.initial_metric), init_damping, damping_decrease, damping_increase, min_damping, max_damping, - linear_solver, + _config_static_key(linear_solver, baked=False), jacobian_mode, - ad_solver, + _config_static_key(ad_solver, baked=True), has_aux, self.cache_jacobian, geodesic_acceleration, @@ -214,9 +253,11 @@ def init(self, x0, args=None, *, p=None): dtype = residual.dtype min_damping = _damping_floor(self.min_damping, dtype) damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) - hooks = self._init_hook_state(theta, LMState(damping), args, p) + instances = dict( + metric=self.initial_metric, preconditioner=self.initial_preconditioner + ) if not self.cache_jacobian: - return LMState(damping, **hooks) + return LMState(damping, **instances) return LMState( damping, resid=jnp.zeros(residual.shape, dtype=dtype), @@ -226,17 +267,23 @@ def init(self, x0, args=None, *, p=None): solver_cache=self.linear_solver.new_cache( residual.size, theta.size, n_m, dtype, False ), - **hooks, + **instances, ) def _solve_lm_state(self, x0, args, p, lm_state): if lm_state is not None: - return lm_state - if self.cache_jacobian or self._metric_prepares or self._precond_prepares: + # A hand-built pre-seeding state enters the loop with the + # constructor instances; the carry needs them present. + return self._resolved_state(lm_state) + if self.cache_jacobian: return self.init(x0, args, p=p) # Nothing needs sizing from a residual evaluation, so skip it: the # loop recasts the damping dtype itself. - return LMState(jnp.asarray(self.init_damping)) + return LMState( + jnp.asarray(self.init_damping), + metric=self.initial_metric, + preconditioner=self.initial_preconditioner, + ) def _initial_info(self, x, lm_state, args, p): # grad_norm is a +inf sentinel (computing it would cost a Jacobian @@ -315,14 +362,8 @@ def JT(cotangent): ) n_m, n_f = self._block_sizes(theta.shape[0]) - metric_state, precond_state = self._hook_state(theta, lm_state, args, p) ctx = SolverContext( - x=theta, - lm_state=lm_state, - args=args, - p=p, - metric_state=metric_state, - preconditioner_state=precond_state, + x=theta, lm_state=self._resolved_state(lm_state), args=args, p=p ) zero = jnp.zeros((), dtype=resid.dtype) step_solver = self.linear_solver.prepare( @@ -418,13 +459,9 @@ def first_jvp(th): new_damping = jnp.maximum(new_damping, min_damping) loss = jnp.where(improved, loss_candidate, loss_old) - hooks = {} - if self._metric_prepares: - hooks["metric_state"] = metric_state - hooks["metric_valid"] = ~improved - if self._precond_prepares: - hooks["precond"] = precond_state - hooks["precond_valid"] = ~improved + # The input state's instances pass through verbatim -- None stays + # None, so a user's own loop around update keeps its carry structure. + instances = dict(metric=lm_state.metric, preconditioner=lm_state.preconditioner) if self.cache_jacobian: new_lm_state = LMState( new_damping, @@ -434,10 +471,10 @@ def first_jvp(th): aux=aux, hyper=lm_state.hyper, solver_cache=step_solver.make_cache(~improved), - **hooks, + **instances, ) else: - new_lm_state = LMState(new_damping, hyper=lm_state.hyper, **hooks) + new_lm_state = LMState(new_damping, hyper=lm_state.hyper, **instances) return ( unravel(theta_new), new_lm_state, @@ -519,12 +556,23 @@ def _resolved_ad_solver(self, m, n): def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point): if p is None: return jax.tree.map(_zero_tangent_leaf, x) + # The carried instances are frozen conditioning data at the solution; + # a failed lane reads the differentiation-inert pre-loop instances + # instead (a callback may have left invalid arrays behind). lm_state = jax.lax.stop_gradient(result.lm_state) + initial_instances = jax.lax.stop_gradient(initial_ad_point[3:5]) + lm_state = dataclasses.replace( + lm_state, + metric=_where_tree(ad_success, lm_state.metric, initial_instances[0]), + preconditioner=_where_tree( + ad_success, lm_state.preconditioner, initial_instances[1] + ), + ) theta, unravel, residual, theta_jvp, residual_p_dot = self._ad_linearization( x, args, p, p_dot ) resolved = self._resolved_ad_solver(residual.shape[0], theta.shape[0]) - ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) + ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) n_m, n_f = self._block_sizes(theta.shape[0]) dtype = residual.dtype @@ -604,11 +652,12 @@ def Bt(w): return whiten_transpose(JT(w)) apply_M = None - if self.ad_solver_preconditioner is not None: + ad_preconditioner = self._ad_preconditioner(ctx.lm_state) + if ad_preconditioner is not None: # The AD system is undamped, so the preconditioner sees zero # damping (requires_positive_damping hooks were rejected). def apply_M(v): - return self.ad_solver_preconditioner.apply(v, zero_damping, ctx) + return ad_preconditioner.apply(v, zero_damping, ctx) def cg(matvec, rhs, preconditioner=apply_M): solution, _ = jsp_sparse_linalg.cg( diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index ebed324..376dd8b 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -17,6 +17,7 @@ import jax.scipy.linalg as jsp_linalg from nlls_gram.lm_types import SolverContext +from nlls_gram.utilities import register_pytree_dataclass __all__ = [ "CholeskyMetric", @@ -50,15 +51,28 @@ class Metric: Provided for callers; the solvers measure in the whitened variable and never call it. - Every callback receives a :class:`~nlls_gram.SolverContext` carrying the - solver's live state, so an exotic metric can key off the iterate; - :meth:`prepare` covers the iterate-dependent case. + Every op receives a :class:`~nlls_gram.SolverContext` carrying the + solver's live state, so an exotic metric can key off the iterate through + ``ctx.x`` and ``ctx.lm_state``. + + Metric instances are JAX PYTREES: array fields are traced leaves, the + type plus its static fields are structure. Every concrete class must be + registered with + :func:`~nlls_gram.register_pytree_dataclass` -- the solvers reject + unregistered instances. The instance rides inside the solver state + (``lm_state.metric``), so a ``solve`` callback replaces the metric by + constructing a new instance of the same type (same static fields, same + leaf shapes and dtypes) -- pure traced ops, no recompilation. Equal-config + instances with fresh arrays share one compiled solve loop. + ``dataclasses.replace`` works too: metric constructors only validate and + derive shapes, so re-running them under trace is cheap. ``free_scale`` weights the free block in the whitened variable: ``1.0`` (the default) leaves it Euclidean. The ridge solver never penalizes the free block whatever the scale -- ``free_scale`` only changes its trust-region geometry -- while for the metric solver it IS that block's - damping weight. + damping weight. It is a traced leaf, canonicalized by each constructor to + the factor's float dtype, so changing it never recompiles. Contracts: the factor must be EXACT. The solver hardcodes the identity penalty block in the whitened variable, so an approximate factor silently @@ -66,40 +80,13 @@ class Metric: The ridge weight never enters the factorization, so ridge continuation composes unchanged. How a subclass fulfills the ops -- prefactorized storage, factorize-in-``__init__``, fully matrix-free -- is its - constructor's business. - - Metrics hash and compare by identity (``eq=False`` frozen dataclasses -- - array fields make value-hashing impossible): construct one at setup scope - and reuse it, since rebuilding an equal-config metric per call would key a - fresh solver compilation. + constructor's business, and the constructor must be traceable when the + metric is rebuilt inside a jitted callback. """ size: int free_scale: float = 1.0 - def prepare(self, theta, ctx): - """Build this metric's numeric state from the current iterate. - - The default is ``None`` -- a fixed metric, whose state slot compiles - away. Override for an iterate-dependent metric (a kernel Gram factor - over state points that live in ``x``, say): the returned pytree rides - on ``lm_state.metric_state`` and comes back as ``ctx.metric_state`` in - the factor ops. It is rebuilt on accepted steps and reused across - rejected ones, and is FROZEN at the solution under implicit AD -- the - state-dependence is not differentiated, the same contract as a fixed - metric closing over constants. Its pytree structure must not change - between rebuilds. - - Unlike a preconditioner, the metric defines the subproblem, so the - factor it yields must be exact for the state it was built from. - """ - return None - - def rebuild(self, ctx): - """Traced predicate gating a rebuild on an accepted step. The default - rebuilds every accepted step.""" - return True - def factor_apply(self, v, ctx): """``F v`` for a metric-block vector or leading-axis-batched matrix.""" raise NotImplementedError @@ -117,11 +104,14 @@ def norm(self, v, ctx): return jnp.linalg.norm(self.factor_apply(v, ctx)) -def _check_free_scale(free_scale): +def _canonical_free_scale(free_scale, dtype): # F_bar = blockdiag(F, sqrt(free_scale) I), so a non-positive scale makes - # the whitening noninvertible or complex. - if free_scale <= 0: + # the whitening noninvertible or complex. Traced values skip the sign + # check; the strong-typed cast keeps rebuilt instances aval-identical to + # the originals inside lax.cond/while_loop. + if not isinstance(free_scale, (jax.Array, jax.core.Tracer)) and free_scale <= 0: raise ValueError("free_scale must be positive") + return jnp.asarray(free_scale, dtype=dtype) def _check_leading_size(v, size): @@ -146,7 +136,11 @@ class IdentityMetric(Metric): def __post_init__(self): if self.size < 0: raise ValueError("size must be nonnegative") - _check_free_scale(self.free_scale) + object.__setattr__( + self, + "free_scale", + _canonical_free_scale(self.free_scale, jnp.result_type(float)), + ) def factor_apply(self, v, ctx): _check_leading_size(v, self.size) @@ -165,6 +159,11 @@ def norm(self, v, ctx): return jnp.linalg.norm(v) +register_pytree_dataclass( + IdentityMetric, data_fields=("free_scale",), meta_fields=("size",) +) + + @dataclass(frozen=True, eq=False) class CholeskyMetric(Metric): """Dense metric ``W = L L'`` from its lower-triangular Cholesky factor. @@ -183,9 +182,13 @@ def __post_init__(self): L = jnp.asarray(self.L) if L.ndim != 2 or L.shape[0] != L.shape[1] or L.shape[0] == 0: raise ValueError("L must be a nonempty square matrix") - _check_free_scale(self.free_scale) object.__setattr__(self, "L", L) object.__setattr__(self, "size", L.shape[0]) + object.__setattr__( + self, + "free_scale", + _canonical_free_scale(self.free_scale, jnp.result_type(L, 1.0)), + ) def factor_apply(self, v, ctx): _check_leading_size(v, self.size) @@ -200,6 +203,11 @@ def factor_solve_transpose(self, v, ctx): return jsp_linalg.solve_triangular(self.L, v, lower=True) +register_pytree_dataclass( + CholeskyMetric, data_fields=("L", "free_scale"), meta_fields=("size",) +) + + @dataclass(frozen=True, eq=False) class DiagonalMetric(Metric): """The diagonal metric ``W = diag(weights)``; ``F = diag(sqrt(weights))``. @@ -216,9 +224,13 @@ def __post_init__(self): weights = jnp.asarray(self.weights) if weights.ndim != 1: raise ValueError("weights must be 1-D") - _check_free_scale(self.free_scale) object.__setattr__(self, "weights", weights) object.__setattr__(self, "size", weights.shape[0]) + object.__setattr__( + self, + "free_scale", + _canonical_free_scale(self.free_scale, jnp.result_type(weights, 1.0)), + ) def _scaled(self, v, factor): _check_leading_size(v, self.size) @@ -234,6 +246,11 @@ def factor_solve_transpose(self, v, ctx): return self.factor_solve(v, ctx) +register_pytree_dataclass( + DiagonalMetric, data_fields=("weights", "free_scale"), meta_fields=("size",) +) + + @dataclass(frozen=True, eq=False) class RepeatedFactorMetric(Metric): """``repeats`` copies of one block factor: ``W = blockdiag(F'F, ...)``. @@ -266,9 +283,11 @@ def __post_init__(self): raise TypeError("F must have a real floating-point dtype") if self.repeats < 1: raise ValueError("repeats must be a positive integer") - _check_free_scale(self.free_scale) object.__setattr__(self, "F", F.astype(dtype)) object.__setattr__(self, "size", self.repeats * F.shape[0]) + object.__setattr__( + self, "free_scale", _canonical_free_scale(self.free_scale, dtype) + ) def _map_blocks(self, block_op, v): _check_leading_size(v, self.size) @@ -295,3 +314,10 @@ def factor_solve_transpose(self, v, ctx): return self._map_blocks( lambda m: jsp_linalg.solve_triangular(self.F.T, m, lower=True), v ) + + +register_pytree_dataclass( + RepeatedFactorMetric, + data_fields=("F", "free_scale"), + meta_fields=("repeats", "size"), +) diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index f37d666..a0c6f3b 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -10,16 +10,18 @@ approximations and staleness are safe. """ -from dataclasses import dataclass, field +from dataclasses import InitVar, dataclass, field from typing import Any import jax import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg +from nlls_gram.utilities import register_pytree_dataclass + class Preconditioner: - """SPD preconditioner for ``RidgeLevenbergMarquardt``'s CG paths. + """SPD preconditioner for the solvers' CG paths. ``apply(v, damping, ctx)`` returns an SPD approximation of the damped operator's inverse -- ``(J~'J~ + ridge E + damping I)^{-1}`` in parameter @@ -27,12 +29,23 @@ class Preconditioner: residual space under :class:`~nlls_gram.GramCG`. In the forward role it sits in CG's ``M`` slot with the live damping; in the ``ad_solver`` role the implicit system is undamped and ``damping`` is zero. ``ctx`` is the - same :class:`~nlls_gram.SolverContext` the metric factor ops receive, so a - preconditioner can key off the solver state. - - Implement a custom one as a small dataclass (``eq=False`` identity hashing - when it holds arrays -- construct once at setup scope and reuse, since the - instance enters the solver's compile-cache key):: + same :class:`~nlls_gram.SolverContext` the metric factor ops receive. + + Preconditioner instances are JAX PYTREES: array fields are traced + leaves, the type plus its static fields are structure. Every concrete + class must be registered with + :func:`~nlls_gram.register_pytree_dataclass` -- the solvers reject + unregistered instances. The instance rides inside the solver state + (``lm_state.preconditioner``), so a ``solve`` callback refreshes it by + calling the CONSTRUCTOR again with fresh arrays -- same type, same leaf + shapes and dtypes, pure traced ops, no recompilation. Never + ``dataclasses.replace`` a preconditioner: ``replace`` re-runs + ``__init__``, re-paying any eigendecomposition or sketch, and + construction-time-only inputs are not stored to re-supply. A stale + instance only changes the CG iteration path, never the converged step, + so refreshing rarely (or never) is always safe. + + Implement a custom one as a small registered frozen dataclass:: @dataclass(frozen=True, eq=False) class JacobiPreconditioner(Preconditioner): @@ -41,6 +54,8 @@ class JacobiPreconditioner(Preconditioner): def apply(self, v, damping, ctx): return v / (self.diagonal + damping) + register_pytree_dataclass(JacobiPreconditioner, data_fields=("diagonal",)) + Subclasses whose ``apply`` divides by the live damping must set ``requires_positive_damping = True``; the constructor rejects them for the AD role, where damping is zero. @@ -48,33 +63,6 @@ def apply(self, v, damping, ctx): requires_positive_damping = False - def prepare(self, theta, ctx): - """Build this preconditioner's numeric state from the current iterate. - - The default is ``None`` -- a stateless preconditioner, whose state - slot compiles away. Override to hold traced arrays that must track the - iterate: the returned pytree rides on ``lm_state.precond`` and comes - back as ``ctx.preconditioner_state`` in :meth:`apply`. It is rebuilt on - accepted steps and reused across rejected ones (where ``x`` did not - move), runs inside the jitted loop as traced ops, and is frozen at the - solution under implicit AD. Its pytree structure must not change - between rebuilds. - - Expensive setup that does NOT depend on the iterate belongs in - ``__init__``, where it is paid once. - """ - return None - - def rebuild(self, ctx): - """Traced predicate gating a rebuild on an accepted step. - - The default rebuilds every accepted step. Return ``False`` to keep the - carried state -- staleness only changes the CG iteration path, never - the converged step, so declining is always safe and often much - cheaper (e.g. rebuild only when ridge continuation advances a level). - """ - return True - def apply(self, v, damping, ctx): raise NotImplementedError @@ -85,17 +73,21 @@ class IdentityPreconditioner(Preconditioner): Nobody should run Krylov methods without thinking about preconditioning, so opting out is an explicit, greppable decision rather than a silent - default. Stateless and value-equal: two instances compare equal, so - equal ``CG`` configs share one compiled solve loop. + default. Stateless: every instance compares equal, so equal ``CG`` + configs share one compiled solve loop. """ def apply(self, v, damping, ctx): return v +register_pytree_dataclass(IdentityPreconditioner, data_fields=()) + + @dataclass(frozen=True, eq=False) class BlockEigenPreconditioner(Preconditioner): - """Block-diagonal eigenbasis preconditioner that owns its state. + """Block-diagonal eigenbasis preconditioner over grouped whitened + coordinates. The workhorse for structured whitened normal operators ``J~'J~ + ridge E + damping I`` built from repeated interacting blocks @@ -108,38 +100,72 @@ class BlockEigenPreconditioner(Preconditioner): per block -- analytic in both the live ``damping`` (traced; it changes per LM step) and the live ``ridge`` (read from ``ctx.lm_state.ridge``, so - ridge continuation composes with no rebuild). + ridge continuation composes with no refresh). - ``blocks_fn(theta, ctx)`` returns the family list that - :func:`block_eigen_state` packs: ``(blocks, ridge_weight)`` pairs whose + ``families`` is a sequence of ``(blocks, ridge_weight)`` pairs: ``blocks`` has shape ``(groups, size, size)`` -- the stacked diagonal blocks of ``J~'J~`` restricted to that family's coordinate groups, in permuted order. Families in the metric block set ``ridge_weight = 1`` - (their diagonal carries the ``ridge`` spectral floor); free-block families - set ``0`` (damping-only, so the zero-damping AD role applies their plain - inverse -- positive definite whenever the free block is identified). - ``permutation`` reorders the flattened whitened vector into family-major - order; ``jnp.arange(n)`` serves when the natural layout already is. - - The eigendecomposition runs in :meth:`prepare` from the live iterate, so - it is rebuilt on accepted steps and reused across rejected ones. Override - ``rebuild`` to decline -- a stale state only changes the CG iteration - path, never the converged step, so refreshing only when ridge continuation - advances a level is a pure saving:: - - class OnLevelChange(BlockEigenPreconditioner): - def rebuild(self, ctx): - return ctx.lm_state.ridge < self.last_ridge + (their diagonal carries the ``ridge`` spectral floor); free-block + families set ``0`` (damping-only, so the zero-damping AD role applies + their plain inverse -- positive definite whenever the free block is + identified). Blocks are symmetrized and eigendecomposed HERE, once; + positive semidefiniteness is assumed, not validated (entries may be + traced). ``permutation`` is the 1-D integer array reordering the + flattened whitened parameter vector into family-major order + (``v_permuted = v[permutation]``); families are consumed in sequence and + must cover it exactly. ``jnp.arange(n)`` serves when the natural layout + already is family-major. + + The constructor is fully traceable, so a ``solve`` callback refreshes + the preconditioner from the live iterate by constructing a new instance + -- gate the rebuild with ``jax.lax.cond`` (e.g. on a ridge-continuation + level advance) so the eigendecomposition is paid only when it fires; a + ``jnp.where`` merge would pay it every step. """ - blocks_fn: Any + families: InitVar[Any] permutation: jax.Array - - def prepare(self, theta, ctx): - return block_eigen_state(self.blocks_fn(theta, ctx), self.permutation) + eigenvectors: tuple = field(init=False) + eigenvalues: tuple = field(init=False) + ridge_weights: tuple = field(init=False) + inverse_permutation: jax.Array = field(init=False) + + def __post_init__(self, families): + permutation = jnp.asarray(self.permutation) + if permutation.ndim != 1 or not jnp.issubdtype(permutation.dtype, jnp.integer): + raise ValueError("permutation must be a 1-D integer array") + eigenvectors, eigenvalues, ridge_weights = [], [], [] + covered = 0 + for blocks, ridge_weight in families: + blocks = jnp.asarray(blocks) + if blocks.ndim != 3 or blocks.shape[1] != blocks.shape[2]: + raise ValueError( + "each family's blocks must have shape (groups, size, size); " + f"got {blocks.shape}" + ) + symmetrized = 0.5 * (blocks + jnp.swapaxes(blocks, 1, 2)) + values, vectors = jnp.linalg.eigh(symmetrized) + # eigh of a numerically PSD block can return tiny negative + # eigenvalues; clamped at zero the apply shift stays positive for + # any positive ridge/damping (and the zero-damping AD role stays + # SPD whenever the family itself is). + eigenvalues.append(jnp.maximum(values, 0.0)) + eigenvectors.append(vectors) + ridge_weights.append(jnp.asarray(ridge_weight, dtype=blocks.dtype)) + covered += blocks.shape[0] * blocks.shape[1] + if covered != permutation.shape[0]: + raise ValueError( + f"families cover {covered} coordinates but the permutation " + f"has {permutation.shape[0]}" + ) + object.__setattr__(self, "permutation", permutation) + object.__setattr__(self, "eigenvectors", tuple(eigenvectors)) + object.__setattr__(self, "eigenvalues", tuple(eigenvalues)) + object.__setattr__(self, "ridge_weights", tuple(ridge_weights)) + object.__setattr__(self, "inverse_permutation", jnp.argsort(permutation)) def apply(self, v, damping, ctx): - state = ctx.preconditioner_state # LevenbergMarquardt carries no ridge, so its metric-block families # shift by the damping alone. carried = ctx.lm_state.ridge @@ -148,88 +174,33 @@ def apply(self, v, damping, ctx): if carried is None else jnp.asarray(carried, dtype=v.dtype) ) - permuted = v[state["permutation"]] + permuted = v[self.permutation] pieces = [] offset = 0 - for family in state["families"]: - V = family["eigenvectors"] - eigenvalues = family["eigenvalues"] + for V, values, ridge_weight in zip( + self.eigenvectors, self.eigenvalues, self.ridge_weights, strict=True + ): groups, size = V.shape[0], V.shape[1] segment = permuted[offset : offset + groups * size] offset += groups * size - shift = family["ridge_weight"] * ridge + damping + shift = ridge_weight * ridge + damping coefficients = jnp.einsum("gab,ga->gb", V, segment.reshape(groups, size)) - solved = coefficients / (eigenvalues + shift) - pieces.append(jnp.einsum("gab,gb->ga", V, solved).reshape(-1)) - if offset != permuted.shape[0]: - raise ValueError( - f"block_eigen_state families cover {offset} coordinates but " - f"the parameter vector has {permuted.shape[0]}" + pieces.append( + jnp.einsum("gab,gb->ga", V, coefficients / (values + shift)).reshape(-1) ) - return jnp.concatenate(pieces)[state["inverse_permutation"]].astype(v.dtype) - + return jnp.concatenate(pieces)[self.inverse_permutation].astype(v.dtype) -def block_eigen_state(families, permutation): - """Pack stacked SPD diagonal blocks into a - :class:`BlockEigenPreconditioner` state pytree. - - ``families`` is a sequence of ``(blocks, ridge_weight)`` pairs: - ``blocks`` has shape ``(groups, size, size)`` -- the stacked diagonal - blocks of the whitened normal operator ``J~'J~`` restricted to that - family's coordinate groups, in permuted order -- and ``ridge_weight`` is - ``1.0`` for metric-block families (the apply shift includes the live - ridge) or ``0.0`` for free-block families (damping-only). Blocks are - symmetrized and eigendecomposed here, once; positive semidefiniteness is - assumed, not validated (entries may be traced). - - ``permutation`` is the 1-D integer array reordering the flattened - whitened parameter vector into family-major order - (``v_permuted = v[permutation]``); families are consumed in sequence - and must cover it exactly. The identity ``jnp.arange(p)`` serves when - the natural layout is already family-major. - - Fully traceable, so an adaptive rebuild can run inside a jitted solve - callback; the state's pytree structure (family count and shapes) is - static and must not change across rebuilds. - """ - permutation = jnp.asarray(permutation) - if permutation.ndim != 1 or not jnp.issubdtype(permutation.dtype, jnp.integer): - raise ValueError("permutation must be a 1-D integer array") - packed = [] - covered = 0 - for blocks, ridge_weight in families: - blocks = jnp.asarray(blocks) - if blocks.ndim != 3 or blocks.shape[1] != blocks.shape[2]: - raise ValueError( - "each family's blocks must have shape (groups, size, size); " - f"got {blocks.shape}" - ) - symmetrized = 0.5 * (blocks + jnp.swapaxes(blocks, 1, 2)) - eigenvalues, eigenvectors = jnp.linalg.eigh(symmetrized) - # eigh of a numerically PSD block can return tiny negative - # eigenvalues; clamped at zero the apply shift stays positive for - # any positive ridge/damping (and the zero-damping AD role stays - # SPD whenever the family itself is). - eigenvalues = jnp.maximum(eigenvalues, 0.0) - packed.append( - { - "eigenvectors": eigenvectors, - "eigenvalues": eigenvalues, - "ridge_weight": jnp.asarray(ridge_weight, dtype=blocks.dtype), - } - ) - covered += blocks.shape[0] * blocks.shape[1] - if covered != permutation.shape[0]: - raise ValueError( - f"families cover {covered} coordinates but the permutation has " - f"{permutation.shape[0]}" - ) - return { - "permutation": permutation, - "inverse_permutation": jnp.argsort(permutation), - "families": tuple(packed), - } +register_pytree_dataclass( + BlockEigenPreconditioner, + data_fields=( + "permutation", + "eigenvectors", + "eigenvalues", + "ridge_weights", + "inverse_permutation", + ), +) @dataclass(frozen=True, eq=False) @@ -244,22 +215,39 @@ class ShermanMorrisonPreconditioner(Preconditioner): ``(c^2/m) u u'`` into ``J M^{-1} J'``. The live ``damping`` is ignored -- spectral closeness to the damped operator is all a preconditioner needs -- which also makes it valid in the zero-damping ``ad_solver`` role. + + ``solve`` applies ``A^{-1}`` and is called on every ``apply``, so it is a + STATIC field: a fixed hashable callable whose identity enters the + instance's pytree structure, with anything it closes over entering the + compiled program as constants. This class is a setup-scope object for a + fixed dual operator, not a callback-refresh target. """ - solve: object + solve: Any u: jax.Array - weight: float - _solve_u: jax.Array = field(init=False) - _denominator: jax.Array = field(init=False) + weight: Any + solve_u: jax.Array = field(init=False) + denominator: jax.Array = field(init=False) def __post_init__(self): - solve_u = self.solve(self.u) - object.__setattr__(self, "_solve_u", solve_u) - object.__setattr__(self, "_denominator", 1.0 / self.weight + self.u @ solve_u) + u = jnp.asarray(self.u) + weight = jnp.asarray(self.weight, dtype=jnp.result_type(u, 1.0)) + solve_u = self.solve(u) + object.__setattr__(self, "u", u) + object.__setattr__(self, "weight", weight) + object.__setattr__(self, "solve_u", solve_u) + object.__setattr__(self, "denominator", 1.0 / weight + u @ solve_u) def apply(self, v, damping, ctx): y = self.solve(v) - return y - self._solve_u * ((self.u @ y) / self._denominator) + return y - self.solve_u * ((self.u @ y) / self.denominator) + + +register_pytree_dataclass( + ShermanMorrisonPreconditioner, + data_fields=("u", "weight", "solve_u", "denominator"), + meta_fields=("solve",), +) @dataclass(frozen=True, eq=False) @@ -271,14 +259,15 @@ class WoodburyPreconditioner(Preconditioner): capacitance ``C = diag(1/weights) + U' A^{-1} U``; ``A^{-1}U`` (one matrix solve) and the Cholesky factor of the k x k capacitance are precomputed. ``weights`` must be positive -- not validated, since inputs may be traced. - Like Sherman-Morrison it ignores ``damping`` and so serves the AD role too. + Like Sherman-Morrison it ignores ``damping`` and so serves the AD role + too, and its ``solve`` is the same STATIC always-called field. """ - solve: object + solve: Any U: jax.Array weights: jax.Array - _solve_U: jax.Array = field(init=False) - _factor: tuple = field(init=False) + solve_U: jax.Array = field(init=False) + capacitance_factor: jax.Array = field(init=False) def __post_init__(self): U, weights = jnp.asarray(self.U), jnp.asarray(self.weights) @@ -287,13 +276,25 @@ def __post_init__(self): object.__setattr__(self, "U", U) object.__setattr__(self, "weights", weights) solve_U = self.solve(U) - object.__setattr__(self, "_solve_U", solve_U) + object.__setattr__(self, "solve_U", solve_U) capacitance = jnp.diag(1.0 / weights) + U.T @ solve_U - object.__setattr__(self, "_factor", jsp_linalg.cho_factor(capacitance)) + object.__setattr__( + self, "capacitance_factor", jsp_linalg.cho_factor(capacitance)[0] + ) def apply(self, v, damping, ctx): y = self.solve(v) - return y - self._solve_U @ jsp_linalg.cho_solve(self._factor, self.U.T @ y) + correction = jsp_linalg.cho_solve( + (self.capacitance_factor, False), self.U.T @ y + ) + return y - self.solve_U @ correction + + +register_pytree_dataclass( + WoodburyPreconditioner, + data_fields=("U", "weights", "solve_U", "capacitance_factor"), + meta_fields=("solve",), +) @dataclass(frozen=True, eq=False) @@ -338,6 +339,11 @@ def apply(self, v, damping, ctx): ) +register_pytree_dataclass( + PaddedPreconditioner, data_fields=("base",), meta_fields=("n_real",) +) + + @dataclass(frozen=True, eq=False) class NystromPreconditioner(Preconditioner): """Randomized Nystrom preconditioner (Frangella-Tropp-Udell) for a PSD @@ -360,32 +366,34 @@ class NystromPreconditioner(Preconditioner): where the dual operator is the ``m x m`` empirical NTK Gram ``J J'`` -- fast spectral decay plus the LM damping shift is exactly the FTU regime. ``matvec`` must apply a symmetric PSD operator to ``(n, k)`` matrices; an - indefinite one silently produces NaN through the Cholesky square root. The - build costs ``rank`` operator applications plus an ``O(n rank^2)`` - QR/SVD, paid once at construction, so for a nonlinear problem it - approximates the dual at the linearization point it was built from - (staleness is safe). Each apply is two ``(n, rank)`` matvecs. + indefinite one silently produces NaN through the Cholesky square root. It + is consumed at construction -- the build costs ``rank`` operator + applications plus an ``O(n rank^2)`` QR/SVD, and only the sketch is + stored, so for a nonlinear problem the instance approximates the dual at + the linearization point it was built from (staleness is safe; a callback + refreshes by constructing a new instance from a fresh ``matvec``). Each + apply is two ``(n, rank)`` matvecs. ``key`` is an explicit PRNG key; the same key reproduces the same preconditioner. ``dtype=None`` uses the JAX default float -- pass the operator dtype explicitly for a float32 problem under enabled x64. """ - matvec: object + matvec: InitVar[Any] n: int rank: int - key: jax.Array - dtype: object = None - _basis: jax.Array = field(init=False) - _eigenvalues: jax.Array = field(init=False) + key: InitVar[Any] + dtype: InitVar[Any] = None + basis: jax.Array = field(init=False) + eigenvalues: jax.Array = field(init=False) - def __post_init__(self): + def __post_init__(self, matvec, key, dtype): if not 0 < self.rank <= self.n: raise ValueError("rank must be a positive int <= n") - dtype = jnp.result_type(float) if self.dtype is None else self.dtype + dtype = jnp.result_type(float) if dtype is None else dtype shape = (self.n, self.rank) - Omega = jnp.linalg.qr(jax.random.normal(self.key, shape, dtype))[0] - Y = self.matvec(Omega) + Omega = jnp.linalg.qr(jax.random.normal(key, shape, dtype))[0] + Y = matvec(Omega) # The floor keeps the shift usable for a (near-)zero operator, where # eps * ||Y||_F alone would leave the core singular; tiny/eps stays # clear of the subnormal range through the downstream products. @@ -396,12 +404,19 @@ def __post_init__(self): L = jnp.linalg.cholesky(0.5 * (core + core.T)) B = jsp_linalg.solve_triangular(L, Y_nu.T, lower=True).T U, sigma, _ = jnp.linalg.svd(B, full_matrices=False) - object.__setattr__(self, "_basis", U) - object.__setattr__(self, "_eigenvalues", jnp.maximum(sigma**2 - nu, 0.0)) + object.__setattr__(self, "basis", U) + object.__setattr__(self, "eigenvalues", jnp.maximum(sigma**2 - nu, 0.0)) def apply(self, v, damping, ctx): # Regrouped so the apply is two (n, rank) matvecs instead of three. - U, lam = self._basis, self._eigenvalues + U, lam = self.basis, self.eigenvalues rho = lam[-1] Utv = U.T @ v return U @ (Utv / (lam + damping) - Utv / (rho + damping)) + v / (rho + damping) + + +register_pytree_dataclass( + NystromPreconditioner, + data_fields=("basis", "eigenvalues"), + meta_fields=("n", "rank"), +) diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 288f662..d5988c4 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -5,7 +5,7 @@ and a positive-definite :class:`~nlls_gram.Metric` ``W`` on the metric block ``x_m`` (the free block ``x_f`` stays unpenalized), with the ridge weight ``lambda`` carried as traced state that a ``solve`` callback may anneal -toward zero (:func:`ridge_continuation`). Selection of the minimum-seminorm +toward zero (:class:`AnnealRidge`). Selection of the minimum-seminorm interpolant lives in the OBJECTIVE -- classical nonlinear Tikhonov regularization (Engl-Kunisch-Neubauer 1989; Engl-Hanke-Neubauer 1996 Ch. 10; the seminorm formulation goes back to Elden 1982) -- rather than in an @@ -35,40 +35,39 @@ CholeskyCache, QRCache, Subproblem, + _config_static_key, ) from nlls_gram.lm_core import LevenbergMarquardtBase from nlls_gram.lm_types import ( + LMAction, LMInfo, - LMSolveAction, LMState, SolverContext, _cast_hyper, _damping_floor, ) -from nlls_gram.metrics import Metric -from nlls_gram.preconditioners import Preconditioner from nlls_gram.utilities import ( _static_key_component, + _where_tree, _zero_tangent_leaf, canonicalize_residual, ) __all__ = [ + "AnnealRidge", "CholeskyCache", - "RidgeContinuation", "QRCache", "RidgeLevenbergMarquardt", - "ridge_continuation", ] -def ridge_continuation( - *, decrease=0.1, ridge_floor, grad_rtol=1e-2, stall_rtol=0.0, dtype=None -): - """Build ``(callback, user_state0)`` implementing ridge continuation. +@dataclass(frozen=True) +class AnnealRidge: + """Ridge-continuation ``solve`` callback: multiply ``lm_state.ridge`` by + ``decrease`` whenever the current level has yielded what it can, never + below ``ridge_floor``. - The callback multiplies ``lm_state.ridge`` by ``decrease`` whenever the - current level has yielded what it can, never below ``ridge_floor``: + A level has yielded what it can when it is - **stationary**: ``info.grad_norm`` fell below ``grad_rtol`` relative to its reference value at the current ridge level (the level's first @@ -80,65 +79,73 @@ def ridge_continuation( demand approaches ``grad_rtol ** levels`` times the initial gradient, and the anneal can freeze below the problem's noise floor while steps keep being accepted with negligible progress. Enable with - ``stall_rtol ~ 0.99`` when that happens (advancing on stagnation is - still more conservative than the cited iteratively regularized - Gauss-Newton method, which anneals every step). Off by default - because it cannot distinguish a converged level from an accepted - micro-step under temporarily high damping early in a hard solve -- - where a false advance collapses the schedule prematurely; widening - ``decrease`` (e.g. ``0.01``) is the alternative fix for a frozen - anneal, since larger jumps keep the per-level references generous. + ``stall_rtol ~ 0.99`` when that happens. Off by default because it + cannot distinguish a converged level from an accepted micro-step under + temporarily high damping early in a hard solve -- where a false + advance collapses the schedule prematurely; widening ``decrease`` + (e.g. ``0.01``) is the alternative fix for a frozen anneal, since + larger jumps keep the per-level references generous. ``ridge_floor`` is REQUIRED and strictly positive (``ridge = 0`` is out - of the solver's contract). The callback returns an - :class:`~nlls_gram.LMSolveAction` replacing ``lm_state`` AND - ``user_state`` (the per-level reference and previous gradient live in - ``user_state`` as fixed-shape scalars, since a ``lax.while_loop`` carry - cannot grow from ``None`` mid-loop -- hence the factory shape):: - - cb, us0 = ridge_continuation(ridge_floor=1e-10) - result = solver.solve(x0, callback=cb, user_state=us0, + of the solver's contract). Usage:: + + anneal = AnnealRidge(ridge_floor=1e-10) + result = solver.solve(x0, callback=anneal, + user_state=anneal.init_state(), gtol=1e-8, atol=1e-8) The solved-out continuation path converges to the minimum-seminorm solution by nonlinear Tikhonov theory (Engl-Kunisch-Neubauer 1989; - Engl-Hanke-Neubauer 1996), while annealing per accepted stationarity event - rather than per fully solved level is the iteratively regularized + Engl-Hanke-Neubauer 1996), while annealing per accepted stationarity + event rather than per fully solved level is the iteratively regularized Gauss-Newton method (Bakushinskii 1992; Blaschke-Neubauer-Scherzer 1997; - Kaltenbacher-Neubauer-Scherzer 2008), whose theory wants exactly this kind - of monotone, boundedly geometric schedule. Pair the schedule with the - conjunctive stopping rule: choose ``atol`` BETWEEN the ridge-floor + Kaltenbacher-Neubauer-Scherzer 2008), whose theory wants exactly this + kind of monotone, boundedly geometric schedule. Pair the schedule with + the conjunctive stopping rule: choose ``atol`` BETWEEN the ridge-floor residual and the last intermediate level's residual (they differ by roughly ``1 / decrease``), so the solve can only stop at the floor even when ``gtol`` must sit above a variant-dependent stationarity noise floor -- intermediate levels are stationary too, and ``atol`` is what - rules them out. ``dtype`` types the ``user_state0`` scalars (default: - the JAX - default float; pass the problem dtype explicitly for a float32 program - under enabled x64). - """ - - schedule = RidgeContinuation( - decrease=decrease, - ridge_floor=ridge_floor, - grad_rtol=grad_rtol, - stall_rtol=stall_rtol, - ) - infinity = jnp.asarray( - jnp.inf, dtype=jnp.result_type(float) if dtype is None else dtype - ) - return schedule, {"reference": infinity, "previous": infinity} - + rules them out. + + HOW IT WORKS, for composing the schedule into a callback of your own + (data re-draws, damping resets, a preconditioner refresh): the per-level + reference and previous gradient ride in ``user_state`` as two + fixed-shape scalars (``init_state`` builds them; a ``lax.while_loop`` + carry cannot grow from ``None`` mid-loop), with ``+inf`` marking "no + observation at this level yet" -- the first step after a decrease sets + the reference and can never read as stalled. Both trackers reset to + ``+inf`` exactly when the level advances; at the floor the ridge stops + changing, so the solver stops suppressing convergence and ``gtol``/ + ``atol`` can fire. All comparisons run at the ridge dtype and the + returned trackers are cast back to the ``user_state`` dtype. A wrapping + callback calls the instance, inspects ``action.lm_state.ridge < + ctx.lm_state.ridge`` for a level advance, and returns a + ``dataclasses.replace`` of the action -- e.g. gating an expensive + preconditioner rebuild on the advance with ``jax.lax.cond`` so the + eigendecomposition is paid only when it fires (a ``jnp.where`` merge + would pay it every step):: + + def driver_callback(ctx): + action = anneal(ctx) + advanced = action.lm_state.ridge < ctx.lm_state.ridge + precond = jax.lax.cond( + advanced, + lambda: BlockEigenPreconditioner(families(ctx.x), PERM), + lambda: ctx.lm_state.preconditioner, + ) + return dataclasses.replace( + action, + lm_state=dataclasses.replace( + action.lm_state, preconditioner=precond + ), + ) -@dataclass(frozen=True) -class RidgeContinuation: - """The callback :func:`ridge_continuation` builds; see it for the schedule. - - A frozen dataclass rather than a closure because ``solve`` marks the - callback a jit STATIC argument: a fresh closure would key a fresh - compilation of the whole solve loop on every construction. Two equal - schedules compare equal and share one compiled loop. ``ridge_floor`` must - be a concrete float for that sharing -- a traced value is unhashable and + A frozen dataclass with scalar fields rather than a closure because + ``solve`` marks the callback a jit STATIC argument: equal schedules + compare equal and share one compiled loop, while a fresh closure per + construction would key a fresh compilation. ``ridge_floor`` must be a + concrete float for that sharing -- a traced value is unhashable and falls back to identity. """ @@ -162,6 +169,15 @@ def __post_init__(self): if not 0 <= self.stall_rtol < 1: raise ValueError("stall_rtol must lie in [0, 1)") + def init_state(self, dtype=None): + """The initial ``user_state``: both trackers at ``+inf``. ``dtype`` + defaults to the JAX default float; pass the problem dtype explicitly + for a float32 program under enabled x64.""" + infinity = jnp.asarray( + jnp.inf, dtype=jnp.result_type(float) if dtype is None else dtype + ) + return {"reference": infinity, "previous": infinity} + def __call__(self, ctx): ridge = ctx.lm_state.ridge dtype = ridge.dtype @@ -198,7 +214,7 @@ def __call__(self, ctx): advanced = new_ridge < ridge fresh_level = jnp.asarray(jnp.inf, dtype) state_dtype = jnp.asarray(ctx.user_state["reference"]).dtype - return LMSolveAction( + return LMAction( lm_state=dataclasses.replace(ctx.lm_state, ridge=new_ridge), user_state={ "reference": jnp.where(advanced, fresh_level, reference).astype( @@ -241,7 +257,7 @@ class RidgeLevenbergMarquardt(LevenbergMarquardtBase): package's alternative is metric-damped :class:`~nlls_gram.LevenbergMarquardt`; this solver instead makes every inner problem a well-posed NLLS. Annealing ``ridge`` per stationarity - event (:func:`ridge_continuation`) is the iteratively regularized + event (:class:`AnnealRidge`) is the iteratively regularized Gauss-Newton method (Bakushinskii 1992; Kaltenbacher-Neubauer-Scherzer 2008). For kernel metrics each inner step is a kernel ridge regression of the relinearized equations (Chen-Hosseini-Owhadi-Stuart 2021). @@ -369,8 +385,8 @@ class RidgeLevenbergMarquardt(LevenbergMarquardtBase): callback-produced value). The init/update/solve protocol, callback contract - (:class:`~nlls_gram.LMSolveContext` -> - :class:`~nlls_gram.LMSolveAction`), ``multi_start``, ``save_steps``, and + (:class:`~nlls_gram.LMContext` -> + :class:`~nlls_gram.LMAction`), ``multi_start``, ``save_steps``, and :class:`~nlls_gram.LMSolveResult` are shared with :class:`~nlls_gram.LevenbergMarquardt`; code written against that solver ports by changing the constructor (its damping metric -> this metric) @@ -380,6 +396,10 @@ class RidgeLevenbergMarquardt(LevenbergMarquardtBase): when they share a continuation schedule. """ + # The metric defines the ridge objective, so a callback-replaced metric + # is a problem change (convergence suppressed for that step). + _metric_defines_objective = True + def __init__( self, residual_fn, @@ -407,7 +427,7 @@ def __init__( ): raise ValueError( "ridge must be strictly positive (ridge = 0 is unsupported: " - "use ridge_continuation with a positive ridge_floor to " + "use AnnealRidge with a positive ridge_floor to " "approach the ridgeless limit)" ) if init_damping <= 0 or damping_decrease <= 0 or damping_increase <= 0: @@ -420,7 +440,8 @@ def __init__( raise ValueError("max_damping must be at least init_damping") self.residual_fn = canonical_residual self.residual_arity = residual_arity - self.metric = metric + self.initial_metric = metric + self._check_registered_instance(metric, "metric") self.ridge = ridge self.init_damping = init_damping self.damping_decrease = damping_decrease @@ -440,47 +461,75 @@ def __init__( # approximation of (J~'J~ + ridge E + damping I)^{-1}, posed on # the whitened variable. IdentityPreconditioner() opts out # explicitly. - self.normal_cg_preconditioner = linear_solver.preconditioner + if linear_solver.preconditioner is None: + raise ValueError( + "the forward linear_solver requires a preconditioner; " + "IdentityPreconditioner() is the explicit opt-out " + "(preconditioner=None is legal only in the ad_solver role)" + ) + self._check_registered_instance( + linear_solver.preconditioner, "linear_solver.preconditioner" + ) + self.initial_preconditioner = linear_solver.preconditioner # tol=None resolves per residual dtype in hyperparams(), the # _ad_cg_tol convention. self.iterative_tol = linear_solver.tol self.iterative_atol = linear_solver.atol self.iterative_maxiter = linear_solver.maxiter else: - self.normal_cg_preconditioner = None + self.initial_preconditioner = None self.iterative_tol = 0.0 self.iterative_atol = 0.0 self.iterative_maxiter = 8 if isinstance(ad_solver, CG): - if ad_solver.preconditioner.requires_positive_damping: - raise ValueError( - "this preconditioner divides by the live damping and " - "cannot serve in ad_solver (the AD system is undamped)" - ) self.ad_solver_tol = ad_solver.tol self.ad_solver_atol = ad_solver.atol self.ad_solver_maxiter = ad_solver.maxiter - self.ad_solver_preconditioner = ad_solver.preconditioner + if ad_solver.preconditioner is None: + # preconditioner=None in the AD role inherits the CARRIED + # forward instance at the solution (callback refreshes + # included) while pinning the AD tolerance and budget. + self.ad_solver_preconditioner = None + if self.initial_preconditioner is None: + self._ad_preconditioner_source = "none" + elif self.initial_preconditioner.requires_positive_damping: + raise ValueError( + "ad_solver preconditioner=None inherits the forward " + "preconditioner, but this one divides by the live " + "damping and cannot serve the undamped AD system" + ) + else: + self._ad_preconditioner_source = "carried" + else: + if ad_solver.preconditioner.requires_positive_damping: + raise ValueError( + "this preconditioner divides by the live damping and " + "cannot serve in ad_solver (the AD system is undamped)" + ) + self._check_registered_instance( + ad_solver.preconditioner, "ad_solver.preconditioner" + ) + self.ad_solver_preconditioner = ad_solver.preconditioner + self._ad_preconditioner_source = "explicit" else: self.ad_solver_tol = None self.ad_solver_atol = 0.0 self.ad_solver_maxiter = None + self.ad_solver_preconditioner = None # ad_solver=None matches the forward family, and a CG forward - # also hands its preconditioner to the undamped implicit solve: - # the AD operator IS the forward operator at zero damping, the - # typed apply is damping-analytic there, and unpreconditioned + # also hands its CARRIED preconditioner to the undamped implicit + # solve: the AD operator IS the forward operator at zero damping, + # the typed apply is damping-analytic there, and unpreconditioned # implicit CG degrades exactly like the forward as the ridge # shrinks. The AD tolerance and budget stay at the AD defaults # (run to tolerance); damping-dividing hooks fall back to # unpreconditioned. - if ( + inherit = ( ad_solver is None and isinstance(linear_solver, CG) and not linear_solver.preconditioner.requires_positive_damping - ): - self.ad_solver_preconditioner = linear_solver.preconditioner - else: - self.ad_solver_preconditioner = None + ) + self._ad_preconditioner_source = "carried" if inherit else "none" self.has_aux = has_aux # Only the dense paths materialize J' (and the cholesky/qr caches ride # on the same reject-reuse lifecycle), so the flag is inert for the @@ -488,35 +537,27 @@ def __init__( self.cache_jacobian = cache_jacobian and not isinstance(linear_solver, CG) self.geodesic_acceleration = geodesic_acceleration self.geodesic_acceptance_ratio = geodesic_acceptance_ratio - # The forward preconditioner is the one whose prepared state is carried - # (the AD role runs once, at the solution). Whether a hook is stateful - # is a static property of its class, so the slots and their lax.cond - # compile away entirely for the stateless default. - self.preconditioner = self.normal_cg_preconditioner - self._metric_prepares = type(metric).prepare is not Metric.prepare - self._precond_prepares = self.preconditioner is not None and ( - type(self.preconditioner).prepare is not Preconditioner.prepare - ) # Value-based identity: the jitted solve loop marks the solver itself # static, so equal-config solvers built around the same residual and - # metric share the compiled loop across instances. Keyed on the - # constructor arguments -- every derived attribute is a function of - # them. Metrics hash by identity, so a rebuilt equal-config metric - # keys a fresh compilation. + # metric-STRUCTURE share the compiled loop across instances. The + # metric and forward preconditioner key by pytree structure (their + # arrays are threaded through the carried state); an explicit AD + # instance keys by identity (its arrays are baked into the tangent + # program). self._static_key = tuple( _static_key_component(value) for value in ( residual_fn, - metric, + jax.tree_util.tree_structure(metric), ridge, init_damping, damping_decrease, damping_increase, min_damping, max_damping, - linear_solver, + _config_static_key(linear_solver, baked=False), jacobian_mode, - ad_solver, + _config_static_key(ad_solver, baked=True), has_aux, self.cache_jacobian, geodesic_acceleration, @@ -547,9 +588,11 @@ def init(self, x0, args=None, *, p=None): min_damping = _damping_floor(self.min_damping, dtype) damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) ridge = self._resolve_ridge(dtype) - hooks = self._init_hook_state(theta, LMState(damping, ridge), args, p) + instances = dict( + metric=self.initial_metric, preconditioner=self.initial_preconditioner + ) if not self.cache_jacobian: - return LMState(damping, ridge, **hooks) + return LMState(damping, ridge, **instances) p_dim = theta.size m = residual.size return LMState( @@ -560,7 +603,7 @@ def init(self, x0, args=None, *, p=None): jacobian_valid=jnp.asarray(False, dtype=jnp.bool_), aux=jax.tree.map(jnp.zeros_like, aux), solver_cache=self.linear_solver.new_cache(m, p_dim, n_m, dtype, True), - **hooks, + **instances, ) def _initial_info(self, x, lm_state, args, p): @@ -572,9 +615,10 @@ def _initial_info(self, x, lm_state, args, p): theta, _ = ravel_pytree(x) ridge = jnp.asarray(lm_state.ridge, dtype=residual.dtype) n_m = self._block_sizes(theta.shape[0])[0] - ctx = self._carried_ctx(theta, lm_state, args, p) + resolved = self._resolved_state(lm_state) + ctx = SolverContext(x=theta, lm_state=resolved, args=args, p=p) y_m = jnp.asarray( - self.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype + resolved.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype ) penalty_value = jnp.sum(y_m**2) loss = resid_loss + ridge * penalty_value @@ -671,16 +715,11 @@ def JT(cotangent): # including the reported norms -- is the whitened one. y_m doubles as # the pre-step penalty value ||y_m||^2. n_m, n_f = self._block_sizes(theta.shape[0]) - metric_state, precond_state = self._hook_state(theta, lm_state, args, p) - ctx = SolverContext( - x=theta, - lm_state=lm_state, - args=args, - p=p, - metric_state=metric_state, - preconditioner_state=precond_state, + resolved_state = self._resolved_state(lm_state) + ctx = SolverContext(x=theta, lm_state=resolved_state, args=args, p=p) + y_m = jnp.asarray( + resolved_state.metric.factor_apply(theta[:n_m], ctx), dtype=resid.dtype ) - y_m = jnp.asarray(self.metric.factor_apply(theta[:n_m], ctx), dtype=resid.dtype) penalty_value_old = jnp.sum(y_m**2) penalty_gradient = jnp.concatenate([y_m, jnp.zeros(n_f, dtype=resid.dtype)]) @@ -812,18 +851,13 @@ def accelerated_objective(_): loss = jnp.where(improved, loss_candidate, loss_old) resid_loss = jnp.where(improved, resid_loss_candidate, resid_loss_old) penalty_value = jnp.where(improved, penalty_candidate, penalty_value_old) - # Thread the caches and prepared hook state built at this step's - # pre-step (x, ridge): valid = ~improved marks them reusable exactly - # when the step was rejected (x did not move). ridge passes through - # unchanged -- only init() and callbacks set it. The input hyper (not - # the fallback) passes through so the loop carry structure is stable. - hooks = {} - if self._metric_prepares: - hooks["metric_state"] = metric_state - hooks["metric_valid"] = ~improved - if self._precond_prepares: - hooks["precond"] = precond_state - hooks["precond_valid"] = ~improved + # Thread the caches built at this step's pre-step (x, ridge): + # valid = ~improved marks them reusable exactly when the step was + # rejected (x did not move). ridge and the carried instances pass + # through unchanged -- only init() and callbacks set them. The input + # hyper (not the fallback) passes through so the loop carry structure + # is stable. + instances = dict(metric=lm_state.metric, preconditioner=lm_state.preconditioner) if self.cache_jacobian: new_lm_state = LMState( new_damping, @@ -834,10 +868,12 @@ def accelerated_objective(_): aux, lm_state.hyper, solver_cache=step_solver.make_cache(~improved), - **hooks, + **instances, ) else: - new_lm_state = LMState(new_damping, ridge, hyper=lm_state.hyper, **hooks) + new_lm_state = LMState( + new_damping, ridge, hyper=lm_state.hyper, **instances + ) return ( unravel(theta_new), new_lm_state, @@ -901,17 +937,20 @@ def _solve_lm_state(self, x0, args, p, lm_state): # Recast a hand-replaced ridge to the carried scalar dtype: a # weak-typed replace(state, ridge=1e-4) would change the jit input # aval and retrace the loop. - return dataclasses.replace( - lm_state, - ridge=jnp.asarray( - lm_state.ridge, dtype=jnp.asarray(lm_state.damping).dtype - ), + return self._resolved_state( + dataclasses.replace( + lm_state, + ridge=jnp.asarray( + lm_state.ridge, dtype=jnp.asarray(lm_state.damping).dtype + ), + ) ) def _initial_ad_point(self, x, lm_state, args, p): - # The pre-loop ridge rides along: a failed lane's callback may have - # left an invalid ridge behind, so the failed tangent uses this one. - return (x, args, p, lm_state.ridge) + # The pre-loop ridge and instances ride along: a failed lane's + # callback may have left an invalid ridge or metric behind, so the + # failed tangent uses these. + return (x, args, p, lm_state.metric, lm_state.preconditioner, lm_state.ridge) def _check_action_state(self, lm_state): if lm_state.ridge is None: @@ -963,10 +1002,11 @@ def _ranking_objective(self, result, p, callback): residual = self._residual_and_aux(result.x, result.args, p)[0] theta, _ = ravel_pytree(result.x) n_m = self._block_sizes(theta.shape[0])[0] - ctx = self._carried_ctx(theta, result.lm_state, result.args, p) + resolved = self._resolved_state(result.lm_state) + ctx = SolverContext(x=theta, lm_state=resolved, args=result.args, p=p) ridge = jnp.asarray(result.lm_state.ridge, dtype=residual.dtype) y_m = jnp.asarray( - self.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype + resolved.metric.factor_apply(theta[:n_m], ctx), dtype=residual.dtype ) loss = jnp.sum(residual**2) + ridge * jnp.sum(y_m**2) return jnp.where( @@ -982,16 +1022,24 @@ def _resolved_ad_solver(self): def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point): if p is None: return jax.tree.map(_zero_tangent_leaf, x) - # A successful tangent uses the winner's own final ridge; a failed one - # the pre-loop initial ridge. Both are stop-gradient'd -- lambda is - # inert conditioning data, and the returned state rides along as - # equally inert SolverContext data for the factor callbacks. + # A successful tangent uses the winner's own final ridge and carried + # instances; a failed one the pre-loop initial ones (a callback may + # have left invalid values behind). All are stop-gradient'd -- inert + # conditioning data for the factor callbacks. final_ridge = jax.lax.stop_gradient(result.lm_state.ridge) - initial_ridge = jax.lax.stop_gradient(initial_ad_point[3]) + initial_ridge = jax.lax.stop_gradient(initial_ad_point[5]) ridge = jnp.where( ad_success, final_ridge, jnp.asarray(initial_ridge, final_ridge.dtype) ) lm_state = jax.lax.stop_gradient(result.lm_state) + initial_instances = jax.lax.stop_gradient(initial_ad_point[3:5]) + lm_state = dataclasses.replace( + lm_state, + metric=_where_tree(ad_success, lm_state.metric, initial_instances[0]), + preconditioner=_where_tree( + ad_success, lm_state.preconditioner, initial_instances[1] + ), + ) if self._resolved_ad_solver() == "cholesky": return self._ad_tangent_cholesky(x, args, p, p_dot, ridge, lm_state) return self._ad_tangent_normal_cg(x, args, p, p_dot, ridge, lm_state) @@ -1005,7 +1053,7 @@ def _ad_tangent_cholesky(self, x, args, p, p_dot, ridge, lm_state): x, args, p, p_dot ) n_m = self._block_sizes(theta.shape[0])[0] - ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) + ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) Jt = self._assemble_jt(theta_jvp, theta, residual) ridge_typed = jnp.asarray(ridge, dtype=residual.dtype) Jt_sub = jnp.asarray( @@ -1025,7 +1073,7 @@ def _ad_tangent_normal_cg(self, x, args, p, p_dot, ridge, lm_state): x, args, p, p_dot ) n_m, n_f = self._block_sizes(theta.shape[0]) - ctx = self._frozen_ctx(theta, lm_state, args, p, self.ad_solver_preconditioner) + ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) theta_transpose = jax.linear_transpose(theta_jvp, theta) def JT(cotangent): @@ -1052,7 +1100,8 @@ def normal_matvec(u): cg_tol = self._ad_cg_tol(residual.dtype) cg_atol = jnp.asarray(self.ad_solver_atol, dtype=residual.dtype) - if self.ad_solver_preconditioner is None: + ad_preconditioner = self._ad_preconditioner(lm_state) + if ad_preconditioner is None: apply_M = None else: # The AD system is undamped, so the preconditioner sees zero @@ -1061,7 +1110,7 @@ def normal_matvec(u): zero_damping = jnp.zeros((), dtype=residual.dtype) def apply_M(v): - return self.ad_solver_preconditioner.apply(v, zero_damping, ctx) + return ad_preconditioner.apply(v, zero_damping, ctx) def solve(matvec, rhs_value): solution, _ = jsp_sparse_linalg.cg( diff --git a/src/nlls_gram/solve_loop.py b/src/nlls_gram/solve_loop.py index 5791987..b65c898 100644 --- a/src/nlls_gram/solve_loop.py +++ b/src/nlls_gram/solve_loop.py @@ -9,7 +9,7 @@ import jax import jax.numpy as jnp -from nlls_gram.lm_types import LMSolveContext, LMSolveResult, LMStatus +from nlls_gram.lm_types import LMContext, LMSolveResult, LMStatus # save_steps bookkeeping shared by the jitted and Python solve loops: row `step` of @@ -129,7 +129,7 @@ def body(carry): action = None if callback is not None: - ctx = LMSolveContext( + ctx = LMContext( step, x, x_old, @@ -247,7 +247,7 @@ def _solve_python_impl( break action = None if callback is not None: - ctx = LMSolveContext( + ctx = LMContext( jnp.asarray(steps, dtype=jnp.int32), x, x_old, diff --git a/src/nlls_gram/utilities.py b/src/nlls_gram/utilities.py index 2013762..8de4ef4 100644 --- a/src/nlls_gram/utilities.py +++ b/src/nlls_gram/utilities.py @@ -5,12 +5,74 @@ ``LevenbergMarquardt`` and ``RidgeLevenbergMarquardt`` share. """ +import dataclasses import inspect import jax import jax.numpy as jnp +def register_pytree_dataclass(cls, *, data_fields, meta_fields=()): + """Register a frozen dataclass as a pytree whose unflatten bypasses + ``__init__``/``__post_init__``. + + ``data_fields`` become traced leaves (subtrees, if a field holds a + container); ``meta_fields`` become static structure and must hold + hashable values. Unflatten rebuilds the instance with ``object.__new__`` + plus ``object.__setattr__``, so constructors are free to compute derived + leaves and validate eagerly -- reconstruction inside jit, ``vmap``, or a + loop carry restores the stored fields verbatim without re-running any of + it. Static values are type-tagged, so treedefs compare and hash by value + with jit's strict-type semantics (``1``, ``1.0``, and ``True`` stay + distinct). Every dataclass field must appear in exactly one of the two + lists. Returns ``cls``. + + Every concrete :class:`~nlls_gram.Metric` and + :class:`~nlls_gram.Preconditioner` class must be registered this way + (subclassing a registered base does not register the subclass); the + solvers reject unregistered instances at construction. + """ + data_fields = tuple(data_fields) + meta_fields = tuple(meta_fields) + declared = {f.name for f in dataclasses.fields(cls)} + listed = set(data_fields) | set(meta_fields) + if len(data_fields) + len(meta_fields) != len(listed) or listed != declared: + raise ValueError( + f"register_pytree_dataclass({cls.__name__}): data_fields + " + f"meta_fields must cover every dataclass field exactly once; " + f"declared {sorted(declared)}, listed {sorted(listed)}" + ) + + def static_aux(instance): + # The typed tag makes equality/hash strict-typed; the raw value rides + # alongside so unflatten can restore it verbatim. + return tuple( + (_typed_key(value), value) + for value in (getattr(instance, name) for name in meta_fields) + ) + + def flatten_with_keys(instance): + children = [ + (jax.tree_util.GetAttrKey(name), getattr(instance, name)) + for name in data_fields + ] + return children, static_aux(instance) + + def flatten(instance): + return [getattr(instance, name) for name in data_fields], static_aux(instance) + + def unflatten(aux, children): + instance = object.__new__(cls) + for name, value in zip(data_fields, children, strict=True): + object.__setattr__(instance, name, value) + for name, (_, value) in zip(meta_fields, aux, strict=True): + object.__setattr__(instance, name, value) + return instance + + jax.tree_util.register_pytree_with_keys(cls, flatten_with_keys, unflatten, flatten) + return cls + + def _tree_changed(new, old): new_leaves, new_treedef = jax.tree_util.tree_flatten(new) old_leaves, old_treedef = jax.tree_util.tree_flatten(old) @@ -18,7 +80,12 @@ def _tree_changed(new, old): return jnp.asarray(True) changed = jnp.asarray(False) for new_leaf, old_leaf in zip(new_leaves, old_leaves, strict=True): - # equal_nan: an unchanged NaN sentinel is not a change. + # The same tracer/array object is the same value: a callback that + # passes a subtree through dataclasses.replace untouched costs no + # comparison ops. equal_nan: an unchanged NaN sentinel is not a + # change. + if new_leaf is old_leaf: + continue changed = changed | ~jnp.array_equal(new_leaf, old_leaf, equal_nan=True) return changed diff --git a/tests/test_compilation.py b/tests/test_compilation.py index 4eea631..2366462 100644 --- a/tests/test_compilation.py +++ b/tests/test_compilation.py @@ -18,6 +18,7 @@ from nlls_gram import ( CG, QR, + AnnealRidge, BlockEigenPreconditioner, Cholesky, CholeskyMetric, @@ -27,7 +28,6 @@ MultiStart, RepeatedFactorMetric, RidgeLevenbergMarquardt, - ridge_continuation, ) from nlls_gram.multi_start import ( _multi_start_parallel_jit, @@ -98,26 +98,49 @@ def sized(x, args, p): assert compilations() == 2 -# Metrics hold arrays, so they hash by identity and the documented contract is -# build-once-at-setup-scope. What must not happen is a recompilation when the -# same metric is reused and only the solver around it is rebuilt. +# Metric instances key compilation by pytree STRUCTURE (type + static +# fields); their arrays are threaded through the carried state. A fresh +# equal-config metric per solve must therefore share one compiled loop -- +# and, the other half of the guarantee, its VALUES must actually be used. METRICS = { - "cholesky": lambda: CholeskyMetric(jnp.eye(N, dtype=jnp.float32)), - "diagonal": lambda: DiagonalMetric(jnp.ones(N, jnp.float32)), - "repeated": lambda: RepeatedFactorMetric(jnp.eye(N, dtype=jnp.float32)), + "cholesky": lambda scale=1.0: CholeskyMetric(scale * jnp.eye(N, dtype=jnp.float32)), + "diagonal": lambda scale=1.0: DiagonalMetric(scale * jnp.ones(N, jnp.float32)), + "repeated": lambda scale=1.0: RepeatedFactorMetric( + scale * jnp.eye(N, dtype=jnp.float32) + ), } @pytest.mark.parametrize("name", list(METRICS)) -def test_reused_metric_survives_solver_rebuilds(name): - metric = METRICS[name]() +def test_fresh_equal_config_metric_compiles_once(name): for scale in (1.0, 2.0, 3.0): - LevenbergMarquardt(residual, metric=metric).solve( + LevenbergMarquardt(residual, metric=METRICS[name]()).solve( jnp.zeros(N), p=make_p(scale), **SOLVE ) assert compilations() == 1 +def test_shared_compile_uses_each_metrics_own_values(): + # Two same-treedef, different-valued metrics share one compiled loop; a + # leftover static read would silently reuse the first metric's factor + # for the second solver. The damping geometry selects the returned root + # of this underdetermined system, so different weights must move x. + def solve_with(scale): + return LevenbergMarquardt( + residual, + metric=DiagonalMetric( + jnp.asarray([100.0, 1.0, 1.0, 1.0, 100.0], jnp.float32) ** scale + ), + ).solve(jnp.zeros(N), p=make_p(), max_steps=60, atol=1e-6) + + heavy_ends = solve_with(1.0) + heavy_middle = solve_with(-1.0) + assert compilations() == 1 + assert not np.allclose( + np.asarray(heavy_ends.x), np.asarray(heavy_middle.x), atol=1e-4 + ) + + def test_stateless_preconditioner_is_value_equal(): # IdentityPreconditioner holds nothing, so even a freshly constructed one # keys the same compilation -- the closure it replaced did not. @@ -135,12 +158,12 @@ def ridge_solver(): def run_continuation(solver, ridge_floor, scale=1.0): - callback, user_state = ridge_continuation(ridge_floor=ridge_floor) + callback = AnnealRidge(ridge_floor=ridge_floor) return solver.solve( jnp.zeros(N), p=make_p(scale), callback=callback, - user_state=user_state, + user_state=callback.init_state(), max_steps=20, gtol=1e-6, ) @@ -261,16 +284,51 @@ def test_save_steps_makes_max_steps_static(): assert compilations() == 3 -def test_a_stateful_preconditioner_reused_shares_one_compilation(): - # BlockEigenPreconditioner holds a closure and an array, so it hashes by - # identity: reusing the instance must not recompile, and its per-step - # prepare() must not either. - preconditioner = BlockEigenPreconditioner( - lambda theta, ctx: [(jnp.eye(N, dtype=jnp.float32)[None], 0.0)], - jnp.arange(N), - ) +def test_fresh_equal_config_preconditioner_compiles_once(): + # BlockEigenPreconditioner keys by structure too: a fresh equal-config + # instance per solve (same family count, shapes, permutation length) + # shares the compiled loop; its eigendecomposition arrays ride in the + # carried state. for scale in (1.0, 2.0, 3.0): + preconditioner = BlockEigenPreconditioner( + [(scale * jnp.eye(N, dtype=jnp.float32)[None], 0.0)], jnp.arange(N) + ) LevenbergMarquardt( residual, linear_solver=CG(preconditioner, tol=1e-8, maxiter=16) ).solve(jnp.zeros(N), p=make_p(scale), **SOLVE) assert compilations() == 1 + + +def test_callback_instance_swap_does_not_recompile(): + # A callback that rebuilds the carried metric/preconditioner inside the + # loop constructs same-structure instances: no recompilation across + # solves, and none from the swap itself. + import dataclasses as dc + + from nlls_gram import LMAction + + metric0 = DiagonalMetric(jnp.ones(N, jnp.float32)) + + def swap(ctx): + fresh = jax.lax.cond( + ctx.step == 2, + lambda: DiagonalMetric(2.0 * jnp.ones(N, jnp.float32)), + lambda: ctx.lm_state.metric, + ) + return LMAction(lm_state=dc.replace(ctx.lm_state, metric=fresh)) + + for scale in (1.0, 2.0): + LevenbergMarquardt(residual, metric=metric0).solve( + jnp.zeros(N), p=make_p(scale), callback=swap, **SOLVE + ) + assert compilations() == 1 + + +def test_a_different_instance_structure_is_a_different_program(): + LevenbergMarquardt(residual, metric=DiagonalMetric(jnp.ones(N, jnp.float32))).solve( + jnp.zeros(N), p=make_p(), **SOLVE + ) + LevenbergMarquardt( + residual, metric=RepeatedFactorMetric(jnp.eye(N, dtype=jnp.float32)) + ).solve(jnp.zeros(N), p=make_p(), **SOLVE) + assert compilations() == 2 diff --git a/tests/test_failed_implicit_ad.py b/tests/test_failed_implicit_ad.py index ab4e475..22e071b 100644 --- a/tests/test_failed_implicit_ad.py +++ b/tests/test_failed_implicit_ad.py @@ -1,3 +1,6 @@ +import dataclasses +from dataclasses import dataclass + import jax import jax.numpy as jnp import pytest @@ -8,33 +11,39 @@ GramCG, IdentityPreconditioner, LevenbergMarquardt, - LMSolveAction, + LMAction, LMStatus, Metric, MultiStart, + register_pytree_dataclass, ) -class AuxWeightedMetric(Metric): - """An iterate-dependent metric: the diagonal weights ride on prepare's - traced state, rebuilt from the live iterate and frozen at the solution - under implicit AD.""" - - size = 1 +@dataclass(frozen=True, eq=False) +class WeightedMetric(Metric): + """A metric whose diagonal weight is a carried leaf: a callback rebuilds + it from the live iterate, and the carried instance is frozen at the + solution under implicit AD.""" - def prepare(self, theta, ctx): - return 1.0 + jnp.sqrt(jnp.abs(theta)) + weight: jax.Array + size: int = 1 + free_scale: float = 1.0 def factor_apply(self, v, ctx): - return jnp.sqrt(ctx.metric_state) * v + return jnp.sqrt(self.weight) * v def factor_solve(self, v, ctx): - return v / jnp.sqrt(ctx.metric_state) + return v / jnp.sqrt(self.weight) def factor_solve_transpose(self, v, ctx): return self.factor_solve(v, ctx) +register_pytree_dataclass( + WeightedMetric, data_fields=("weight", "free_scale"), meta_fields=("size",) +) + + def test_failed_lane_uses_initial_point_under_vmap_jvp_and_vjp(): def residual(x, _, p): return x - p @@ -85,26 +94,33 @@ def solve_one(parameter, atol): assert jnp.allclose(cotangent, jnp.asarray([1.0, 0.0]), atol=1e-6) -def test_invalid_failed_result_uses_initial_point_for_a_prepared_metric(): +def test_invalid_failed_result_uses_initial_instances_for_a_carried_metric(): def residual(x, _, p): root = jnp.sqrt(x) return root - p, {"weight": 1.0 + root} + x0 = jnp.ones(1) solver = LevenbergMarquardt( residual, has_aux=True, - metric=AuxWeightedMetric(), + metric=WeightedMetric(1.0 + jnp.sqrt(jnp.abs(x0))), ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) - x0 = jnp.ones(1) - def invalidate(_): - return LMSolveAction( + def invalidate(ctx): + # Poison BOTH the iterate and the carried metric: the failed-lane + # tangent program must read the pre-loop instances, or the NaN + # weight reaches the whitening and the zero-tangent contract breaks. + return LMAction( stop=True, status=LMStatus.NONFINITE, x=-jnp.ones(1), + lm_state=dataclasses.replace( + ctx.lm_state, + metric=WeightedMetric(jnp.full((1,), jnp.nan)), + ), ) def failed_outputs(p): diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index 0ed59cc..b2916a4 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -191,7 +191,7 @@ def test_float64_multi_start_modes_and_float32_data_under_x64(): import jax.numpy as jnp from nlls_gram import ( - LMSolveAction, + LMAction, LMStatus, MultiStart, LevenbergMarquardt, @@ -214,7 +214,7 @@ def keep_running(_): return jnp.asarray(False), jnp.asarray(LMStatus.RUNNING) stop, status = jax.lax.cond(ctx.step % 2 == 0, check, keep_running, None) - return LMSolveAction(stop=stop, status=status) + return LMAction(stop=stop, status=status) callback_solver = LevenbergMarquardt(residual_fn, init_damping=1e-2) @@ -482,10 +482,10 @@ def test_ridge_continuation_matches_metric_lm_min_seminorm_float64(): from nlls_gram import ( QR, + AnnealRidge, LevenbergMarquardt, RepeatedFactorMetric, RidgeLevenbergMarquardt, - ridge_continuation, ) rng = np.random.default_rng(9) @@ -533,7 +533,8 @@ def residual(theta): # O(ridge) bias against the eps/ridge stationarity resolution -- pushing the # floor lower makes the answer WORSE, not better. gtol must sit well below # ridge times the target selection accuracy. -callback, user_state0 = ridge_continuation(ridge_floor=1e-8, decrease=0.1) +callback = AnnealRidge(ridge_floor=1e-8, decrease=0.1) +user_state0 = callback.init_state() ridge_solver = RidgeLevenbergMarquardt( residual, metric=RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=repeats), @@ -599,14 +600,14 @@ def spd_blocks(key, groups, size): family_free = spd_blocks(keys[1], 1, 2) permutation = jnp.asarray(np.random.default_rng(0).permutation(8)) families = [(family_a, 1.0), (family_free, 0.0)] -preconditioner = BlockEigenPreconditioner(lambda theta, ctx: families, permutation) -state = preconditioner.prepare(jnp.zeros(8), None) -for leaf in jax.tree.leaves(state["families"]): - assert leaf.dtype == jnp.float64, leaf.dtype +preconditioner = BlockEigenPreconditioner(families, permutation) +for leaf in jax.tree.leaves(preconditioner): + assert jnp.issubdtype(leaf.dtype, jnp.integer) or leaf.dtype == jnp.float64, ( + leaf.dtype + ) ridge = 3e-9 ctx = SolverContext( lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), - preconditioner_state=state, ) v = jax.random.normal(keys[2], (8,)) selection = jnp.eye(8)[permutation] @@ -645,12 +646,13 @@ def residual(x, args, p): F_bar = jsp_linalg.block_diag(F, F, jnp.eye(N_F)) J_whitened = jnp.linalg.solve(F_bar.T, A.T).T G = J_whitened.T @ J_whitened -def exact_blocks(theta, ctx): - return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] def exact_preconditioner(): - return BlockEigenPreconditioner(exact_blocks, jnp.arange(P_DIM)) + return BlockEigenPreconditioner( + [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)], + jnp.arange(P_DIM), + ) p_value = {"scale": jnp.asarray(1.0)} diff --git a/tests/test_multi_start.py b/tests/test_multi_start.py index 1388825..7782a7e 100644 --- a/tests/test_multi_start.py +++ b/tests/test_multi_start.py @@ -7,7 +7,7 @@ from nlls_gram import ( SVD, LevenbergMarquardt, - LMSolveAction, + LMAction, LMStatus, MultiStart, ) @@ -321,7 +321,7 @@ def residual(theta, args, p): return jnp.array([theta[0] - args, theta[0] - args - 10.0]) def mutating_callback(ctx): - return LMSolveAction(x=ctx.x + 100.0, args=ctx.args + 1.0) + return LMAction(x=ctx.x + 100.0, args=ctx.args + 1.0) solver = LevenbergMarquardt(residual, init_damping=1.0) x0 = jnp.array([2.0]) @@ -695,7 +695,7 @@ def fresh(_): return {"data": data, "key": carry_key} new_args = jax.lax.cond(ctx.step == 1, fresh, lambda _: ctx.args, None) - return LMSolveAction(args=new_args) + return LMAction(args=new_args) solver = LevenbergMarquardt(residual, init_damping=1e-2, ad_solver=SVD()) args0 = {"data": jnp.array([1.0, -2.0, 0.5]), "key": jax.random.key(22)} diff --git a/tests/test_ridge_lm.py b/tests/test_ridge_lm.py index b86822a..1062b82 100644 --- a/tests/test_ridge_lm.py +++ b/tests/test_ridge_lm.py @@ -20,6 +20,7 @@ QRCache, RepeatedFactorMetric, RidgeLevenbergMarquardt, + register_pytree_dataclass, ) # Analytic linear-Gaussian testbed: r(theta) = A theta - b with m < p, the @@ -455,6 +456,8 @@ def apply(self, v, damping, ctx): seen.append(ctx is not None and ctx.lm_state is not None) return v / (self.scale + damping) + register_pytree_dataclass(JacobiPreconditioner, data_fields=("scale",)) + scale = jnp.asarray(RNG.uniform(0.5, 2.0, size=P_DIM), dtype=jnp.float32) preconditioned = build( "normal_cg", ridge=1e-3, preconditioner=JacobiPreconditioner(scale) diff --git a/tests/test_ridge_metrics.py b/tests/test_ridge_metrics.py index 78d4b0d..1c0166f 100644 --- a/tests/test_ridge_metrics.py +++ b/tests/test_ridge_metrics.py @@ -9,6 +9,7 @@ RepeatedFactorMetric, RidgeLevenbergMarquardt, SolverContext, + register_pytree_dataclass, ) REPEATS = 3 @@ -119,6 +120,8 @@ def factor_apply(self, v, ctx): factor_solve = factor_apply factor_solve_transpose = factor_apply + register_pytree_dataclass(Probe, data_fields=("free_scale",), meta_fields=("size",)) + A = jnp.asarray(np.random.default_rng(0).normal(size=(2, 4)), jnp.float32) def residual(theta): diff --git a/tests/test_ridge_preconditioners.py b/tests/test_ridge_preconditioners.py index 8746223..ff38c20 100644 --- a/tests/test_ridge_preconditioners.py +++ b/tests/test_ridge_preconditioners.py @@ -1,5 +1,7 @@ # Float32 coverage for BlockEigenPreconditioner. The float64 primary coverage # lives in test_float64_subprocess.py, matching the production default. +import dataclasses + import jax import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg @@ -10,12 +12,12 @@ CG, BlockEigenPreconditioner, Cholesky, + LMAction, LMState, LMStatus, RepeatedFactorMetric, RidgeLevenbergMarquardt, SolverContext, - block_eigen_state, ) @@ -41,10 +43,9 @@ def test_apply_matches_dense_inverse(damping): ridge_mask = jnp.concatenate([jnp.ones(10), jnp.zeros(2)]) ridge = 0.05 - preconditioner = BlockEigenPreconditioner(lambda theta, ctx: families, permutation) + preconditioner = BlockEigenPreconditioner(families, permutation) ctx = SolverContext( - lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)), - preconditioner_state=preconditioner.prepare(jnp.zeros(12), None), + lm_state=LMState(damping=jnp.asarray(1e-3), ridge=jnp.asarray(ridge)) ) v = jax.random.normal(jax.random.key(1), (12,)) @@ -56,13 +57,13 @@ def test_apply_matches_dense_inverse(damping): np.testing.assert_allclose(result, expected, rtol=2e-4, atol=2e-5) -def test_block_eigen_state_rejects_mismatched_layouts(): +def test_constructor_rejects_mismatched_layouts(): with pytest.raises(ValueError, match="permutation"): - block_eigen_state([(jnp.eye(2)[None], 1.0)], jnp.zeros(2)) + BlockEigenPreconditioner([(jnp.eye(2)[None], 1.0)], jnp.zeros(2)) with pytest.raises(ValueError, match="groups, size, size"): - block_eigen_state([(jnp.eye(2), 1.0)], jnp.arange(2)) + BlockEigenPreconditioner([(jnp.eye(2), 1.0)], jnp.arange(2)) with pytest.raises(ValueError, match="cover"): - block_eigen_state([(jnp.eye(2)[None], 1.0)], jnp.arange(3)) + BlockEigenPreconditioner([(jnp.eye(2)[None], 1.0)], jnp.arange(3)) REPEATS = 2 @@ -94,13 +95,20 @@ def residual(x, args, p): def exact_preconditioner(G): # The exact whitened normal blocks -- one metric-block group, one free - # group -- so CG converges in a handful of iterations. The residual is - # linear, so the operator does not move with the iterate and blocks_fn - # ignores theta. - def blocks_fn(theta, ctx): - return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] + # group -- so CG converges in a handful of iterations. + return BlockEigenPreconditioner( + [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)], + jnp.arange(P_DIM), + ) - return BlockEigenPreconditioner(blocks_fn, jnp.arange(P_DIM)) + +def scrambled_preconditioner(): + # Same treedef as the exact one (one group of N_M, one of N_F), useless + # values: a plain diagonal that ignores the whitened operator's structure. + return BlockEigenPreconditioner( + [(100.0 * jnp.eye(N_M)[None], 1.0), (100.0 * jnp.eye(N_F)[None], 0.0)], + jnp.arange(P_DIM), + ) def cholesky_reference(metric, residual): @@ -136,45 +144,54 @@ def test_cg_solve_matches_cholesky(): np.testing.assert_allclose(result.x, reference.x, rtol=2e-3, atol=2e-4) -def test_prepared_state_is_rebuilt_from_the_live_iterate(): - # blocks_fn sees the whitened iterate: a counter proves prepare runs - # inside the loop, and the carried state tracks it. +def test_callback_refresh_reaches_the_next_inner_solve(): + # A callback-constructed instance replaces the carried one and drives the + # very next CG solve: with a starved inner budget, a scrambled + # preconditioner cannot reach gtol within the step cap, while refreshing + # to the exact one at step 1 converges almost as fast as exact-from-start + # -- and the swap is not a problem change, so convergence fires normally. metric, residual, G = build_problem() - seen = [] - - def blocks_fn(theta, ctx): - seen.append(theta) - return [(G[:N_M, :N_M][None], 1.0), (G[N_M:, N_M:][None], 0.0)] - - solver = RidgeLevenbergMarquardt( - residual, - metric=metric, - ridge=RIDGE, - linear_solver=CG( - BlockEigenPreconditioner(blocks_fn, jnp.arange(P_DIM)), - tol=1e-7, - maxiter=200, - ), - ) + p = {"scale": jnp.asarray(1.0)} x0 = jnp.zeros(P_DIM) - state = solver.init(x0, {"data": jnp.asarray(1.0)}, p={"scale": jnp.asarray(1.0)}) - # init builds the state at x0 and marks it valid there. - assert state.precond is not None - assert bool(state.precond_valid) - assert len(seen) == 1 - x1, state1, info = solver.update( - x0, state, {"data": jnp.asarray(1.0)}, {"scale": jnp.asarray(1.0)} + + def build(callback=None): + solver = RidgeLevenbergMarquardt( + residual, + metric=metric, + ridge=RIDGE, + linear_solver=CG(scrambled_preconditioner(), tol=0.0, maxiter=3), + ) + return solver.solve(x0, p=p, max_steps=60, gtol=1e-5, callback=callback) + + def refresh(ctx): + fresh = jax.lax.cond( + ctx.step == 1, + lambda: exact_preconditioner(G), + lambda: ctx.lm_state.preconditioner, + ) + return LMAction( + lm_state=dataclasses.replace(ctx.lm_state, preconditioner=fresh) + ) + + stale = build() + refreshed = build(refresh) + assert int(stale.status) == int(LMStatus.MAX_STEPS) + assert int(refreshed.status) == int(LMStatus.CONVERGED) + assert int(refreshed.steps) <= 12 + # The carried instance in the result is the refreshed one. + np.testing.assert_allclose( + refreshed.lm_state.preconditioner.eigenvalues[0], + exact_preconditioner(G).eigenvalues[0], + rtol=1e-6, ) - # An accepted step moved x, so the carried state is marked for rebuild. - assert bool(info.accepted) - assert not bool(state1.precond_valid) -@pytest.mark.parametrize("explicit_ad_solver", [True, False]) -def test_ad_tangent_matches_cholesky(explicit_ad_solver): +@pytest.mark.parametrize("ad_mode", ["explicit", "inherit", "inherit_knobs"]) +def test_ad_tangent_matches_cholesky(ad_mode): # The zero-damping AD role applies the same typed preconditioner. With - # ad_solver=None the forward config's preconditioner is inherited, at the - # AD-default tolerance and budget. + # ad_solver=None the forward CARRIED instance is inherited at the + # AD-default tolerance and budget; CG(None, ...) inherits it while + # pinning the knobs. metric, residual, G = build_problem() p = {"scale": jnp.asarray(1.0)} p_dot = {"scale": jnp.asarray(1.0)} @@ -188,17 +205,21 @@ def run(p_value): return jax.jvp(run, (p,), (p_dot,))[1] forward = CG(exact_preconditioner(G), tol=1e-7, maxiter=200) - ad_solver = ( - CG(exact_preconditioner(G), tol=1e-7, maxiter=200) - if explicit_ad_solver - else None - ) + ad_solver = { + "explicit": CG(exact_preconditioner(G), tol=1e-7, maxiter=200), + "inherit": None, + "inherit_knobs": CG(None, tol=1e-7, maxiter=200), + }[ad_mode] cg_solver = RidgeLevenbergMarquardt( residual, metric=metric, ridge=RIDGE, linear_solver=forward, ad_solver=ad_solver ) - if not explicit_ad_solver: - assert cg_solver.ad_solver_preconditioner is forward.preconditioner + if ad_mode == "inherit": + assert cg_solver._ad_preconditioner_source == "carried" assert cg_solver.ad_solver_tol is None + if ad_mode == "inherit_knobs": + assert cg_solver._ad_preconditioner_source == "carried" + assert cg_solver.ad_solver_tol == 1e-7 + assert cg_solver.ad_solver_maxiter == 200 reference = solved_x(cholesky_reference(metric, residual)) np.testing.assert_allclose(solved_x(cg_solver), reference, rtol=1e-3, atol=1e-4) diff --git a/tests/test_ridge_solve_features.py b/tests/test_ridge_solve_features.py index 2452494..abd2cee 100644 --- a/tests/test_ridge_solve_features.py +++ b/tests/test_ridge_solve_features.py @@ -7,14 +7,15 @@ from nlls_gram import ( CG, + AnnealRidge, IdentityMetric, IdentityPreconditioner, - LMSolveAction, + LMAction, LMStatus, MultiStart, RepeatedFactorMetric, RidgeLevenbergMarquardt, - ridge_continuation, + register_pytree_dataclass, ) CG_CONFIG = CG(IdentityPreconditioner(), maxiter=40) @@ -59,7 +60,8 @@ def test_ridge_continuation_beats_any_single_moderate_ridge(): fixed_result = fixed.solve(jnp.zeros(P_DIM), max_steps=300, gtol=1e-5) fixed_error = np.linalg.norm(np.asarray(fixed_result.x) - x_dagger) - callback, user_state0 = ridge_continuation(ridge_floor=1e-6, decrease=0.1) + callback = AnnealRidge(ridge_floor=1e-6, decrease=0.1) + user_state0 = callback.init_state() solver = RidgeLevenbergMarquardt(linear_residual, metric=make_metric(), ridge=1e-2) result = solver.solve( jnp.zeros(P_DIM), @@ -82,7 +84,7 @@ def test_callback_ridge_change_suppresses_convergence(): # hand-rolled callback assigning a weak-typed Python float must not # change the while_loop carry aval (the solver recasts it). def always_shrink(ctx): - return LMSolveAction( + return LMAction( lm_state=dataclasses.replace(ctx.lm_state, ridge=ctx.lm_state.ridge * 0.5) ) @@ -97,7 +99,7 @@ def always_shrink(ctx): assert int(plain.status) == int(LMStatus.CONVERGED) def clumsy(ctx): - return LMSolveAction(lm_state=dataclasses.replace(ctx.lm_state, ridge=5e-3)) + return LMAction(lm_state=dataclasses.replace(ctx.lm_state, ridge=5e-3)) result = solver.solve(jnp.zeros(P_DIM), max_steps=50, gtol=1e-4, callback=clumsy) assert result.lm_state.ridge.dtype == jnp.float32 @@ -191,7 +193,8 @@ def test_has_aux(): def test_jit_false_parity(): - callback, user_state0 = ridge_continuation(ridge_floor=1e-5, decrease=0.1) + callback = AnnealRidge(ridge_floor=1e-5, decrease=0.1) + user_state0 = callback.init_state() results = {} for jit in (True, False): solver = RidgeLevenbergMarquardt( @@ -266,6 +269,9 @@ def build(): linear_solver=CG(IdentityPreconditioner(), maxiter=40), ) assert a == rebuilt_config + # Metrics key by pytree STRUCTURE: a rebuilt equal-config metric (fresh + # arrays, same statics) shares the compile, and its values flow through + # the carried state rather than being baked in. rebuilt_metric = RidgeLevenbergMarquardt( residual, metric=make_metric(), @@ -273,7 +279,16 @@ def build(): cache_jacobian=False, linear_solver=CG_CONFIG, ) - assert a != rebuilt_metric + assert a == rebuilt_metric + assert hash(a) == hash(rebuilt_metric) + different_structure = RidgeLevenbergMarquardt( + residual, + metric=IdentityMetric(P_DIM), + ridge=1e-3, + cache_jacobian=False, + linear_solver=CG_CONFIG, + ) + assert a != different_structure def test_traced_changes_do_not_retrace_the_loop(): @@ -306,7 +321,8 @@ def residual(theta): # The continuation callback (a NEW problem: callback identity keys the # compile) traces once, then repeat solves with the same callback reuse # the compiled loop. - callback, us0 = ridge_continuation(ridge_floor=1e-6, decrease=0.1) + callback = AnnealRidge(ridge_floor=1e-6, decrease=0.1) + us0 = callback.init_state() solver.solve(x0, max_steps=60, gtol=1e-4, callback=callback, user_state=us0) with_callback = traces["count"] solver.solve(x0, max_steps=60, gtol=1e-4, callback=callback, user_state=us0) @@ -328,6 +344,10 @@ def factor_solve_transpose(self, v, ctx): jax.debug.callback(lambda: counters.append(1), ordered=True) return v + register_pytree_dataclass( + CountingMetric, data_fields=("free_scale",), meta_fields=("size",) + ) + def residual(theta): # Nonlinear scalar tail engineered so the near-Newton step from a # small residual overshoots and gets rejected at tiny damping. From cb1213146cf12ed588de2fd4050bf9ef5f7cd08f Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 10:23:34 -0700 Subject: [PATCH 14/22] test+docs: pin the carried-instance contract; rewrite adaptation docs New pins: same-treedef different-valued instances give different answers under the shared compile; callback swaps neither recompile nor (for preconditioners) invalidate; ridge metric swaps suppress that step's convergence while metric-solver swaps do not; the untouched-instance identity short-circuit emits no comparison ops; GramCG equation-space preconditioning with a mid-solve refresh plus a CG-budget schedule; the implicit tangent uses the carried metric at the solution. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- README.md | 6 +- benchmarks/test_implicit_ad_benchmark.py | 56 ++- docs/api.md | 9 +- docs/callbacks.md | 77 +++- docs/design/pytree_state.md | 511 ----------------------- docs/implicit_ad.md | 16 +- docs/index.md | 6 +- docs/metrics.md | 69 +-- docs/ridge_lm.md | 115 +++-- docs/tuning_guide.md | 14 +- tests/test_instance_state.py | 268 ++++++++++++ 11 files changed, 499 insertions(+), 648 deletions(-) delete mode 100644 docs/design/pytree_state.md create mode 100644 tests/test_instance_state.py diff --git a/README.md b/README.md index a99b023..f0c38aa 100644 --- a/README.md +++ b/README.md @@ -44,7 +44,7 @@ uv add nlls-gram "jax[cuda13]" ```python import jax.numpy as jnp -from nlls_gram import RidgeLevenbergMarquardt, RepeatedFactorMetric, ridge_continuation +from nlls_gram import AnnealRidge, RidgeLevenbergMarquardt, RepeatedFactorMetric # W = blockdiag(K, K): the RKHS seminorm over two coefficient blocks. The # constructor takes the FACTOR; shift a semidefinite K by epsilon*I first. @@ -53,8 +53,8 @@ metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=2) solver = RidgeLevenbergMarquardt(collocation_residual, metric=metric, ridge=1e-4) # Anneal the ridge toward the interpolating limit on stationarity. -callback, user_state = ridge_continuation(ridge_floor=1e-10) -result = solver.solve(x0, callback=callback, user_state=user_state, +anneal = AnnealRidge(ridge_floor=1e-10) +result = solver.solve(x0, callback=anneal, user_state=anneal.init_state(), gtol=1e-8, atol=1e-8) ``` diff --git a/benchmarks/test_implicit_ad_benchmark.py b/benchmarks/test_implicit_ad_benchmark.py index e6dd3e1..e5e4cd0 100644 --- a/benchmarks/test_implicit_ad_benchmark.py +++ b/benchmarks/test_implicit_ad_benchmark.py @@ -1,5 +1,8 @@ """Opt-in successful-solve implicit-AD benchmarks.""" +import dataclasses +from dataclasses import dataclass + import jax import jax.numpy as jnp import pytest @@ -7,8 +10,10 @@ from nlls_gram import ( SVD, LevenbergMarquardt, + LMAction, LMStatus, Metric, + register_pytree_dataclass, ) @@ -40,47 +45,66 @@ def status(parameter): return solve, p, status -class PreparedDiagonalMetric(Metric): - """An iterate-dependent metric: the weights come from prepare(), so the - solver rebuilds them per accepted step and freezes them at the solution.""" +@dataclass(frozen=True, eq=False) +class TrackedDiagonalMetric(Metric): + """An iterate-tracking metric: the weights are a carried leaf, rebuilt + from the live iterate by the solve callback and frozen at the solution.""" - size = 8 + weights: jax.Array + size: int = 8 + free_scale: float = 1.0 - def prepare(self, theta, ctx): - return 1.0 + 0.1 * theta**2 + def _scaled(self, v, factor): + return v * factor.reshape(factor.shape + (1,) * (v.ndim - 1)) def factor_apply(self, v, ctx): - return jnp.sqrt(ctx.metric_state) * v + return self._scaled(v, jnp.sqrt(self.weights)) def factor_solve(self, v, ctx): - return v / jnp.sqrt(ctx.metric_state) + return self._scaled(v, 1.0 / jnp.sqrt(self.weights)) def factor_solve_transpose(self, v, ctx): return self.factor_solve(v, ctx) -def _prepared_metric_problem(): +register_pytree_dataclass( + TrackedDiagonalMetric, data_fields=("weights", "free_scale"), meta_fields=("size",) +) + + +def _tracked_metric_problem(): design = jnp.reshape(jnp.linspace(-0.8, 1.0, 32), (4, 8)) def residual(x, _, p): return design @ x - p, {"weight": 1.0 + 0.1 * x**2} + x0 = jnp.zeros(8) solver = LevenbergMarquardt( residual, has_aux=True, - metric=PreparedDiagonalMetric(), + metric=TrackedDiagonalMetric(1.0 + 0.1 * x0**2), ad_solver=SVD(), cache_jacobian=False, geodesic_acceleration=False, ) - x0 = jnp.zeros(8) p = jnp.linspace(-0.2, 0.3, 4) + def track_iterate(ctx): + return LMAction( + lm_state=dataclasses.replace( + ctx.lm_state, metric=TrackedDiagonalMetric(1.0 + 0.1 * ctx.x**2) + ) + ) + def solve(parameter): - return solver.solve(x0, p=parameter, max_steps=48, atol=1e-6).x + return solver.solve( + x0, p=parameter, max_steps=48, atol=1e-6, callback=track_iterate + ).x def status(parameter): - return solver.solve(x0, p=parameter, max_steps=48, atol=1e-6).status + return solver.solve( + x0, p=parameter, max_steps=48, atol=1e-6, callback=track_iterate + ).status return solve, p, status @@ -117,8 +141,8 @@ def _make_problem(case): return _direct_problem(has_aux=False) if case == "direct_aux": return _direct_problem(has_aux=True) - if case == "prepared_metric": - return _prepared_metric_problem() + if case == "tracked_metric": + return _tracked_metric_problem() return _vmapped_problem() @@ -143,7 +167,7 @@ def transformed(parameter): return transformed, p -@pytest.mark.parametrize("case", ["direct", "direct_aux", "prepared_metric", "vmapped"]) +@pytest.mark.parametrize("case", ["direct", "direct_aux", "tracked_metric", "vmapped"]) @pytest.mark.parametrize("transform", ["jvp", "vjp"]) def test_successful_implicit_ad(benchmark, case, transform): _, status_parameter, status = _make_problem(case) diff --git a/docs/api.md b/docs/api.md index c752240..518c200 100644 --- a/docs/api.md +++ b/docs/api.md @@ -4,8 +4,7 @@ ::: nlls_gram.RidgeLevenbergMarquardt ::: nlls_gram.LevenbergMarquardt -::: nlls_gram.RidgeContinuation -::: nlls_gram.ridge_continuation +::: nlls_gram.AnnealRidge ## Linear solvers @@ -28,7 +27,6 @@ ::: nlls_gram.Preconditioner ::: nlls_gram.IdentityPreconditioner ::: nlls_gram.BlockEigenPreconditioner -::: nlls_gram.block_eigen_state ::: nlls_gram.NystromPreconditioner ::: nlls_gram.ShermanMorrisonPreconditioner ::: nlls_gram.WoodburyPreconditioner @@ -40,10 +38,11 @@ ::: nlls_gram.LMInfo ::: nlls_gram.LMStatus ::: nlls_gram.LMHyperparams -::: nlls_gram.LMSolveContext -::: nlls_gram.LMSolveAction +::: nlls_gram.LMContext +::: nlls_gram.LMAction ::: nlls_gram.LMSolveResult ::: nlls_gram.SolverContext +::: nlls_gram.register_pytree_dataclass ## Multi-start diff --git a/docs/callbacks.md b/docs/callbacks.md index 2d4586b..d77f936 100644 --- a/docs/callbacks.md +++ b/docs/callbacks.md @@ -59,7 +59,7 @@ Status codes are integer constants: | `LMStatus.CALLBACK_STOP` | A callback stopped without a custom status. | | `LMStatus.RUNNING` | Internal running state, not a final successful status. | -Callbacks receive an `LMSolveContext`: +Callbacks receive an `LMContext`: | Field | Meaning | | --- | --- | @@ -69,7 +69,7 @@ Callbacks receive an `LMSolveContext`: | `initial_lm_state` | State supplied to `solve` or created by `init`. | | `args`, `p`, `user_state` | Current auxiliary data, read-only external data, and user state. | -A callback returns `None` or `LMSolveAction(...)`. Omitted action fields are left +A callback returns `None` or `LMAction(...)`. Omitted action fields are left unchanged. The callback may set `stop`, `status`, `x`, `lm_state`, `args`, or `user_state`; it cannot replace `p`. When an action changes the values of `x` or `args`, that step's tolerance checks are skipped — the diagnostics describe @@ -94,7 +94,7 @@ any of them mid-solve — exactly like a damping reset: new_hyper = dataclasses.replace( ctx.lm_state.hyper, iterative_maxiter=jnp.asarray(40, jnp.int32) ) -return LMSolveAction(lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper)) +return LMAction(lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper)) ``` Two contracts: knobs constructed as `None` (uncapped `max_damping`, @@ -102,7 +102,7 @@ backend-default `iterative_maxiter`) are compiled out and stay `None` — a callback cannot turn them on; and replacement values must be arrays of the same dtype (use `jnp.asarray`/`jnp.where`), since they live in the jitted loop carry. Static configuration — `linear_solver`, `geodesic_acceleration`, `cache_jacobian`, -`has_aux`, the metric — shapes the compiled program and stays on the solver. +`has_aux` — shapes the compiled program and stays on the solver. `init()` leaves `hyper=None`, which falls back to the constructor values and compiles to the same program with no extra per-call buffers — manual `update()` loops pay nothing. To schedule hyperparameters in a manual loop, @@ -111,6 +111,52 @@ When chaining solves, a warm-started `lm_state` carries the *first* solver's hyperparameters; pass `dataclasses.replace(lm_state, hyper=None)` to re-derive them from the second solver's constructor. +### Adapting the metric and preconditioner + +The metric and preconditioner instances ride in `lm_state.metric` and +`lm_state.preconditioner`, so a callback adapts either by **constructing a +new instance** — same type, same static fields, same leaf shapes and dtypes +(a mismatch raises at trace time, naming the field). Construction is pure +traced ops and never recompiles the loop. Gate an expensive rebuild +(`BlockEigenPreconditioner`'s eigendecomposition, a `Nystrom` sketch) with +`jax.lax.cond`, so it is paid only when the condition fires — a `jnp.where` +merge over an unconditional rebuild pays it every step: + +```python +def refresh(ctx): + precond = jax.lax.cond( + ctx.step % 32 == 0, + lambda: BlockEigenPreconditioner(build_families(ctx.x), PERMUTATION), + lambda: ctx.lm_state.preconditioner, + ) + return LMAction(lm_state=dataclasses.replace(ctx.lm_state, preconditioner=precond)) +``` + +What the solver does with a change: + +- a **preconditioner** refresh is free: staleness only moves the CG + iteration path, so nothing is invalidated and convergence tests run + normally; +- a **metric** change stales the whitened solver caches (never the Jacobian + cache — \(J = \partial r/\partial x\) does not see the metric). For + `RidgeLevenbergMarquardt` it is additionally a **problem change** — the + metric defines the objective — so that step's convergence test is + suppressed, exactly like a ridge change. A consequence worth knowing: a + metric rebuilt on *every* accepted step suppresses convergence on every + accepted step, so `xtol` (accepted-only) can never fire — rebuild + conditionally, or stop via `gtol`/`atol`. `LevenbergMarquardt`'s metric is + damping geometry only (\(\|r\|^2\) did not move), so no suppression there. +- detection is **by value** with a trace-time identity short-circuit: an + action built with `dataclasses.replace(ctx.lm_state, ...)` that passes the + instances through untouched costs no comparison ops at all. + +A callback that replaces `x` or `args` and uses a metric built from them +must rebuild the metric **in the same action**. Under multi-start, drawn +lanes inherit the caller's initial instances, so a lane's first step runs +under the initial metric and the callback corrects it from step two. +Under implicit AD the carried instances at the returned solution are frozen +conditioning data — see [Implicit AD](implicit_ad.md). + Under `jit=True`, callbacks must be JAX-traceable and return the same pytree structure on every iteration. Use `jnp.where` or `jax.lax.cond` for data-dependent choices rather than Python `if` statements over arrays. @@ -121,14 +167,14 @@ residual-norm threshold: ```python import jax.numpy as jnp -from nlls_gram import LMSolveAction, LMStatus +from nlls_gram import LMAction, LMStatus def stopping_callback(ctx): nonfinite = ~jnp.isfinite(ctx.info.loss_candidate) converged = jnp.sqrt(ctx.info.loss) < 1e-8 status = jnp.where(nonfinite, LMStatus.NONFINITE, LMStatus.CONVERGED) - return LMSolveAction(stop=nonfinite | converged, status=status) + return LMAction(stop=nonfinite | converged, status=status) result = solver.solve( @@ -277,7 +323,7 @@ divergence: ```python def divergence_callback(ctx): nonfinite = ~jnp.isfinite(ctx.info.loss_candidate) - return LMSolveAction(stop=nonfinite, status=LMStatus.NONFINITE) + return LMAction(stop=nonfinite, status=LMStatus.NONFINITE) ``` ### Epoch Resampling and Damping Reset @@ -304,7 +350,7 @@ def epoch_callback(ctx): damping=jnp.where(boundary, ctx.initial_lm_state.damping, ctx.lm_state.damping), ) new_key = jnp.where(boundary, key, ctx.user_state) - return LMSolveAction(args=new_args, lm_state=new_lm_state, user_state=new_key) + return LMAction(args=new_args, lm_state=new_lm_state, user_state=new_key) result = solver.solve( @@ -318,9 +364,10 @@ result = solver.solve( (`dataclasses` here is the standard-library module.) This recipe composes with `cache_jacobian=True` without extra care: any action that changes the -values of `x` or `args` invalidates the Jacobian cache automatically — and -likewise the `metric_factory` prepared state, which is rebuilt at the new -point on the next update. +values of `x` or `args` invalidates the Jacobian cache automatically. A +metric built from `x` or `args` is the callback's own responsibility — +rebuild it in the same action (see "Adapting the metric and preconditioner" +above). ### Scheduled Inner-Solve Accuracy @@ -343,7 +390,7 @@ def grow_budget(ctx): ctx.lm_state.hyper.iterative_maxiter, ) new_hyper = dataclasses.replace(ctx.lm_state.hyper, iterative_maxiter=new_maxiter) - return LMSolveAction(lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper)) + return LMAction(lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper)) result = solver.solve(x0, args, max_steps=200, atol=1e-8, callback=grow_budget) @@ -365,7 +412,7 @@ their thresholds: def validation_callback(ctx): val_residual = validation_residual_fn(ctx.x, val_data) val_mse = jnp.mean(val_residual**2) - return LMSolveAction(stop=val_mse < val_threshold) + return LMAction(stop=val_mse < val_threshold) ``` Evaluating validation metrics every step costs a residual pass per step; gate @@ -400,7 +447,7 @@ def time_limit_callback(ctx): ctx.user_state, # (start_time, budget_seconds) ctx.step, # loop-varying arg so the call cannot be hoisted ) - return LMSolveAction(stop=timed_out, status=TIME_LIMIT_STATUS) + return LMAction(stop=timed_out, status=TIME_LIMIT_STATUS) result = solver.solve( @@ -447,7 +494,7 @@ def history_callback(ctx): ctx.user_state["damping"], ctx.info.damping[None], (ctx.step - 1,) ), } - return LMSolveAction(user_state=history) + return LMAction(user_state=history) result = solver.solve( diff --git a/docs/design/pytree_state.md b/docs/design/pytree_state.md deleted file mode 100644 index 51ba935..0000000 --- a/docs/design/pytree_state.md +++ /dev/null @@ -1,511 +0,0 @@ -# Pytree metric/preconditioner state and caller-owned adaptation - -Design proposal for review. Branch `refactor/unify-solver-contracts`, version -stays 2.7.0. Breaking changes are free: all callers are our own repos -(`kernels`, `spooky`), ported in the same effort. No shims, no deprecations. -Revision 2, incorporating the first external review. - -## Problem - -The current contract conflates three things: - -1. **Construction** — how metric/preconditioner numeric state is built - (`prepare(theta, ctx)` on each class, plus the `block_eigen_state` free - function, plus `blocks_fn` closure fields). -2. **Refresh policy** — when it is rebuilt (`rebuild(ctx)` predicates, - `metric_valid`/`precond_valid` reject-reuse flags, the subclass-override - idiom for "rebuild on ridge advance"). -3. **Hashing** — instances hold arrays and closures, so they identity-hash - into the solver's static key, and a rebuilt equal-config instance keys a - fresh compilation of the whole solve loop. - -Symptoms: the kernels driver threads preconditioner state through `args` with -~25 lines of callback plumbing; `rebuild` receives a context without the -carried state it would need to decide; four `LMState` fields and three -`lm_core` methods exist only to shepherd hook state around. - -## Design - -### Instances are pytrees - -Every concrete `Metric` and `Preconditioner` class is registered as a JAX -pytree: array fields are traced leaves, the type plus its static fields are -structure. Instances ride **inside `LMState`** (`lm_state.metric`, -`lm_state.preconditioner`) as nested carried state, so their arrays flow -through the jitted loop, `vmap`, and the implicit-AD rule like any other -state. - -**Rebuild = call the constructor again.** There is no `prepare`, no -`rebuild`, no `remake`. A callback that wants a fresh preconditioner -constructs a new instance of the same type inside the traced callback — pure -traced ops, same treedef, no recompilation. A different type or field -structure is a loud trace-time error. Constructors must canonicalize their -leaf dtypes (`jnp.asarray(..., dtype)`), so a rebuilt instance's leaf avals -match the carried ones inside the user's `lax.cond`. - -`dataclasses.replace` semantics: fine for **metrics** (their `__post_init__` -is validation plus shape derivation, cheap under trace); **preconditioners -are rebuilt by constructor, never `replace`d** — `replace` re-runs -`__init__`, which re-pays the eigendecomposition/sketch, and the -construction-time-only inputs below are not stored to re-supply. Documented -on the base classes. - -### Registration helper (public) - -`jax.tree_util.register_dataclass` unflattens by calling the constructor, -which re-runs `__post_init__` (re-`eigh`, tracer-hostile validation) on -every carry reconstruction — verified against the installed JAX. So the -package ships its own ~20-line helper in `utilities.py`, exported as public -API: - -```python -def register_pytree_dataclass(cls, *, data_fields, meta_fields=()): - """Register a frozen dataclass as a pytree whose unflatten BYPASSES - __init__/__post_init__ (object.__new__ + object.__setattr__). - data_fields are traced leaves; meta_fields are static structure and - must be hashable. Returns cls.""" -``` - -Consequences: - -- Constructors freely compute derived leaves once (`eigh` in - `BlockEigenPreconditioner`, the sketch in `NystromPreconditioner`) and - validate eagerly; unflatten restores fields verbatim. -- Aux data is the tuple of static field values passed through the existing - `_typed_key` type-tagging, so treedefs hash and compare **by value with - jit's strict-type semantics**: two equal-config instances with fresh - arrays have equal treedefs, while `1`, `1.0`, and `True` in a static - field stay distinct (raw tuples would collapse them). -- The helper validates that every dataclass field appears exactly once in - `data_fields` or `meta_fields`, so a forgotten field is a registration - error rather than a silently dropped leaf. -- `tree_map` over an instance rebuilds it without re-running the - constructor, so a transform that changes leaf shapes or breaks a derived - invariant (`permutation` without `inverse_permutation`) produces an - inconsistent instance. Documented: shape-changing or invariant-coupled - mutation goes through the constructor; `tree_map` is for - transform-machinery (vmap batching, tangent zeroing), which preserves - both. -- Each concrete class registers itself (subclassing a registered base does - not register the subclass); the custom-metric and custom-preconditioner - doc recipes lead with the registration call. The solver raises a clear - error at construction when handed an unregistered instance (one that - flattens as a leaf), pointing at the helper. -- `_EuclideanMetric` — the `metric=None` default — is registered too (a - frozen dataclass with no leaves), so the default path passes the same - check. - -Static/leaf split for the shipped classes (construction-time-only inputs are -`dataclasses.InitVar`s — consumed by `__post_init__`, never stored): - -| class | leaves (traced) | static (structure) | InitVar (consumed) | -|---|---|---|---| -| `IdentityMetric` | `free_scale` | `size` | | -| `CholeskyMetric` | `L`, `free_scale` | `size` | | -| `DiagonalMetric` | `weights`, `free_scale` | `size` | | -| `RepeatedFactorMetric` | `F`, `free_scale` | `repeats`, `size` | | -| `IdentityPreconditioner` | — | — | | -| `BlockEigenPreconditioner` | per-family eigenvectors/eigenvalues/ridge_weight, `permutation`, `inverse_permutation` | family count (structure; array shapes live in the leaf avals) | `families` | -| `ShermanMorrisonPreconditioner` | `u`, `weight`, `solve_u`, `denominator` | `solve` | | -| `WoodburyPreconditioner` | `U`, `weights`, `solve_U`, `capacitance_factor` (array only — `cho_factor`'s `lower` bool is passed as a literal in `apply`, never stored as a leaf) | `solve` | | -| `PaddedPreconditioner` | `base` (subtree) | `n_real` | | -| `NystromPreconditioner` | `basis`, `eigenvalues` | `n`, `rank` | `matvec`, `key`, `dtype` | - -`ShermanMorrison`/`Woodbury` call `solve` on **every** `apply` (it is the -action of `A^{-1}`), so it cannot be consumed at construction; it is a -**static field**: a fixed hashable callable whose identity enters the -treedef, and whose closed-over arrays are compile-time constants. These two -classes are setup-scope objects for fixed dual operators, not -callback-refresh targets; rebuilding with the *same* `solve` callable keeps -the treedef. `NystromPreconditioner.matvec` genuinely is construction-only -(its `apply` uses only the stored sketch) and stays an `InitVar`. -`experimental.StateSpaceMetric` gets the same deliberate split when it is -registered: `transition` is construction-only, `parallel` static (its ops -branch on it in Python). - -`free_scale` is a **leaf**: changing it must not recompile. (`_free_scale` -loses its `scale == 1.0` Python short-circuit — a tracer breaks it — and -always divides.) Constructors canonicalize it to a strongly-typed scalar of -the factor's float dtype (default float when the metric holds no arrays), -so an initial Python `1.0` and a callback-rebuilt value have identical -avals. Validation of possibly-traced fields follows the existing -convention: concrete values are validated eagerly, tracers/arrays skip the -sign checks. - -`BlockEigenPreconditioner` drops `blocks_fn` entirely: - -```python -BlockEigenPreconditioner(families, permutation) -# families: sequence of (blocks, ridge_weight) pairs, blocks shaped -# (groups, size, size) — the constructor symmetrizes, eigendecomposes, -# and stores the results as leaves (absorbing today's block_eigen_state, -# which is deleted). -``` - -### Contracts shrink - -```python -class Metric: - size: int # static - free_scale # leaf - def factor_apply(self, v, ctx): ... - def factor_solve(self, v, ctx): ... - def factor_solve_transpose(self, v, ctx): ... - def norm(self, v, ctx): ... # defaulted via factor_apply - -class Preconditioner: - requires_positive_damping = False - def apply(self, v, damping, ctx): ... -``` - -Ops read `self` — the carried instance. Deleted: `Metric.prepare`, -`Metric.rebuild`, `Preconditioner.prepare`, `Preconditioner.rebuild`, -`block_eigen_state`, `SolverContext.metric_state`, -`SolverContext.preconditioner_state`, `LMState.metric_state`, -`LMState.metric_valid`, `LMState.precond`, `LMState.precond_valid`, -`lm_core`'s `_init_hook_state`/`_hook_state`/`_frozen_ctx`, and the -duplicate `_block_sizes` definition in `lm_core.py`. - -`SolverContext` keeps `x`, `lm_state`, `args`, `p` — an exotic metric can -still key off the live iterate, and reaches any carried state through -`ctx.lm_state`. - -### Every traced read goes through the carried instance - -This is the load-bearing rule, and it covers **`linear_solvers.py`** too: -`CG.prepare` and `GramCG.prepare` currently build `apply_M` from -`self.preconditioner` — a jit-static object whose arrays are compile-time -constants. All such sites move to the carried instances -(`sub.ctx.lm_state.preconditioner`; the metric via the ctx the whiten -closures already close over). To make any stray old-style read fail loudly -instead of silently baking one instance's arrays into a shared compile, the -solver's constructor-held attributes are renamed: `self.initial_metric`, -`self.initial_preconditioner`. They exist to seed `init`/`_cold_state`, to -key compilation, and for static reads (`metric.size` — sound either way, -since the treedef contract pins statics). The config fields -(`CG.preconditioner`) keep their names as the initial-instance source but -are never read inside `prepare`. - -The enforcement is a correctness test, not just a convention: two solvers -built around same-treedef, **different-valued** metrics (and -preconditioners) must produce different answers on every linear-solver path -— under the new value-based static key they share one compiled loop, so any -leftover static read reproduces the first solver's geometry and fails this -test. (The old identity-hashed keys made that bug impossible; the new tests -are what make the sharing safe.) - -### LMState - -```python -@dataclass(frozen=True) -class LMState: - damping: jax.Array - ridge: jax.Array | None = None - resid / Jt / jacobian_valid / aux # Jacobian cache, unchanged - hyper: LMHyperparams | None = None - solver_cache: Any = None - metric: Metric | None = None # NEW: the carried instance - preconditioner: Preconditioner | None = None # NEW -``` - -Ownership contract, stated in the docs: **callback-owned** state is -`damping`, `ridge`, `metric`, `preconditioner`, and the `hyper` group -(replaceable as a unit); everything else (`resid`/`Jt`/`jacobian_valid`/ -`aux`/`solver_cache`) is **solver-owned** — preserve it with -`dataclasses.replace(ctx.lm_state, ...)`. No deeper nesting: grouping the -live `damping` with its schedule would mix a solver-written scalar with -callback-owned knobs and force nested replaces in the hot update path. - -`init` and `_cold_state` seed the constructor instances into the state, and -so does the metric solver's minimal-state fast path in `_solve_lm_state` -(today it returns a bare `LMState(damping)`; that would break the carry -structure) — so every state entering the solve loop carries instances. -Inside the loop every traced read goes through the carried instances. -`update` handed a hand-built state with `metric=None` **reads** through -`initial_metric`/`initial_preconditioner` but **passes the `None` -through** to the returned state — injecting an instance would change the -carry structure of a user's own `lax.while_loop` around `update`. With -`prepare` gone, a manual loop that wants an iterate-tracking metric -rebuilds the instance between its own calls. `_cast_state` casts named -scalars only (`damping`, `ridge`, `hyper`, cache ridge) and never touches -instance leaves. - -### All adaptive policy lives in the single per-step callback - -Ridge anneal, preconditioner refresh, metric swap, data re-draw, damping -reset, custom stop — one callback, running where it does today: after the -accept/reject update, before the termination test. (Validated against -spooky's `epoch_callback`, which keeps working unchanged modulo the rename -below.) - -The solver keeps only the reactive, non-policy automation, all as extensions -of the existing `_apply_action` + `problem_changed` machinery: - -1. **Metric mutation is detected automatically by value**, the same rule as - `x`/`args` today: `_apply_action` compares the action's metric leaves - against the carried ones with `_tree_changed`, short-circuiting at trace - time on leaf **identity** — a callback that used - `dataclasses.replace(ctx.lm_state, ridge=...)` hands back the same - tracer objects for the metric subtree, so the untouched-metric case - emits no comparison ops at all (large factors pay the `array_equal` - reduction only on steps that actually rebuild). What a change *means* - differs by solver, because the metric's role differs: - - **`RidgeLevenbergMarquardt`**: the metric defines the objective, so a - change sets `problem_changed` — suppressing that iteration's - convergence test (the step's diagnostics were computed under the old - geometry) — and invalidates the solver caches (`G`/`R` embed the - whitening). - - **`LevenbergMarquardt`**: the metric is damping geometry only; the - objective `||r||^2` did not move, so convergence is **not** - suppressed. The solver caches are still invalidated (the assembled - whitened normal matrix embeds the factor). - - The Jacobian cache is **never** cleared by a metric change: `J = dr/dx` - does not depend on the metric, and whitening is applied fresh from the - cached `Jt` each step. - - Consequence worth stating for the ridge solver: an iterate-dependent - metric rebuilt on *every* accepted step suppresses convergence on every - accepted step, so `xtol` (accepted-only) can never fire and termination - comes from `gtol`/`atol` on rejected steps or from a conditional rebuild - (`lax.cond` on progress). Rebuild-when-it-matters is the documented - pattern. Two more caller obligations replace deleted automation, both - documented: a callback that replaces `x` or `args` and uses a metric - built from them must rebuild the metric **in the same action** (the old - `metric_valid` clearing is gone with the flags); and under multi-start, - drawn lanes inherit the caller's initial instances, so a lane's *first* - step runs under the initial metric — the callback corrects it from step - two (the old per-lane `prepare` re-ran at the drawn point before the - first step). -2. **Preconditioner changes are neither compared nor invalidated.** - Staleness is safe by contract (it only changes the CG iteration path), - so a refresh costs nothing beyond the refresh. -3. **Structure enforcement**: `_apply_action` guards the returned - `metric`/`preconditioner` like it already guards `hyper` — treedef AND - leaf dtype/weak-type must match the carried ones — with an error naming - the field, rather than letting a raw carry mismatch surface downstream. -4. Ridge changes keep their existing detection (`_apply_action_state`). - -### Renames - -`LMSolveAction` → **`LMAction`**, `LMSolveContext` → **`LMContext`**. They -are the callback protocol's types; "solve" in the name was noise. -`LMSolveResult` keeps its name — it is specifically what `solve` returns. -`LMAction` keeps `stop`/`status` (spooky needs them). No aliases. - -### Compilation identity - -The solver's `_static_key` replaces the identity-hashed metric and -preconditioner components with `jax.tree_util.tree_structure(instance)`. -Linear-solver configs containing a preconditioner (`CG`, `GramCG`) are keyed -as (type, scalar knobs, treedef of the preconditioner). Equal-config -instances with fresh arrays therefore share one compiled loop; instances -with different static fields have different treedefs and key different -programs. Leaf *values* stay free to change because they enter the compiled -program as traced carry leaves; leaf *shapes/dtypes* retrace through the -ordinary jit input avals, not through the static key. - -The keying rule is exactly "treedef-hash what is threaded, identity-hash -what is baked": an **explicit `ad_solver=CG(instance)`** keeps -identity-based keying for that instance, because its arrays enter the -tangent program as closed-over constants — treedef keying there would let -two solvers with different AD preconditioner values compare equal and -silently share one baked-in program. - -New `test_compilation.py` pins: - -- a fresh equal-config metric/preconditioner per solve compiles once (the - old tests pinned the weaker reuse-the-same-object property); -- a callback-driven instance swap does not recompile; -- a changed static field does; -- **companion correctness pins** (the other half of the guarantee): two - same-treedef different-valued metrics produce different solutions, and a - callback-swapped preconditioner demonstrably changes the CG iteration - path (tight `maxiter`, exact vs. identity), so cache sharing can never - hide a static-read bug. - -### Implicit AD - -At the solution the converged instances ride in `result.lm_state`, which the -tangent rule already stop-gradients: their leaves are frozen inputs to the -implicit system, replacing `_frozen_ctx`'s prepare-at-solution. The -state-dependence of a callback-refreshed metric is not differentiated. - -One deliberate contract change, stated plainly: `_frozen_ctx` used to -re-run `prepare` **at the returned solution**, whatever the forward refresh -policy had been; the new rule freezes the **carried** instance — the -geometry the solve actually converged under, which may be one refresh -behind the solution point. For a fixed metric (every real caller today) the -two are identical. An iterate-dependent metric that wants the old -at-solution semantics refreshes on every accepted step, making the carried -instance current at convergence. This is documented and pinned by a test -rather than silently absorbed. - -Failed lanes: the tangent program must not read callback-mutated instances -from a failed solve (a swapped metric can be as invalid as a swapped ridge). -`_initial_ad_point` grows the pre-loop instances alongside the pre-loop -ridge it already carries, and `_ad_x_tangent` selects per-lane between the -result instances and the initial ones with the existing `_where_tree` -success mask — structure equality is already enforced, so the select is -well-posed. - -AD-role preconditioning: `ad_solver=None` keeps today's inherit-the-forward -rule, now reading the **carried instance from `result.lm_state`** (the -callback-refreshed one at the solution). `ad_solver=CG(None, tol=..., -maxiter=...)` — `preconditioner=None` is newly legal in the AD role only — -also inherits the carried instance while pinning the AD tolerance and -budget (the kernels driver needs exactly this; with `ad_solver=None` the AD -budget falls back to CG defaults, which is tens of thousands of iterations -at that problem size). An explicit `ad_solver=CG(instance, ...)` uses the -given instance as-is (identity-keyed, see above). `preconditioner=None` -stays invalid in the forward role — opting out of forward preconditioning -remains the explicit `IdentityPreconditioner()`. The -`requires_positive_damping` exclusion is preserved in every AD form: an -inherited forward instance carrying that flag (e.g. `Padded`) falls back to -unpreconditioned, and an explicit one is rejected at construction, exactly -as today. - -### Multi-start - -Sequential and Python modes: drawn lanes start from `_cold_state` of the -caller's initial state, so they inherit the caller's initial instances and -never see another lane's callback mutations. Unchanged. - -Parallel (vmapped) mode: **supported, no guard** — this resolves the open -question differently from the plan's lean. Instance leaves batch under -`vmap` like every other carried array (verified: an unbatched instance in -the initial carry with per-lane `lax.cond` rebuilds returns correctly -batched leaves), so per-lane mutation of leaf *values* is correct by -construction; lanes cannot diverge in structure, shape, or dtype — the same -rule as every other vmapped carry. The old design couldn't batch -identity-hashed closures, but the new one has nothing left to guard. The -real cost is documented instead: under `vmap` a `lax.cond` rebuild lowers -to a select that pays both branches every step — keep refresh logic behind -`lax.cond` for sequential drivers, and expect the rebuild cost per step if -you vmap it. - -### `ridge_continuation` becomes `AnnealRidge`, a shipped convenience callback - -The `ridge_continuation` factory and the `RidgeContinuation` name leave the -API. What ships instead is **`AnnealRidge`** — a frozen-dataclass callable -with today's full semantics and validation (`ridge_floor > 0`, -`0 < decrease < 1`, `grad_rtol > 0`, `stall_rtol` in `[0, 1)`), plus an -`init_state(dtype=None)` method replacing the factory's returned -`user_state0`: - -```python -anneal = AnnealRidge(ridge_floor=1e-10) -result = solver.solve(x0, callback=anneal, - user_state=anneal.init_state(dtype), - gtol=1e-8, atol=1e-8) -``` - -Its **docstring documents the implementation** — the per-level reference in -`user_state`, the `+inf` fresh-level sentinel, the reset-on-advance, the -interplay with convergence suppression — so a driver that needs more than -annealing composes it inside its own callback rather than forking it: - -```python -def driver_callback(ctx): - action = anneal(ctx) - advanced = action.lm_state.ridge < ctx.lm_state.ridge - precond = jax.lax.cond( - advanced, - lambda: BlockEigenPreconditioner( - build_families(ctx.x, ctx.args), PERMUTATION - ), - lambda: ctx.lm_state.preconditioner, - ) - return dataclasses.replace( - action, - lm_state=dataclasses.replace(action.lm_state, preconditioner=precond), - ) -``` - -`lax.cond` branches trace once, so the `eigh` is paid only when the level -advances. The docs call out the anti-pattern explicitly: merging with -`jnp.where` over an unconditional rebuild pays the `eigh` every step — the -old kernels wrapper's actual behavior. The dtype handling keeps today's -contract: the stationarity comparison runs at the ridge dtype (the tracker -is cast in, results cast back to the tracker's dtype), and equal schedules -stay value-hashable so rebuilding one does not recompile the loop. - -Callback hashing contract (documented): a callback is built once per -process — a module-level function, a frozen dataclass callable with -scalar-only fields, or a setup-scope closure the driver constructs once. -What recompiles is rebuilding a *fresh closure per solve call*. Closures -over large arrays (the kernels rebuild needs `K`, `K_tilde`, `F`, physics -constants — more than `ctx` carries) are fine at driver scope: -identity-hashed, one compile per run, and cross-run persistent-cache hits -are keyed on the traced HLO, which closure identity does not enter. - -## Before/after: the external callers - -### kernels `multicountry_growth_kernel.py` (CG path) - -Before (~25 lines): `args = {"preconditioner": build_preconditioner_state(theta_0)}`, -a wrapper callback that calls the continuation, detects `advanced`, rebuilds -the state, `jnp.where`-merges it (paying the eigh every step), and threads it -back through `args`; an explicit `ad_solver=CG(BlockEigenPreconditioner(), ...)` -so the AD solve can find the state in `result.args`. - -After: `multicountry_block_eigen_state` returns the family arrays; the -driver builds `BlockEigenPreconditioner(families(theta_0), permutation)` -once, passes it to `CG(...)`, and uses a driver-scope callback composing -the shipped `AnnealRidge` with the `lax.cond` rebuild closing over the -kernel matrices. -`ad_solver=CG(None, tol=lm_set.cg_tol, maxiter=lm_set.cg_maxiter)` inherits -the refreshed carried instance at the solution while keeping the pinned AD -budget, so the args-threading is deleted. - -### spooky `mv2020_rbc_continuous.py` - -`epoch_callback` (data re-draw + damping reset + custom stop on epoch -boundaries via `lax.cond`) keeps working verbatim modulo -`LMSolveAction` → `LMAction`. It touches neither metric nor preconditioner, -so no invalidation fires beyond the existing args-change rule. - -### Full migration inventory - -- `kernels/multicountry_growth_kernel.py` + `multicountry_growth_preconditioner.py` - (above; the preconditioner module returns families instead of calling - `block_eigen_state`). -- `kernels/open_economy_growth_kernel.py` (`ridge_continuation` → - `AnnealRidge`). -- `kernels/extra/neoclassical_growth_kernel_recursive_adaptive.py` - (`LMSolveAction` rename). -- `kernels/tests/test_python_models.py` → moves to `extra/tests/` (dead - import + one dead-API test deleted). -- `kernels/trade_growth/` → moves to `extra/trade_growth/` wholesale; it - targets a pre-2.7 API and is excluded from the sweep. -- `spooky/mv2020_rbc_continuous.py`, `spooky/mv2020_rbc_discrete.py`, and - the annotated qmd (rename only; ported after kernels). - -## Out of scope (settled elsewhere) - -- **dtype policy**: one consistent dtype inferred from the problem; the - float64-solve promotion knob stays out until a float32 test campaign - motivates it (decision of 2026-07-25). -- No new `DampingSettings` grouping: `hyper` already is the settings group. - -## Test plan (Stage 4) - -- Compilation pins and companion correctness pins listed above. -- Callback swaps metric → ridge solver: that iteration cannot report - `CONVERGED`, solver caches invalidated, Jacobian cache retained; metric - solver: no suppression, caches invalidated. Preconditioner swap → no - invalidation, demonstrably different CG path. Wrong-type/structure swap → - loud `_apply_action` error naming the field. -- Block-eigen constructor numerics vs a dense reference. -- `AnnealRidge` reproduces today's `ridge_continuation` results on the - existing fixtures (including the `stall_rtol` variant), and the - composition recipe from its docstring works as written. -- Failed-lane AD with a callback-mutated metric uses the initial instances - (extends the existing failed-lane ridge tests). -- The untouched-metric identity short-circuit: a callback returning - `dataclasses.replace(ctx.lm_state, ridge=...)` every step adds no - comparison ops for the metric subtree (jaxpr inspection). -- AD-contract pin: the tangent uses the carried (frozen) instances; the - `requires_positive_damping` inherited-AD fallback still applies. -- Prune tests of deleted machinery. -- AD: rerun the reverse/forward tangent suites — the frozen-at-solution - semantics replace `_frozen_ctx`. diff --git a/docs/implicit_ad.md b/docs/implicit_ad.md index 9fe4811..3001d0b 100644 --- a/docs/implicit_ad.md +++ b/docs/implicit_ad.md @@ -40,12 +40,16 @@ which rule is valid where. The short version: A Krylov rule used outside its valid shape raises rather than returning a quietly wrong tangent. -## Frozen hooks - -Under differentiation the metric's and preconditioner's `prepare` run **once, -at the returned solution**, and their state-dependence is not differentiated — -the same contract as a fixed metric closing over constants. The solver state -rides along as inert conditioning data under `stop_gradient`. +## Frozen instances + +Under differentiation the **carried** metric and preconditioner instances — +the geometry the solve actually converged under, callback refreshes included +— are frozen inputs to the implicit system: their leaves ride along as inert +conditioning data under `stop_gradient`, and the state-dependence of a +callback-refreshed instance is not differentiated. An iterate-tracking +metric that wants the tangent taken at the exact solution geometry refreshes +on every accepted step, which makes the carried instance current at +convergence. ## Failed solves diff --git a/docs/index.md b/docs/index.md index 58a5ded..a2915ce 100644 --- a/docs/index.md +++ b/docs/index.md @@ -53,7 +53,7 @@ result.x, result.status, result.steps ```python import jax.numpy as jnp -from nlls_gram import RidgeLevenbergMarquardt, RepeatedFactorMetric, ridge_continuation +from nlls_gram import AnnealRidge, RidgeLevenbergMarquardt, RepeatedFactorMetric # W = blockdiag(K, K) for a kernel Gram matrix K: the RKHS seminorm over two # coefficient blocks. The constructor takes the FACTOR. @@ -62,8 +62,8 @@ metric = RepeatedFactorMetric(jnp.linalg.cholesky(K, upper=True), repeats=2) solver = RidgeLevenbergMarquardt(collocation_residual, metric=metric, ridge=1e-4) # Anneal the ridge toward the interpolating limit on stationarity. -callback, user_state = ridge_continuation(ridge_floor=1e-10) -result = solver.solve(x0, callback=callback, user_state=user_state, +anneal = AnnealRidge(ridge_floor=1e-10) +result = solver.solve(x0, callback=anneal, user_state=anneal.init_state(), gtol=1e-8, atol=1e-8) ``` diff --git a/docs/metrics.md b/docs/metrics.md index 83fa1c3..122ab71 100644 --- a/docs/metrics.md +++ b/docs/metrics.md @@ -7,6 +7,13 @@ things: - a **`Preconditioner`** only changes the CG iteration path, so it may approximate freely. +Instances of both are **JAX pytrees**: array fields are traced leaves, the +type plus its static fields are structure. They ride inside the solver state +(`lm_state.metric`, `lm_state.preconditioner`), so a `solve` callback adapts +one by **calling the constructor again** with fresh arrays — same type, same +leaf shapes and dtypes, pure traced ops, no recompilation. See +[Callbacks](callbacks.md) for the adaptation rules. + ## `Metric` A positive-definite \(W\) given through callbacks for an invertible factor @@ -15,8 +22,8 @@ never materializes either. ```python class Metric: - size: int # the metric block: the leading coordinates of x - free_scale = 1.0 # damping weight on everything past it + size: int # static: the metric block, the leading coordinates of x + free_scale = 1.0 # traced leaf: damping weight on everything past it def factor_apply(v, ctx): ... # F v def factor_solve(v, ctx): ... # F^-1 v @@ -24,8 +31,10 @@ class Metric: def norm(v, ctx): ... # ||F v||, defaulted ``` -Ops act on metric-block vectors, or matrices whose *leading* axis is `size` -(columns are batched). Shipped implementations: +Ops read `self` and act on metric-block vectors, or matrices whose *leading* +axis is `size` (columns are batched). `ctx` is a `SolverContext` carrying the +flat iterate and the live `LMState`, so an exotic metric can key off either. +Shipped implementations: | | \(W\) | |---|---| @@ -55,12 +64,18 @@ choice, not a default. | | approximates | |---|---| | `IdentityPreconditioner()` | \(I\) | -| `BlockEigenPreconditioner(blocks_fn, permutation)` | a block-diagonal eigenbasis, analytic in both ridge and damping | +| `BlockEigenPreconditioner(families, permutation)` | a block-diagonal eigenbasis, analytic in both ridge and damping | | `NystromPreconditioner(matvec, n, rank, key)` | a randomized rank-\(k\) sketch (Frangella-Tropp-Udell) | | `ShermanMorrisonPreconditioner(solve, u, weight)` | \(A + wuu^\top\) from a solve with \(A\) | | `WoodburyPreconditioner(solve, U, weights)` | the rank-\(k\) generalization | | `PaddedPreconditioner(base, n_real)` | a base extended over exactly-zero padded rows | +Expensive derived state (`BlockEigen`'s eigendecompositions, `Nystrom`'s +sketch) is computed once in the constructor and stored as leaves; refreshing +mid-solve means constructing a new instance in the callback, usually behind +`jax.lax.cond` so the cost is paid only when the refresh fires. Staleness is +always safe — it moves the CG iteration path, never the converged step. + **Range preservation.** On rank-deficient problems the minimum-norm selection rests on the CG iterates staying in \(\operatorname{range}(B^\top)\). Unpreconditioned CG from zero does, since the right-hand side starts there and @@ -73,31 +88,37 @@ Safe: the identity, polynomials in the operator, an exact \((B^\top B + \tau I)^{-1}\) at fixed \(\tau > 0\). On full-column-rank problems the condition is vacuous. -## Iterate-dependent state +## Custom types -Both types take the same optional pair when their numbers must track the -iterate: +A custom metric or preconditioner is a small frozen dataclass registered with +`register_pytree_dataclass` — the solvers reject unregistered instances: ```python -def prepare(self, theta, ctx): ... # -> traced pytree, or None (the default) -def rebuild(self, ctx): ... # -> traced bool, True by default -``` +from dataclasses import dataclass -The output rides on the solver state and comes back as `ctx.metric_state` / -`ctx.preconditioner_state`. It is rebuilt on accepted steps and reused across -rejected ones (where `x` did not move), runs inside the jitted loop as traced -ops, and is **frozen at the solution** under implicit AD. Its pytree structure -must not change between rebuilds. Override `rebuild` to decline a refresh — -for a preconditioner that is always safe and often much cheaper. +@dataclass(frozen=True, eq=False) +class JacobiPreconditioner(Preconditioner): + diagonal: jax.Array + + def apply(self, v, damping, ctx): + return v / (self.diagonal + damping) + +register_pytree_dataclass(JacobiPreconditioner, data_fields=("diagonal",)) +``` -Setup that does *not* depend on the iterate belongs in `__init__`, where it is -paid once. +`data_fields` become traced leaves; `meta_fields` (compile-time structure — +sizes, block counts) must be hashable. The constructor may validate and +compute derived leaves eagerly: reconstruction inside jit or a loop carry +restores the stored fields verbatim without re-running it. Constructors must +be traceable when the instance is rebuilt inside a jitted callback. Metrics +also support `dataclasses.replace` (their constructors are cheap); +preconditioners are rebuilt by constructor only. ## Compilation -The solver is a jit **static** argument, so its hooks enter the compile cache -key. Types holding arrays (every metric above, most preconditioners) hash by -identity: **build them once at setup scope and reuse them**, or every -construction keys a fresh compilation of the whole solve loop. Stateless -value-equal types (`IdentityPreconditioner`) are free to construct inline. +Instances key compilation by pytree **structure** — the type plus its static +fields — while their arrays are threaded through the carried state. Two +solvers around equal-config instances with fresh arrays share one compiled +loop, so constructing a metric per solve call is free; a changed static +field (a different `repeats`, a different family layout) keys a new program. `tests/test_compilation.py` pins this. diff --git a/docs/ridge_lm.md b/docs/ridge_lm.md index e5c32fe..11f4429 100644 --- a/docs/ridge_lm.md +++ b/docs/ridge_lm.md @@ -141,14 +141,15 @@ identification condition at every reachable state. ### Ridge continuation -The homotopy \(\lambda \downarrow \lambda_{\min}\) is a **documented -callback recipe**, not solver machinery: +The homotopy \(\lambda \downarrow \lambda_{\min}\) is a **callback**, not +solver machinery — `AnnealRidge` is the shipped schedule, and its docstring +documents the mechanics for composing it into a callback of your own: ```python -from nlls_gram import ridge_continuation +from nlls_gram import AnnealRidge -cb, us0 = ridge_continuation(ridge_floor=1e-8, decrease=0.1) -result = solver.solve(x0, callback=cb, user_state=us0, +anneal = AnnealRidge(ridge_floor=1e-8, decrease=0.1) +result = solver.solve(x0, callback=anneal, user_state=anneal.init_state(), atol=1e-8, max_steps=500) ``` @@ -299,13 +300,13 @@ Shipped metrics: already hold it): `F = jnp.linalg.cholesky(K, upper=True)`. All repeated blocks and all batched columns share a single triangular product/solve. -An `x`- or `p`-dependent metric is deliberately unsupported in this -release: the gradient and the implicit-AD rule treat \(F\) as constant, and -a dependent factor would silently drop derivative terms (the reserved -`metric_factory` keyword raises; its documented contract is a -`prepare`/`build` pair producing a `Metric` from traced `metric_state`, -with `metric_valid` reject-step reuse and a state change treated as a -problem change). +The metric instance rides in `lm_state.metric`, so a callback may replace +it mid-solve by constructing a new instance of the same type (see +[Callbacks](callbacks.md)); the solver treats the change as a problem +change — the metric defines this objective — suppressing that step's +convergence test and invalidating the whitened caches. The gradient and +the implicit-AD rule treat \(F\) as constant between callback actions: the +state-dependence of a callback-refreshed factor is not differentiated. ### Kernel instantiation @@ -389,65 +390,63 @@ A preconditioner changes the CG iteration path, never the subproblem — approximations are safe (unlike the metric factor, which must be exact). For repeated interacting blocks (multiple "agents" coupled through shared -equations), `BlockEigenPreconditioner` is the shipped workhorse: a -block-diagonal approximation over a chosen grouping of the whitened -coordinates, eigendecomposed once per build and applied with the -damping-analytic shift \(\Lambda + \texttt{ridge\_weight}\cdot\lambda + -\mu\) (metric-block families carry the live ridge, free-block families are -damping-only). The instance is stateless and value-hashable; its numeric -state — built by `block_eigen_state` from stacked SPD diagonal blocks and a -family-major permutation — rides in the residual `args` under a fixed key -and is read through `ctx.args` at apply time. - -**Adaptive rebuilds through the solve callback.** Because the state lives -in `args`, a callback can rebuild it from the live iterate with no solver -support: staleness detection is a traced value comparison, so returning -identical values suppresses nothing, and a real swap suppresses only that -step's convergence check. The natural policy pairs rebuilds with -`ridge_continuation` — rebuild exactly when the anneal advances a level, -which already suppresses that step: +equations), `BlockEigenPreconditioner(families, permutation)` is the +shipped workhorse: a block-diagonal approximation over a chosen grouping of +the whitened coordinates, eigendecomposed in the constructor and applied +with the damping-analytic shift \(\Lambda + +\texttt{ridge\_weight}\cdot\lambda + \mu\) (metric-block families carry the +live ridge read from `ctx.lm_state.ridge`, free-block families are +damping-only). The eigenbasis rides in the carried instance +(`lm_state.preconditioner`). + +**Adaptive refreshes through the solve callback.** A callback rebuilds the +instance from the live iterate by calling the constructor; staleness only +moves the CG iteration path, so a refresh is never a problem change. The +natural policy pairs refreshes with `AnnealRidge` — rebuild exactly when +the anneal advances a level, gated with `lax.cond` so the +eigendecomposition is paid only when it fires (a `jnp.where` merge would +pay it every step): ```python -continuation, user_state0 = ridge_continuation(ridge_floor=1e-11) +anneal = AnnealRidge(ridge_floor=1e-11) def callback(ctx): - action = continuation(ctx) + action = anneal(ctx) advanced = action.lm_state.ridge < ctx.lm_state.ridge - fresh = build_state(ctx.x) # model-side analytic assembly - state = jax.tree_util.tree_map( - lambda old, new: jnp.where(advanced, new, old), - ctx.args["preconditioner"], fresh, + precond = jax.lax.cond( + advanced, + lambda: BlockEigenPreconditioner(build_families(ctx.x), PERMUTATION), + lambda: ctx.lm_state.preconditioner, ) - return LMSolveAction( - lm_state=action.lm_state, user_state=action.user_state, - args={**ctx.args, "preconditioner": state}, + return dataclasses.replace( + action, + lm_state=dataclasses.replace(action.lm_state, preconditioner=precond), ) solver = RidgeLevenbergMarquardt( residual_fn, metric=metric, - linear_solver=CG(BlockEigenPreconditioner(), tol=1e-10, maxiter=2500), + linear_solver=CG(BlockEigenPreconditioner(build_families(x0), PERMUTATION), + tol=1e-10, maxiter=2500), ) -result = solver.solve(x0, {"preconditioner": build_state(x0)}, - callback=callback, user_state=user_state0, +result = solver.solve(x0, callback=callback, user_state=anneal.init_state(), max_steps=120, gtol=1e-11) ``` -The AD-role CG reads the state from `result.args` at zero damping — a -callback-rebuilt state is exactly the near-solution build the tangent solve -wants. `ad_solver=None` inherits the forward CG's preconditioner for the -undamped tangent solve (applied at zero damping; hooks marked -`requires_positive_damping` fall back to unpreconditioned) while keeping -the AD-default tolerance and unbounded iteration budget — pass -`ad_solver=CG(...)` explicitly to pin `tol`/`maxiter` instead. One -measured calibration note: with a family layout -whose blocks carry the same ridge floor as the operator, the CG iteration -count SATURATES as the ridge anneals down (it does not grow like -\(1/\sqrt{\lambda}\)) — budget `maxiter` for the saturated count, since a -truncated inner solve stalls the endgame. Two scope cautions for -args-carried state: `save_steps=True` records a full copy of `args` per -step (the whole eigenbasis, every step), and a parallel `multi_start` -vmaps the callback so a `where`-gated rebuild evaluates BOTH branches in -every lane — keep both out of preconditioned-CG production runs. +The AD-role CG applies the **carried** instance at zero damping — a +callback-refreshed eigenbasis is exactly the near-solution build the +tangent solve wants. `ad_solver=None` inherits it at the AD-default +tolerance and unbounded iteration budget; `ad_solver=CG(None, tol=..., +maxiter=...)` inherits it while pinning the knobs; an explicit +`ad_solver=CG(instance, ...)` uses that instance as-is (hooks marked +`requires_positive_damping` fall back to unpreconditioned). One measured +calibration note: with a family layout whose blocks carry the same ridge +floor as the operator, the CG iteration count SATURATES as the ridge +anneals down (it does not grow like \(1/\sqrt{\lambda}\)) — budget +`maxiter` for the saturated count, since a truncated inner solve stalls the +endgame. Two scope cautions: `save_steps=True` records a full copy of +`args` per step, and a parallel `multi_start` vmaps the callback so a +`lax.cond` rebuild lowers to a select that evaluates BOTH branches in every +lane — keep both out of preconditioned-CG production runs. ## Implicit differentiation @@ -507,8 +506,6 @@ original inputs and the *initial* ridge. ::: nlls_gram.BlockEigenPreconditioner -::: nlls_gram.block_eigen_state - ## References - Bakushinskii, A. B. (1992). "The problem of the convergence of the diff --git a/docs/tuning_guide.md b/docs/tuning_guide.md index 61b08f0..fe70195 100644 --- a/docs/tuning_guide.md +++ b/docs/tuning_guide.md @@ -49,7 +49,7 @@ the standard schedule. Reach for the others only on evidence: ## The ridge schedule For `RidgeLevenbergMarquardt`, a fixed ridge leaves an \(O(\text{ridge})\) -bias. `ridge_continuation(ridge_floor=...)` anneals toward the interpolating +bias. `AnnealRidge(ridge_floor=...)` anneals toward the interpolating limit, advancing a level whenever the current one is stationary. Calibrate `gtol` as roughly `1e-3 * ridge * sqrt(q(x*))` — the reported @@ -68,12 +68,14 @@ Traced, so changing them reuses the compiled loop: `atol`/`gtol`/`xtol`, the damping and ridge values, `p`, `args`, `max_steps` (without `save_steps`), and every `LMHyperparams` field. -Static, so changing them compiles a new program: the residual, the metric and -preconditioner objects, the linear-solver config, `has_aux`, -`cache_jacobian`, `geodesic_acceleration`, the callback, and any shape. +Traced too: every metric and preconditioner **array** — the instances ride +in the carried state, so a fresh equal-config instance (and a callback +rebuild) reuses the compiled loop. -Build metrics and preconditioners **once at setup scope** — they hold arrays, -so they hash by identity and a rebuild keys a fresh compilation. +Static, so changing them compiles a new program: the residual, the +linear-solver config, `has_aux`, `cache_jacobian`, `geodesic_acceleration`, +the callback, any shape, and any instance **static field** (a metric's +`size`, a block-eigen family layout). ## Failure signatures diff --git a/tests/test_instance_state.py b/tests/test_instance_state.py new file mode 100644 index 0000000..6c25efe --- /dev/null +++ b/tests/test_instance_state.py @@ -0,0 +1,268 @@ +# The carried-instance contract: metric/preconditioner instances ride in +# LMState, callbacks adapt them by constructing new instances, and the solver +# reacts (or deliberately does not) per its own semantics. +import dataclasses +from dataclasses import dataclass + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from nlls_gram import ( + DiagonalMetric, + GramCG, + IdentityMetric, + LevenbergMarquardt, + LMAction, + LMStatus, + Preconditioner, + RepeatedFactorMetric, + RidgeLevenbergMarquardt, + register_pytree_dataclass, +) + +RNG = np.random.default_rng(21) +M_RESID, BLOCK, REPEATS, FREE = 4, 4, 2, 2 +P_DIM = REPEATS * BLOCK + FREE +A = jnp.asarray(RNG.normal(size=(M_RESID, P_DIM)), jnp.float32) +B = jnp.asarray(RNG.normal(size=M_RESID), jnp.float32) +ROOT = RNG.normal(size=(BLOCK, BLOCK + 2)) +K = jnp.asarray(ROOT @ ROOT.T + 0.5 * np.eye(BLOCK), jnp.float32) + + +def linear_residual(theta): + return A @ theta - B + + +def make_metric(scale=1.0): + return RepeatedFactorMetric( + scale * jnp.linalg.cholesky(K, upper=True), repeats=REPEATS + ) + + +def swap_every_step(ctx): + # A genuinely different metric every step: the scale tracks the step + # counter, so the leaves never repeat. + scale = 1.0 + 0.01 * ctx.step.astype(jnp.float32) + return LMAction( + lm_state=dataclasses.replace(ctx.lm_state, metric=make_metric(scale)) + ) + + +def test_ridge_metric_swap_suppresses_convergence(): + # The metric defines the ridge objective: a callback that swaps it every + # step keeps changing the problem, so a gtol that would otherwise fire + # immediately never stops the loop. + solver = RidgeLevenbergMarquardt(linear_residual, metric=make_metric(), ridge=1e-3) + swapped = solver.solve( + jnp.zeros(P_DIM), max_steps=20, gtol=1e3, callback=swap_every_step + ) + assert int(swapped.status) == int(LMStatus.MAX_STEPS) + plain = solver.solve(jnp.zeros(P_DIM), max_steps=20, gtol=1e3) + assert int(plain.status) == int(LMStatus.CONVERGED) + + +def test_metric_lm_metric_swap_does_not_suppress(): + # For the metric solver the metric is damping geometry only -- ||r||^2 + # did not move -- so the same every-step swap must not block convergence. + solver = LevenbergMarquardt(linear_residual, metric=make_metric()) + swapped = solver.solve( + jnp.zeros(P_DIM), max_steps=20, gtol=1e3, callback=swap_every_step + ) + assert int(swapped.status) == int(LMStatus.CONVERGED) + + +def test_metric_swap_invalidation_semantics(): + # The reactive rules, pinned at the _apply_action seam: a metric swap + # stales the whitening-dependent solver cache but never the Jacobian + # cache (J = dr/dx does not see the metric); problem_changed is + # ridge-solver-only. An untouched metric changes nothing. + for solver_cls, expect_problem_changed in ( + (RidgeLevenbergMarquardt, True), + (LevenbergMarquardt, False), + ): + kwargs = {"ridge": 1e-3} if solver_cls is RidgeLevenbergMarquardt else {} + solver = solver_cls(linear_residual, metric=make_metric(), **kwargs) + x0 = jnp.zeros(P_DIM) + state = solver.init(x0) + state = dataclasses.replace( + state, + jacobian_valid=jnp.asarray(True), + solver_cache=dataclasses.replace( + state.solver_cache, valid=jnp.asarray(True) + ), + ) + + swap = LMAction(lm_state=dataclasses.replace(state, metric=make_metric(2.0))) + _, _, out, _, _, problem_changed = solver._apply_action( + swap, x0, state, None, None + ) + assert bool(problem_changed) == expect_problem_changed + assert bool(out.jacobian_valid) + assert not bool(out.solver_cache.valid) + + untouched = LMAction(lm_state=dataclasses.replace(state, damping=state.damping)) + _, _, out, _, _, problem_changed = solver._apply_action( + untouched, x0, state, None, None + ) + assert not bool(problem_changed) + assert bool(out.jacobian_valid) + assert bool(out.solver_cache.valid) + + +def test_wrong_structure_swap_raises_naming_the_field(): + solver = RidgeLevenbergMarquardt(linear_residual, metric=make_metric(), ridge=1e-3) + x0 = jnp.zeros(P_DIM) + state = solver.init(x0) + wrong_type = LMAction( + lm_state=dataclasses.replace(state, metric=IdentityMetric(REPEATS * BLOCK)) + ) + with pytest.raises(ValueError, match="lm_state.metric"): + solver._apply_action(wrong_type, x0, state, None, None) + wrong_shape = LMAction( + lm_state=dataclasses.replace( + state, + metric=RepeatedFactorMetric(jnp.eye(2, dtype=jnp.float32), repeats=REPEATS), + ) + ) + with pytest.raises(ValueError, match="lm_state.metric"): + solver._apply_action(wrong_shape, x0, state, None, None) + + def swap_in_loop(ctx): + return LMAction( + lm_state=dataclasses.replace( + ctx.lm_state, metric=IdentityMetric(REPEATS * BLOCK) + ) + ) + + with pytest.raises(ValueError, match="lm_state.metric"): + solver.solve(x0, max_steps=5, callback=swap_in_loop) + + +def test_untouched_metric_costs_no_comparison_ops(): + # A callback that anneals the ridge via dataclasses.replace hands the + # metric subtree back as the same tracers: the identity short-circuit + # must emit NO comparison over the (BLOCK, BLOCK) factor leaf. The ridge + # change detection still emits its scalar eq. + solver = RidgeLevenbergMarquardt(linear_residual, metric=make_metric(), ridge=1e-3) + x0 = jnp.zeros(P_DIM) + state = solver.init(x0) + + def apply_anneal(state_in, x_in): + action = LMAction( + lm_state=dataclasses.replace(state_in, ridge=state_in.ridge * 0.5) + ) + return solver._apply_action(action, x_in, state_in, None, None)[5] + + text = str(jax.make_jaxpr(apply_anneal)(state, x0)) + assert f"bool[{BLOCK},{BLOCK}]" not in text + assert "eq" in text # the scalar ridge compare is still there + + +@dataclass(frozen=True, eq=False) +class DualJacobi(Preconditioner): + """Residual-space (equation-structure) preconditioner for GramCG: the + inverse of diag(J J') + damping.""" + + diagonal: jax.Array + + def apply(self, v, damping, ctx): + return v / (self.diagonal + damping) + + +register_pytree_dataclass(DualJacobi, data_fields=("diagonal",)) + + +def test_gram_cg_equation_space_preconditioner_and_budget_schedule(): + # The dual (residual-space) Krylov form takes the same Preconditioner + # interface with v living in equation space. A starved inner budget + # cannot reach gtol; a callback that BOTH refreshes the carried + # preconditioner from live data and grows hyper.iterative_maxiter on a + # schedule converges -- the budget is traced carry, the instance rides in + # lm_state. + def residual(theta): + return A @ theta - B + + dual_diag = jnp.diag(A @ A.T) + + def build(callback=None, maxiter=1): + solver = LevenbergMarquardt( + residual, + linear_solver=GramCG( + DualJacobi(jnp.ones(M_RESID)), tol=0.0, maxiter=maxiter + ), + ) + return solver.solve( + jnp.zeros(P_DIM), max_steps=40, atol=1e-5, callback=callback + ) + + def improve(ctx): + fresh = jax.lax.cond( + ctx.step == 3, + lambda: DualJacobi(dual_diag), + lambda: ctx.lm_state.preconditioner, + ) + grown = jnp.where( + ctx.step >= 3, + jnp.asarray(30, jnp.int32), + ctx.lm_state.hyper.iterative_maxiter, + ) + return LMAction( + lm_state=dataclasses.replace( + ctx.lm_state, + preconditioner=fresh, + hyper=dataclasses.replace(ctx.lm_state.hyper, iterative_maxiter=grown), + ) + ) + + starved = build() + scheduled = build(improve) + assert int(starved.status) == int(LMStatus.MAX_STEPS) + assert int(scheduled.status) == int(LMStatus.CONVERGED) + np.testing.assert_allclose( + scheduled.lm_state.preconditioner.diagonal, dual_diag, rtol=1e-6 + ) + + +def test_ad_uses_the_carried_metric_at_the_solution(): + # The implicit tangent freezes the CARRIED instances: after a mid-solve + # metric swap, the minimum-W-norm tangent selection must use the swapped + # metric, not the construction-time one. Analytic reference for the + # underdetermined linear system r = A x - p from x0 = 0: + # dx/dp = W^{-1} A' (A W^{-1} A')^{-1}. + n = 6 + A_fat = jnp.asarray(RNG.normal(size=(3, n)), jnp.float32) + w_initial = jnp.asarray(RNG.uniform(0.5, 2.0, size=n), jnp.float32) + w_swapped = jnp.asarray(RNG.uniform(4.0, 9.0, size=n), jnp.float32) + + def residual(x, args, p): + return A_fat @ x - p + + def swap(ctx): + fresh = jax.lax.cond( + ctx.step == 2, + lambda: DiagonalMetric(w_swapped), + lambda: ctx.lm_state.metric, + ) + return LMAction(lm_state=dataclasses.replace(ctx.lm_state, metric=fresh)) + + solver = LevenbergMarquardt(residual, metric=DiagonalMetric(w_initial)) + p = jnp.asarray(RNG.normal(size=3), jnp.float32) + + def solved(p_value): + return solver.solve( + jnp.zeros(n), p=p_value, max_steps=60, atol=1e-6, callback=swap + ).x + + assert int( + solver.solve(jnp.zeros(n), p=p, max_steps=60, atol=1e-6, callback=swap).status + ) == int(LMStatus.CONVERGED) + tangent = jax.jacfwd(solved)(p) + + def analytic(weights): + W_inv = jnp.diag(1.0 / weights) + return W_inv @ A_fat.T @ jnp.linalg.inv(A_fat @ W_inv @ A_fat.T) + + np.testing.assert_allclose(tangent, analytic(w_swapped), rtol=2e-4, atol=2e-5) + assert not np.allclose(tangent, analytic(w_initial), atol=1e-3) From 2154dca0c730abc9c435b38fa6001178087611aa Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 10:50:01 -0700 Subject: [PATCH 15/22] fix: reject nested unregistered instances at solver construction Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/lm_core.py | 18 +++++++++++++++++- 1 file changed, 17 insertions(+), 1 deletion(-) diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 28522cd..8324304 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -11,6 +11,7 @@ import jax import jax.numpy as jnp +import numpy as np from jax.flatten_util import ravel_pytree from nlls_gram.lm_types import ( @@ -60,12 +61,27 @@ def __hash__(self): _metric_defines_objective = False def _check_registered_instance(self, instance, keyword): - if instance is not None and jax.tree_util.all_leaves([instance]): + if instance is None: + return + if jax.tree_util.all_leaves([instance]): raise TypeError( f"{keyword} must be a registered pytree ({type(instance).__name__} " "flattens as a leaf); register the class with " "nlls_gram.register_pytree_dataclass" ) + # A nested unregistered object (e.g. PaddedPreconditioner over an + # unregistered base) flattens as an opaque leaf and would fail deep + # inside jit instead of here. + for leaf in jax.tree_util.tree_leaves(instance): + if not isinstance( + leaf, (jax.Array, np.ndarray, np.generic, int, float, complex, bool) + ): + raise TypeError( + f"{keyword} contains a non-array leaf of type " + f"{type(leaf).__name__}; register nested " + "metric/preconditioner classes with " + "nlls_gram.register_pytree_dataclass" + ) def _validate_configuration(self, linear_solver, ad_solver, penalized): """Reject a config in a role it cannot fill, at construction. From 0643a49c261876855b978a836b3a72eac9cc1ef8 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 11:44:41 -0700 Subject: [PATCH 16/22] fix: freeze solvers after construction; weak-type check in the instance guard A mutated solver attribute would keep the stale static key and silently reuse another configuration's compiled loop, so assignment now raises. The callback structure guard compares leaf weak types too: a weak/strong scalar swap passes the carry's physical checks while retracing the body under different promotion rules. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- src/nlls_gram/lm_core.py | 31 +++++++++++++++++++++++++------ src/nlls_gram/metric_lm.py | 1 + src/nlls_gram/ridge_lm.py | 1 + tests/test_failed_implicit_ad.py | 2 +- tests/test_instance_state.py | 26 ++++++++++++++++++++++++++ 5 files changed, 54 insertions(+), 7 deletions(-) diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index 8324304..e7c0ec7 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -56,6 +56,18 @@ def __eq__(self, other): def __hash__(self): return self._static_hash + # Sealed at the end of each subclass __init__: the configuration keys + # the compiled solve loop, so mutate-by-assignment would keep the stale + # key and silently reuse another configuration's compilation. + def __setattr__(self, name, value): + if getattr(self, "_sealed", False): + raise AttributeError( + f"{type(self).__name__} is frozen after construction: its " + "configuration keys the compiled solve loop. Build a new " + "solver instead of assigning attributes" + ) + object.__setattr__(self, name, value) + # Whether a callback-replaced metric moves the objective (the ridge # solver's penalty embeds it) or only the damping geometry. _metric_defines_objective = False @@ -290,20 +302,27 @@ def _action_or_default(self, action): def _check_instance_structure(self, new, previous, name): # Trace-time guard mirroring the hyper contract: a replaced instance # must be the same registered type with matching static fields and - # leaf shapes/dtypes, or the while-loop carry breaks downstream with - # a raw mismatch error that never names the culprit. + # leaf avals -- weak type included, since a weak/strong scalar swap + # passes the while-loop carry's physical checks but retraces the body + # under different promotion rules. def spec(tree): leaves, treedef = jax.tree_util.tree_flatten(tree) return treedef, [ - (jnp.shape(leaf), jnp.result_type(leaf)) for leaf in leaves + ( + jnp.shape(leaf), + jnp.result_type(leaf), + getattr(jax.typeof(jnp.asarray(leaf)), "weak_type", False), + ) + for leaf in leaves ] if spec(new) != spec(previous): raise ValueError( f"the callback action replaced lm_state.{name} with a " - "different type, structure, or leaf shape/dtype; rebuild the " - "same class with arrays matching the carried instance, and " - "preserve untouched fields with dataclasses.replace(ctx.lm_state, ...)" + "different type, structure, or leaf shape/dtype/weak-type; " + "rebuild the same class with arrays matching the carried " + "instance, and preserve untouched fields with " + "dataclasses.replace(ctx.lm_state, ...)" ) def _apply_action(self, action, x, lm_state, args, user_state): diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index 7f09715..d464b97 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -238,6 +238,7 @@ def __init__( ) ) self._static_hash = hash(self._static_key) + self._sealed = True def init(self, x0, args=None, *, p=None): """Build the initial :class:`~nlls_gram.LMState` at ``x0``. diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index d5988c4..69b5f7f 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -565,6 +565,7 @@ def __init__( ) ) self._static_hash = hash(self._static_key) + self._sealed = True def _resolve_ridge(self, dtype): if self.ridge is None: diff --git a/tests/test_failed_implicit_ad.py b/tests/test_failed_implicit_ad.py index 22e071b..8d34af1 100644 --- a/tests/test_failed_implicit_ad.py +++ b/tests/test_failed_implicit_ad.py @@ -119,7 +119,7 @@ def invalidate(ctx): x=-jnp.ones(1), lm_state=dataclasses.replace( ctx.lm_state, - metric=WeightedMetric(jnp.full((1,), jnp.nan)), + metric=WeightedMetric(jnp.full((1,), jnp.nan, dtype=ctx.x.dtype)), ), ) diff --git a/tests/test_instance_state.py b/tests/test_instance_state.py index 6c25efe..c98c919 100644 --- a/tests/test_instance_state.py +++ b/tests/test_instance_state.py @@ -140,6 +140,32 @@ def swap_in_loop(ctx): solver.solve(x0, max_steps=5, callback=swap_in_loop) +def test_solvers_are_frozen_after_construction(): + # The configuration keys the compiled loop, so mutating a constructed + # solver would silently reuse a stale compilation. + solver = LevenbergMarquardt(linear_residual) + with pytest.raises(AttributeError, match="frozen after construction"): + solver.geodesic_acceleration = False + with pytest.raises(AttributeError, match="frozen after construction"): + solver.residual_fn = linear_residual + + +def test_weak_type_instance_swap_raises(): + # A weak/strong scalar swap passes the carry's physical shape/dtype + # checks but retraces the loop body under different promotion rules, so + # the structure guard must reject it. + solver = RidgeLevenbergMarquardt(linear_residual, metric=make_metric(), ridge=1e-3) + x0 = jnp.zeros(P_DIM) + state = solver.init(x0) + leaves, treedef = jax.tree_util.tree_flatten(state.metric) + doctored = jax.tree_util.tree_unflatten( + treedef, [1.0 if jnp.ndim(leaf) == 0 else leaf for leaf in leaves] + ) + action = LMAction(lm_state=dataclasses.replace(state, metric=doctored)) + with pytest.raises(ValueError, match="lm_state.metric"): + solver._apply_action(action, x0, state, None, None) + + def test_untouched_metric_costs_no_comparison_ops(): # A callback that anneals the ridge via dataclasses.replace hands the # metric subtree back as the same tracers: the identity short-circuit From 294593b3112f970239b699b3c17095d35cded820 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 13:58:11 -0700 Subject: [PATCH 17/22] refactor!: drop min_damping/max_damping; keep the anti-underflow floor Both knobs guarded failure modes that are not failures. Without an upper cap, repeated rejections can overflow damping to inf in float32 -- but the step then goes to zero, every trial is rejected, x stays at the last accepted iterate, and the solve ends at MAX_STEPS with the best point it found. The dangerous case, a stall reported as convergence, is already blocked in _converged by `xtol_met & info.accepted`: a stalled solver only produces rejected steps, so xtol cannot fire. max_damping turned MAX_STEPS into MAX_STEPS. min_damping as a user knob was equally inert. It could only ever RAISE the floor (the resolver takes a max against the dtype floor), so the documented advice to "lower it (e.g. 1e-12)" was impossible to follow and would have introduced the endgame truncation it warned about. Damping falling freely is the point: the endgame wants it to vanish so the step approaches Gauss-Newton and the minimum-norm limit. Every test that pinned min_damping=1e-12 passes without it, against a floor 296 orders of magnitude lower. What remains is the internal floor at finfo(dtype).tiny, which guards something genuinely irreversible: the update is multiplicative, so a damping in a backend's flush-to-zero range is absorbing -- 0 * damping_increase stays 0 and the solver could never re-damp again. That floor is far below the scale at which damping still perturbs the Gram diagonal, so it is an anti-underflow backstop, not regularization; RidgeLevenbergMarquardt is the tool for that. A callback clamp replaces both knobs for the rare problem needing a bound, which is where 2.7.0 puts adaptive policy anyway. Behavior is unchanged for every caller that did not pass them: min_damping None already resolved to tiny and max_damping None already skipped the upper clamp. spooky's full replication is bit-identical across the change (387 leaves; only train_time moves) and a warm repeat run still writes zero .jax_cache entries. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/callbacks.md | 35 ++++++++++++++++++++---------- docs/tuning_guide.md | 11 ++++++---- src/nlls_gram/lm_core.py | 5 ----- src/nlls_gram/lm_types.py | 30 +++++++++++--------------- src/nlls_gram/metric_lm.py | 29 ++++++------------------- src/nlls_gram/ridge_lm.py | 29 ++++++------------------- tests/test_float64_subprocess.py | 2 +- tests/test_metric_lm.py | 37 ++++++++++++++------------------ 8 files changed, 73 insertions(+), 105 deletions(-) diff --git a/docs/callbacks.md b/docs/callbacks.md index d77f936..c7c6835 100644 --- a/docs/callbacks.md +++ b/docs/callbacks.md @@ -42,12 +42,25 @@ step, reported even when the step is rejected). Before the first update the loop's `LMInfo` uses sentinels `grad_norm=inf` and `step_norm=0`, so `gtol` and `xtol` cannot fire at step zero. -Repeated rejections multiply the damping by `damping_increase` without bound, -which can overflow in float32. The constructor's `max_damping` clamps the -damping from above; leave it `None` for uncapped classic behavior. Accepted -steps cannot underflow damping to zero: `min_damping=None` uses -`jnp.finfo(residual.dtype).tiny`, while an explicit value selects a larger -absolute floor. +Damping is floored at `jnp.finfo(residual.dtype).tiny`, the smallest positive +normal. This is an anti-underflow backstop, not regularization: the update is +multiplicative, so a damping in a backend's flush-to-zero range would be +absorbing — `0 * damping_increase` stays `0` and the solver could never +re-damp after a rejected step. The floor sits far below the scale at which +damping still perturbs the Gram diagonal, so it never alters a solve that was +going to make progress. To hold a larger floor, or to cap damping from above, +clamp it in a callback: + +```python +damping = jnp.clip(ctx.lm_state.damping, 1e-12, 1e6) +return LMAction(lm_state=dataclasses.replace(ctx.lm_state, damping=damping)) +``` + +Left unclamped, repeated rejections multiply damping by `damping_increase` +without bound and it can overflow to `inf` in float32. That is not a failure +mode worth guarding: the step goes to zero, every trial is rejected, `x` stays +at the last accepted iterate, and the solve ends at `MAX_STEPS` with the best +point it found. For genuine regularization, use `RidgeLevenbergMarquardt`. Status codes are integer constants: @@ -85,9 +98,9 @@ to second-guess a callback's explicit replacement. ### Resettable Hyperparameters `solve()` populates `lm_state.hyper` with an `LMHyperparams` of traced -per-step values: `damping_decrease`, `damping_increase`, `min_damping`, -`max_damping`, `geodesic_acceptance_ratio`, `iterative_tol`, `iterative_atol`, -and `iterative_maxiter`. Because they ride in the lm_state, a callback can reset +per-step values: `damping_decrease`, `damping_increase`, +`geodesic_acceptance_ratio`, `iterative_tol`, `iterative_atol`, and +`iterative_maxiter`. Because they ride in the lm_state, a callback can reset any of them mid-solve — exactly like a damping reset: ```python @@ -97,8 +110,8 @@ new_hyper = dataclasses.replace( return LMAction(lm_state=dataclasses.replace(ctx.lm_state, hyper=new_hyper)) ``` -Two contracts: knobs constructed as `None` (uncapped `max_damping`, -backend-default `iterative_maxiter`) are compiled out and stay `None` — a +Two contracts: knobs constructed as `None` (backend-default +`iterative_maxiter`) are compiled out and stay `None` — a callback cannot turn them on; and replacement values must be arrays of the same dtype (use `jnp.asarray`/`jnp.where`), since they live in the jitted loop carry. Static configuration — `linear_solver`, `geodesic_acceleration`, `cache_jacobian`, diff --git a/docs/tuning_guide.md b/docs/tuning_guide.md index fe70195..8c32433 100644 --- a/docs/tuning_guide.md +++ b/docs/tuning_guide.md @@ -39,13 +39,16 @@ recompilation. `init_damping=1e-3` with `damping_decrease=0.5` / `damping_increase=4.0` is the standard schedule. Reach for the others only on evidence: -- `min_damping` — lower it (e.g. `1e-12`) when the minimum-norm limit is the - point and the default floor is truncating the endgame; -- `max_damping` — cap it when a bad region sends damping to infinity and the - solver stalls instead of failing; - `geodesic_acceptance_ratio` — lower it when the second-order correction is being accepted on steps where it overshoots. +Damping is bounded only by an anti-underflow floor at +`jnp.finfo(residual.dtype).tiny`; there is no upper cap. Letting damping fall +freely is the point — the endgame wants it to vanish so the step approaches +Gauss–Newton and the minimum-norm limit. Clamp it in a callback on the rare +problem that needs a bound (see [Callbacks](callbacks.md)), and use +`RidgeLevenbergMarquardt` when what you actually want is regularization. + ## The ridge schedule For `RidgeLevenbergMarquardt`, a fixed ridge leaves an \(O(\text{ridge})\) diff --git a/src/nlls_gram/lm_core.py b/src/nlls_gram/lm_core.py index e7c0ec7..50927b5 100644 --- a/src/nlls_gram/lm_core.py +++ b/src/nlls_gram/lm_core.py @@ -18,7 +18,6 @@ LMAction, LMHyperparams, LMStatus, - _damping_floor, ) from nlls_gram.multi_start import ( MultiStart, @@ -192,10 +191,6 @@ def hyperparams(self, dtype=None): return LMHyperparams( jnp.asarray(self.damping_decrease, dtype=dtype), jnp.asarray(self.damping_increase, dtype=dtype), - _damping_floor(self.min_damping, dtype), - None - if self.max_damping is None - else jnp.asarray(self.max_damping, dtype=dtype), jnp.asarray(self.geodesic_acceptance_ratio, dtype=dtype), jnp.asarray(iterative_tol, dtype=dtype), jnp.asarray(self.iterative_atol, dtype=dtype), diff --git a/src/nlls_gram/lm_types.py b/src/nlls_gram/lm_types.py index e66f591..2272a46 100644 --- a/src/nlls_gram/lm_types.py +++ b/src/nlls_gram/lm_types.py @@ -77,30 +77,30 @@ class LMHyperparams: the inner CG budget as the loss falls -- via ``dataclasses.replace(ctx.lm_state, hyper=dataclasses.replace( ctx.lm_state.hyper, iterative_maxiter=...))``. A field constructed as - ``None`` (uncapped ``max_damping``, backend-default ``iterative_maxiter``) - is compiled out and stays ``None``. Static configuration -- the linear - solver, the metric, ``geodesic_acceleration``, ``cache_jacobian``, - ``has_aux`` -- shapes the compiled program and lives on the solver. + ``None`` (backend-default ``iterative_maxiter``) is compiled out and stays + ``None``. Static configuration -- the linear solver, the metric, + ``geodesic_acceleration``, ``cache_jacobian``, ``has_aux`` -- shapes the + compiled program and lives on the solver. """ damping_decrease: jax.Array damping_increase: jax.Array - min_damping: jax.Array - max_damping: jax.Array | None geodesic_acceptance_ratio: jax.Array iterative_tol: jax.Array iterative_atol: jax.Array iterative_maxiter: jax.Array | None -def _damping_floor(min_damping, dtype): +def _damping_floor(dtype): + # Smallest positive normal. Damping is updated multiplicatively, so a value + # in a backend's flush-to-zero range is absorbing: `0 * damping_increase` + # stays 0 and the solver could never re-damp after a rejected step. Far + # below the scale at which damping still perturbs the Gram diagonal, so it + # is an anti-underflow backstop, not regularization -- use the ridge solver + # for that. To hold a larger floor, clamp `damping` in a solve callback. if dtype is None: - seed = 0.0 if min_damping is None else min_damping - dtype = jnp.asarray(seed).dtype - dtype_floor = jnp.asarray(jnp.finfo(dtype).tiny, dtype=dtype) - if min_damping is None: - return dtype_floor - return jnp.maximum(jnp.asarray(min_damping, dtype=dtype), dtype_floor) + dtype = jnp.asarray(0.0).dtype + return jnp.asarray(jnp.finfo(dtype).tiny, dtype=dtype) def _cast_hyper(hyper, dtype): @@ -119,10 +119,6 @@ def _cast_hyper(hyper, dtype): return LMHyperparams( jnp.asarray(hyper.damping_decrease, dtype=dtype), jnp.asarray(hyper.damping_increase, dtype=dtype), - _damping_floor(hyper.min_damping, dtype), - None - if hyper.max_damping is None - else jnp.asarray(hyper.max_damping, dtype=dtype), jnp.asarray(hyper.geodesic_acceptance_ratio, dtype=dtype), iterative_tol, jnp.asarray(hyper.iterative_atol, dtype=dtype), diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index d464b97..b7aa5cd 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -107,8 +107,6 @@ def __init__( init_damping=1e-3, damping_decrease=0.5, damping_increase=4.0, - min_damping=None, - max_damping=None, linear_solver=Cholesky(), # noqa: B008 -- frozen, immutable default jacobian_mode="auto", ad_solver=None, @@ -122,10 +120,6 @@ def __init__( raise ValueError( "init_damping, damping_decrease, and damping_increase must be positive" ) - if min_damping is not None and not 0 < min_damping <= init_damping: - raise ValueError("min_damping must be positive and at most init_damping") - if max_damping is not None and max_damping < init_damping: - raise ValueError("max_damping must be at least init_damping") self.residual_fn = canonical_residual self.residual_arity = residual_arity self.initial_metric = _EuclideanMetric() if metric is None else metric @@ -133,8 +127,6 @@ def __init__( self.init_damping = init_damping self.damping_decrease = damping_decrease self.damping_increase = damping_increase - self.min_damping = min_damping - self.max_damping = max_damping self.linear_solver = linear_solver self.jacobian_mode = jacobian_mode self.ad_solver = ad_solver @@ -226,8 +218,6 @@ def __init__( init_damping, damping_decrease, damping_increase, - min_damping, - max_damping, _config_static_key(linear_solver, baked=False), jacobian_mode, _config_static_key(ad_solver, baked=True), @@ -252,8 +242,9 @@ def init(self, x0, args=None, *, p=None): theta, _ = ravel_pytree(x0) n_m, _ = self._block_sizes(theta.size) dtype = residual.dtype - min_damping = _damping_floor(self.min_damping, dtype) - damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) + damping = jnp.maximum( + jnp.asarray(self.init_damping, dtype=dtype), _damping_floor(dtype) + ) instances = dict( metric=self.initial_metric, preconditioner=self.initial_preconditioner ) @@ -357,9 +348,9 @@ def JT(cotangent): ) damping_decrease = jnp.asarray(hyper.damping_decrease, dtype=resid.dtype) damping_increase = jnp.asarray(hyper.damping_increase, dtype=resid.dtype) - min_damping = _damping_floor(hyper.min_damping, resid.dtype) + damping_floor = _damping_floor(resid.dtype) damping = jnp.maximum( - jnp.asarray(lm_state.damping, dtype=resid.dtype), min_damping + jnp.asarray(lm_state.damping, dtype=resid.dtype), damping_floor ) n_m, n_f = self._block_sizes(theta.shape[0]) @@ -449,15 +440,7 @@ def first_jvp(th): improved = jnp.isfinite(loss_candidate) & (loss_candidate < loss_old) theta_new = jnp.where(improved, theta + step, theta) damping_factor = jnp.where(improved, damping_decrease, damping_increase) - new_damping = damping * damping_factor - if hyper.max_damping is not None: - new_damping = jnp.minimum( - new_damping, - jnp.maximum( - jnp.asarray(hyper.max_damping, dtype=resid.dtype), min_damping - ), - ) - new_damping = jnp.maximum(new_damping, min_damping) + new_damping = jnp.maximum(damping * damping_factor, damping_floor) loss = jnp.where(improved, loss_candidate, loss_old) # The input state's instances pass through verbatim -- None stays diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index 69b5f7f..c829307 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -409,8 +409,6 @@ def __init__( init_damping=1e-3, damping_decrease=0.5, damping_increase=4.0, - min_damping=None, - max_damping=None, linear_solver=Cholesky(), # noqa: B008 -- frozen, immutable default jacobian_mode="auto", ad_solver=None, @@ -434,10 +432,6 @@ def __init__( raise ValueError( "init_damping, damping_decrease, and damping_increase must be positive" ) - if min_damping is not None and not 0 < min_damping <= init_damping: - raise ValueError("min_damping must be positive and at most init_damping") - if max_damping is not None and max_damping < init_damping: - raise ValueError("max_damping must be at least init_damping") self.residual_fn = canonical_residual self.residual_arity = residual_arity self.initial_metric = metric @@ -446,8 +440,6 @@ def __init__( self.init_damping = init_damping self.damping_decrease = damping_decrease self.damping_increase = damping_increase - self.min_damping = min_damping - self.max_damping = max_damping self.linear_solver = linear_solver self.jacobian_mode = jacobian_mode self.ad_solver = ad_solver @@ -553,8 +545,6 @@ def __init__( init_damping, damping_decrease, damping_increase, - min_damping, - max_damping, _config_static_key(linear_solver, baked=False), jacobian_mode, _config_static_key(ad_solver, baked=True), @@ -586,8 +576,9 @@ def init(self, x0, args=None, *, p=None): theta, _ = ravel_pytree(x0) n_m, _ = self._block_sizes(theta.size) dtype = residual.dtype - min_damping = _damping_floor(self.min_damping, dtype) - damping = jnp.maximum(jnp.asarray(self.init_damping, dtype=dtype), min_damping) + damping = jnp.maximum( + jnp.asarray(self.init_damping, dtype=dtype), _damping_floor(dtype) + ) ridge = self._resolve_ridge(dtype) instances = dict( metric=self.initial_metric, preconditioner=self.initial_preconditioner @@ -697,9 +688,9 @@ def JT(cotangent): ) damping_decrease = jnp.asarray(hyper.damping_decrease, dtype=resid.dtype) damping_increase = jnp.asarray(hyper.damping_increase, dtype=resid.dtype) - min_damping = _damping_floor(hyper.min_damping, resid.dtype) + damping_floor = _damping_floor(resid.dtype) damping = jnp.maximum( - jnp.asarray(lm_state.damping, dtype=resid.dtype), min_damping + jnp.asarray(lm_state.damping, dtype=resid.dtype), damping_floor ) if lm_state.ridge is None: # A None ridge is a legal LMState (the metric solver leaves it @@ -840,15 +831,7 @@ def accelerated_objective(_): improved = jnp.isfinite(loss_candidate) & (loss_candidate < loss_old) theta_new = jnp.where(improved, theta + step, theta) damping_factor = jnp.where(improved, damping_decrease, damping_increase) - new_damping = damping * damping_factor - if hyper.max_damping is not None: - new_damping = jnp.minimum( - new_damping, - jnp.maximum( - jnp.asarray(hyper.max_damping, dtype=resid.dtype), min_damping - ), - ) - new_damping = jnp.maximum(new_damping, min_damping) + new_damping = jnp.maximum(damping * damping_factor, damping_floor) loss = jnp.where(improved, loss_candidate, loss_old) resid_loss = jnp.where(improved, resid_loss_candidate, resid_loss_old) penalty_value = jnp.where(improved, penalty_candidate, penalty_value_old) diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index b2916a4..235f1ea 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -285,7 +285,7 @@ def sum_x(pv, ms=ms): ) -def test_float64_default_min_damping_uses_float64_normal_floor(): +def test_float64_damping_floor_is_the_float64_normal_floor(): script = r""" import jax jax.config.update("jax_enable_x64", True) diff --git a/tests/test_metric_lm.py b/tests/test_metric_lm.py index 175ce80..86b601b 100644 --- a/tests/test_metric_lm.py +++ b/tests/test_metric_lm.py @@ -99,7 +99,6 @@ def test_converges_to_the_minimum_metric_norm_root(name): linear_residual, metric=metric, linear_solver=FORWARD_SOLVERS[name], - min_damping=1e-12, ) result = solver.solve(jnp.zeros(N), max_steps=200, atol=1e-6) assert int(result.status) == int(LMStatus.CONVERGED) @@ -133,7 +132,7 @@ def test_diagonal_and_dense_metrics_agree_on_the_same_geometry(): dense = CholeskyMetric(jnp.diag(jnp.sqrt(weights))) x0 = jnp.zeros(N) results = [ - LevenbergMarquardt(linear_residual, metric=metric, min_damping=1e-12).solve( + LevenbergMarquardt(linear_residual, metric=metric).solve( x0, max_steps=200, atol=1e-6 ) for metric in (DiagonalMetric(weights), dense) @@ -162,7 +161,7 @@ def test_repeated_factor_metric_matches_its_dense_block_diagonal(): repeated = RepeatedFactorMetric( jnp.asarray(np.linalg.cholesky(K).T, jnp.float32), repeats=repeats ) - solver = LevenbergMarquardt(linear_residual, metric=repeated, min_damping=1e-12) + solver = LevenbergMarquardt(linear_residual, metric=repeated) result = solver.solve(jnp.zeros(N), max_steps=200, atol=1e-6) np.testing.assert_allclose( np.asarray(result.x), min_norm_solution(dense), rtol=3e-3, atol=3e-4 @@ -170,7 +169,7 @@ def test_repeated_factor_metric_matches_its_dense_block_diagonal(): def test_default_metric_is_euclidean(): - plain = LevenbergMarquardt(linear_residual, min_damping=1e-12).solve( + plain = LevenbergMarquardt(linear_residual).solve( jnp.zeros(N), max_steps=200, atol=1e-6 ) np.testing.assert_allclose( @@ -242,12 +241,12 @@ def test_rejected_step_leaves_x_and_marks_the_cache_reusable(): def test_solve_and_manual_update_loop_agree(): - solver = LevenbergMarquardt(linear_residual, min_damping=1e-12) + solver = LevenbergMarquardt(linear_residual) x = jnp.zeros(N) state = solver.init(x) for _ in range(40): x, state, _ = solver.update(x, state) - looped = LevenbergMarquardt(linear_residual, min_damping=1e-12).solve( + looped = LevenbergMarquardt(linear_residual).solve( jnp.zeros(N), max_steps=40, atol=0.0, gtol=0.0, xtol=0.0 ) np.testing.assert_allclose( @@ -264,9 +263,7 @@ def residual(x, args, p): x0 = {"head": jnp.zeros(N), "tail": jnp.zeros(2)} args = {"target": B} p = {"anchor": jnp.asarray([0.25, -0.5], jnp.float32)} - result = LevenbergMarquardt(residual, min_damping=1e-12).solve( - x0, args, p=p, max_steps=200, atol=1e-6 - ) + result = LevenbergMarquardt(residual).solve(x0, args, p=p, max_steps=200, atol=1e-6) assert int(result.status) == int(LMStatus.CONVERGED) np.testing.assert_allclose( np.asarray(result.x["tail"]), np.asarray(p["anchor"]), rtol=1e-4, atol=1e-5 @@ -293,7 +290,6 @@ def test_implicit_jvp_matches_the_analytic_min_norm_map(name): lambda x, args, p: A @ x - p["b"], metric=metric, ad_solver=AD_SOLVERS[name], - min_damping=1e-12, ) p = {"b": B} p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} @@ -312,7 +308,6 @@ def test_implicit_vjp_is_the_transpose_of_the_jvp(name): lambda x, args, p: A @ x - p["b"], metric=CholeskyMetric(L_W), ad_solver=AD_SOLVERS[name], - min_damping=1e-12, ) p = {"b": B} p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} @@ -342,7 +337,7 @@ def test_gram_cg_ad_rejects_the_overdetermined_shape(): def test_nonlinear_residual_solves_and_differentiates(): - solver = LevenbergMarquardt(nonlinear_residual, min_damping=1e-12) + solver = LevenbergMarquardt(nonlinear_residual) p = {"scale": jnp.asarray(1.0)} result = solver.solve(jnp.zeros(N), p=p, max_steps=300, atol=1e-5) assert int(result.status) == int(LMStatus.CONVERGED) @@ -371,12 +366,12 @@ def padded(x, args, p): return jnp.concatenate([A @ x - p["b"], jnp.zeros(pad)]) p = {"b": B} - unpadded = LevenbergMarquardt( - lambda x, args, p: A @ x - p["b"], min_damping=1e-12 - ).solve(jnp.zeros(N), p=p, max_steps=200, atol=1e-6) - padded_result = LevenbergMarquardt( - padded, ad_solver=SVD(), min_damping=1e-12 - ).solve(jnp.zeros(N), p=p, max_steps=200, atol=1e-6) + unpadded = LevenbergMarquardt(lambda x, args, p: A @ x - p["b"]).solve( + jnp.zeros(N), p=p, max_steps=200, atol=1e-6 + ) + padded_result = LevenbergMarquardt(padded, ad_solver=SVD()).solve( + jnp.zeros(N), p=p, max_steps=200, atol=1e-6 + ) # Two independently converged float32 solves, so the agreement is a # measured property rather than a tolerance bound. np.testing.assert_allclose( @@ -385,7 +380,7 @@ def padded(x, args, p): # The point of SVD() here is the TANGENT: padding makes the undamped dual # singular, and the spectral filter recovers the unpadded tangent anyway. p_dot = {"b": jnp.asarray(RNG.normal(size=M), jnp.float32)} - padded_solver = LevenbergMarquardt(padded, ad_solver=SVD(), min_damping=1e-12) + padded_solver = LevenbergMarquardt(padded, ad_solver=SVD()) tangent = jax.jvp( lambda pv: padded_solver.solve(jnp.zeros(N), p=pv, max_steps=200, atol=1e-6).x, (p,), @@ -399,7 +394,7 @@ def test_has_aux_reports_pre_step_aux_and_a_final_value(): def residual(x): return linear_residual(x), {"norm": jnp.sum(x**2)} - solver = LevenbergMarquardt(residual, has_aux=True, min_damping=1e-12) + solver = LevenbergMarquardt(residual, has_aux=True) x0 = jnp.ones(N) _, _, info = solver.update(x0, solver.init(x0)) np.testing.assert_allclose(float(info.aux["norm"]), float(N), rtol=1e-6) @@ -447,7 +442,7 @@ def residual(x, args, p): jnp.linalg.cholesky(jnp.asarray(W_NP[:4, :4], jnp.float32), upper=True), free_scale=free_scale, ) - solver = LevenbergMarquardt(residual, metric=metric, min_damping=1e-12) + solver = LevenbergMarquardt(residual, metric=metric) def run(pv, solver=solver): return solver.solve(jnp.zeros(N), p=pv, max_steps=200, atol=1e-6).x From 1688a9d37ebde76983c09b762c0fd38c591f9ff2 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 15:58:09 -0700 Subject: [PATCH 18/22] fix!: restore shape-aware implicit-AD defaults (LU when square, SVD otherwise) 2.6/2.7 collapsed the AD rules onto Cholesky: ad_solver=None resolved to the assembled normal/dual factorization at every dense shape. That lost both of 2.4.0's shape-appropriate defaults, and each loss is a real defect. Square (a DAE root, a determined system): 2.4.0 factored J itself via ad_solver="direct". Cholesky computes the same map through B'B, at cond(B)^2. Measured on a square constraint in float64, the tangent error tracked cond^2 * eps instead of cond * eps -- 2.6e-10 at cond=1e4, 7.1e-06 at 1e6, and 1.5e-01 at 1e8, where the correct answer is 1.3e-09 and the solve still reports CONVERGED. The new LU config restores it. Squareness is the exact condition that makes a plain solve valid: the tangent is unique, so no norm is minimized and the metric selects nothing, which is also why the square path can skip the whitening round-trip the rectangular rules need. One factorization serves both directions. LU is ad_solver-only (the damped forward subproblem is SPD at every shape) and raises on a rectangular system rather than guessing. Rectangular: 2.4.0 resolved to SVD, and this is the more serious loss. The undamped dual is singular whenever the small side is rank deficient, which is not exotic -- test_float64_svd_ad_solver_near_duplicate_rows already documents the growth-model pathology where a converged simulation duplicates its late-horizon states to ~1e-13. That test pinned the behavior with an explicit ad_solver=SVD(), so it kept passing while the default silently went to Cholesky. spooky's notebooks/growth_recursive_advanced.py, which differentiates a neural solve against a closed-form steady state, returned an all-NaN Jacobian under the Cholesky default and returns the analytically correct one under SVD. Verified across consumers: tinydiffeq 251 passed with the DAE reverse-mode regression closed (vjp-vector16-dae +18.4% -> -1.6%, worst DAE case +22.4% -> +3.2%); spooky's replication bit-identical on 385/385 non-timing leaves with zero new .jax_cache entries; kernels' multicountry AD experiment unchanged at its analytic neutrality bound (1.40e-10 both ways); spooky's advanced AD example NaN -> correct. Cholesky() remains available as the opt-in for a rectangular system whose small side is known to have full rank, trading tangent accuracy for speed. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/api.md | 1 + docs/implicit_ad.md | 15 ++++++--- docs/index.md | 7 +++-- docs/metric_lm.md | 14 +++++++-- src/nlls_gram/__init__.py | 2 ++ src/nlls_gram/linear_solvers.py | 28 +++++++++++++++++ src/nlls_gram/metric_lm.py | 34 +++++++++++++++++++- tests/test_float64_subprocess.py | 53 ++++++++++++++++++++++++++++++++ tests/test_metric_lm.py | 52 +++++++++++++++++++++++++++++++ 9 files changed, 197 insertions(+), 9 deletions(-) diff --git a/docs/api.md b/docs/api.md index 518c200..df0b8bb 100644 --- a/docs/api.md +++ b/docs/api.md @@ -12,6 +12,7 @@ ::: nlls_gram.QR ::: nlls_gram.CG ::: nlls_gram.GramCG +::: nlls_gram.LU ::: nlls_gram.SVD ## Metrics diff --git a/docs/implicit_ad.md b/docs/implicit_ad.md index 3001d0b..6c6fe37 100644 --- a/docs/implicit_ad.md +++ b/docs/implicit_ad.md @@ -26,16 +26,23 @@ Reverse mode comes from JAX transposing that linear tangent program, so `grad`, ## Choosing an `ad_solver` -`None`, the default, matches the forward family. Override it when the shape -or the rank says otherwise — see +`None`, the default, matches the forward family where that operator is +invertible and otherwise picks by shape: `LU()` for a square system, `SVD()` +for a rectangular one. Both err like \(\text{cond}(B)\varepsilon\); the normal +and dual factorizations err like \(\text{cond}(B)^2\varepsilon\), so the +default is also the accurate choice. Override it when you know more than the +shape does — see [Metric LM](metric_lm.md#rank-deficiency-and-implicit-ad) for the table of which rule is valid where. The short version: +- `LU()` for a square system; it is already the default, and it raises rather + than guessing if the system turns out rectangular; - `SVD()` whenever the undamped system is singular by construction — padded - zero residuals are the common case; + zero residuals are the common case, and again the default; - `GramCG(precond)` for \(m \le n\) and `CG(precond)` for \(n \le m\) when the forward solve is matrix-free and you want the tangent to stay so; -- `Cholesky()` otherwise. +- `Cholesky()` to trade tangent accuracy for speed on a rectangular system + whose small side is known to have full rank. A Krylov rule used outside its valid shape raises rather than returning a quietly wrong tangent. diff --git a/docs/index.md b/docs/index.md index a2915ce..d5a4c4f 100644 --- a/docs/index.md +++ b/docs/index.md @@ -84,6 +84,7 @@ method, so it cannot be passed with another. | `QR()` | damping-row QR of \([\tilde J;\sqrt\lambda I]\) | \(n\) | tiny damping or ridge; rank-safe | | `CG(precond)` | matrix-free normal | \(n\) | \(n \lesssim m\), no dense \(J\) | | `GramCG(precond)` | matrix-free dual | \(m\) | \(m \ll n\), no dense \(J\) | +| `LU()` | dense solve of \(B\) | \(n\) | `ad_solver` only: square tangents | | `SVD()` | pseudoinverse | — | `ad_solver` only: rank-deficient tangents | For \(\lambda > 0\) the gram and normal forms compute the *same* step (the @@ -91,8 +92,10 @@ push-through identity), so the choice is about cost, not semantics. A `preconditioner` is required for the Krylov configs — `IdentityPreconditioner()` is the explicit opt-out. -`ad_solver=None` (the default) matches the forward family, falling back to -`Cholesky()` where the forward config's undamped operator would be singular. +`ad_solver=None` (the default) matches the forward family where its undamped +operator is invertible, and otherwise picks by shape: `LU()` when \(m = n\), +`SVD()` when not. Both track \(\text{cond}(B)\); routing either through a +normal or dual factorization would square it. ## Where to go next diff --git a/docs/metric_lm.md b/docs/metric_lm.md index df7b0f4..ae454a9 100644 --- a/docs/metric_lm.md +++ b/docs/metric_lm.md @@ -70,12 +70,22 @@ otherwise: | `ad_solver` | needs | notes | |---|---|---| -| `None` | — | matches the forward family, falling back to `Cholesky()` | -| `Cholesky()` | full rank in the small side | factors whichever of \(BB^\top\), \(B^\top B\) is smaller | +| `None` | — | matches the forward family, else `LU()` if \(m = n\) and `SVD()` if not | +| `LU()` | \(m = n\) | solves \(B\) itself at \(\text{cond}(B)\); rejects a rectangular system | +| `Cholesky()` | full rank in the small side | factors whichever of \(BB^\top\), \(B^\top B\) is smaller, at \(\text{cond}(B)^2\) | | `SVD()` | nothing | spectral filter; the rule for padded zero residuals | | `CG(precond)` | \(n \le m\) | `penalty=` regularizes it for \(n > m\), at an \(O(\text{penalty})\) bias | | `GramCG(precond)` | \(m \le n\) | | +A **square** \(B\) is the case where the tangent is a plain nonsingular solve: +it is unique, so no norm is being minimized and the metric selects nothing. +That is what makes `LU()` valid there and why it is the default — and why the +square rule skips the whitening round-trip the rectangular rules require. It +also means one factorization serves both directions, forward mode solving with +\(B\) and reverse mode with \(B^\top\). `Cholesky()` computes the same map on +a square system but at \(\text{cond}(B)^2\), which costs roughly half the +significant digits of the tangent for nothing. + The **padded zero residual** pattern — appending identically-zero rows so compiled shapes stay stable across problem instances — makes the undamped dual singular by construction. `ad_solver=SVD()` computes the minimum-metric-norm diff --git a/src/nlls_gram/__init__.py b/src/nlls_gram/__init__.py index 9213446..e8341f5 100644 --- a/src/nlls_gram/__init__.py +++ b/src/nlls_gram/__init__.py @@ -28,6 +28,7 @@ from nlls_gram.linear_solvers import ( CG, + LU, QR, SVD, Cholesky, @@ -68,6 +69,7 @@ __all__ = [ "CG", + "LU", "QR", "SVD", "AnnealRidge", diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index 7bf28a3..15d60dd 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -614,6 +614,34 @@ def step(c): ) +@dataclass(frozen=True) +class LU(LinearSolver): + """Direct nonsymmetric solve of a SQUARE system, ``ad_solver`` role only. + + When the whitened Jacobian is square the implicit-AD system ``B u = -dr/dp`` + has a unique solution, so there is no norm being minimized and the metric + does not select among answers. That makes the plain factorization of ``B`` + available, and it is strictly better than routing through a normal or dual + operator: ``cond(B'B) = cond(B)^2``, so Cholesky loses half the significant + digits of the tangent for nothing. One factorization also serves both + directions -- forward mode solves with ``B``, reverse mode with ``B'``. + + This is why ``ad_solver=None`` resolves here for a square dense problem. + It requires squareness and says so: a rectangular system needs a selection + rule (minimum-metric-norm) that a plain solve cannot express, so + :class:`SVD` or the Cholesky forms own that case. + + The forward subproblem is damped and therefore symmetric positive definite + at every shape, so this config has no forward role. + """ + + supports_forward = False + supports_penalty = False + + def prepare(self, sub): + raise NotImplementedError("LU is an ad_solver, not a forward solver") + + @dataclass(frozen=True) class SVD(LinearSolver): """Spectral-filter pseudoinverse, for the ``ad_solver`` role only. diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index b7aa5cd..e011ded 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -25,6 +25,7 @@ from nlls_gram.linear_solvers import ( CG, + LU, SVD, Cholesky, GramCG, @@ -520,7 +521,24 @@ def _resolved_ad_solver(self, m, n): n <= m or self.linear_solver.penalty is not None ): return self.linear_solver - return Cholesky() + # Square: the tangent is a unique plain solve, so factor B itself + # rather than squaring its condition number through B'B. + if m == n: + return LU() + # Rectangular: the undamped system is singular whenever the small + # side is rank deficient, which padded zero residuals produce by + # construction, and the assembled Cholesky rules have no answer + # there. SVD selects the minimum-metric-norm tangent at cond(B) + # rather than cond(B)^2, so it is the safe default; Cholesky() is + # the opt-in when the small side is known to have full rank. + return SVD() + if isinstance(resolved, LU) and m != n: + raise ValueError( + f"ad_solver=LU() needs a square system, but the residual is {m} " + f"and x flattens to {n}: a rectangular tangent is selected by a " + "minimum-metric-norm rule that a plain solve cannot express. " + "Use SVD(), or Cholesky() when the small side has full rank" + ) if isinstance(resolved, GramCG) and m > n: raise ValueError( f"ad_solver=GramCG() needs m <= n, but the residual is {m} and " @@ -556,6 +574,13 @@ def _ad_x_tangent(self, x, args, p, p_dot, result, ad_success, initial_ad_point) x, args, p, p_dot ) resolved = self._resolved_ad_solver(residual.shape[0], theta.shape[0]) + if isinstance(resolved, LU): + # Square: J theta_dot = -dr/dp p_dot has a unique solution, so the + # metric selects nothing and the whitening round-trip below is + # avoidable work -- solve the unwhitened system directly. This is + # the same uniqueness that makes the plain factorization valid. + Jt = self._assemble_jt(theta_jvp, theta, residual) + return unravel(self._ad_tangent_lu(Jt, residual_p_dot)) ctx = SolverContext(x=theta, lm_state=lm_state, args=args, p=p) n_m, n_f = self._block_sizes(theta.shape[0]) dtype = residual.dtype @@ -608,6 +633,13 @@ def _ad_tangent_dense(self, Bt, residual_p_dot): factor = jsp_linalg.cho_factor(Bt @ Bt.T) return -jsp_linalg.cho_solve(factor, Bt @ residual_p_dot) + def _ad_tangent_lu(self, Bt, residual_p_dot): + # Square B: u = -B^{-1} (dr/dp) p_dot, factored directly. The normal + # form (B'B)^{-1}B' is algebraically the same map here but numerically + # worse, at cond(B)^2. Reverse mode transposes this solve, which is the + # same factorization applied to B'. + return -jnp.linalg.solve(Bt.T, residual_p_dot) + def _ad_tangent_svd(self, Bt, residual_p_dot): # Spectral filter: u = -B^+ (dr/dp) p_dot, the minimum-metric-norm # tangent. This is the rule for the singular undamped systems that diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index 235f1ea..49e6dc0 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -715,3 +715,56 @@ def run(p_in): text=True, ) assert result.returncode == 0, result.stderr + result.stdout + + +def test_float64_square_implicit_tangent_tracks_cond_not_cond_squared(): + # The square AD rule factors J directly, so the tangent errs like + # cond(J) * eps. Routing the same system through Cholesky on J'J errs + # like cond(J)^2 * eps -- at cond = 1e8 in float64 that is a tangent with + # no correct digits, reported as a converged solve. + script = r""" +import jax +jax.config.update("jax_enable_x64", True) +import jax.numpy as jnp +import numpy as np + +from nlls_gram import Cholesky, LevenbergMarquardt + +n = 12 +rng = np.random.default_rng(0) +u, _ = np.linalg.qr(rng.standard_normal((n, n))) +v, _ = np.linalg.qr(rng.standard_normal((n, n))) +A_np = u @ np.diag(np.logspace(0, -8, n)) @ v.T +A = jnp.asarray(A_np) +p0 = jnp.asarray(rng.standard_normal(n)) +direction = jnp.asarray(rng.standard_normal(n)) +expected = np.linalg.solve(A_np, np.asarray(direction)) + + +def tangent_error(ad_solver): + solver = LevenbergMarquardt( + lambda x, args, p: A @ x - p, + ad_solver=ad_solver, + cache_jacobian=False, + geodesic_acceleration=False, + ) + + def run(p_value): + return solver.solve(jnp.zeros(n), p=p_value, max_steps=200, atol=1e-13).x + + got = jax.jvp(run, (p0,), (direction,))[1] + return float(jnp.linalg.norm(got - expected) / jnp.linalg.norm(expected)) + + +auto = tangent_error(None) +normal = tangent_error(Cholesky()) +assert auto < 1e-7, auto +assert auto < normal / 1000.0, (auto, normal) +""" + result = subprocess.run( + [sys.executable, "-c", textwrap.dedent(script)], + check=False, + capture_output=True, + text=True, + ) + assert result.returncode == 0, result.stderr + result.stdout diff --git a/tests/test_metric_lm.py b/tests/test_metric_lm.py index 86b601b..e3dbf1a 100644 --- a/tests/test_metric_lm.py +++ b/tests/test_metric_lm.py @@ -16,6 +16,7 @@ from nlls_gram import ( CG, + LU, QR, SVD, Cholesky, @@ -419,6 +420,7 @@ def build(): "kwargs,message", [ (dict(linear_solver=SVD()), "linear_solver"), + (dict(linear_solver=LU()), "linear_solver"), (dict(ad_solver=QR()), "ad_solver"), ], ) @@ -428,6 +430,56 @@ def test_a_config_in_a_role_it_cannot_fill_is_rejected(kwargs, message): LevenbergMarquardt(linear_residual, **kwargs) +def test_auto_ad_solver_is_lu_when_square_and_svd_otherwise(): + # Square has a unique tangent, so the plain factorization applies at + # cond(B); the normal/dual forms would square it for nothing. Rectangular + # needs the minimum-metric-norm selection, and its undamped operator is + # singular exactly where padded residuals make the small side deficient, + # so the rank-safe rule is the default rather than an opt-in. + solver = LevenbergMarquardt(linear_residual) + assert isinstance(solver._resolved_ad_solver(8, 8), LU) + assert isinstance(solver._resolved_ad_solver(4, 8), SVD) + assert isinstance(solver._resolved_ad_solver(8, 4), SVD) + + +def test_lu_ad_solver_requires_a_square_system(): + solver = LevenbergMarquardt(linear_residual, ad_solver=LU()) + assert isinstance(solver._resolved_ad_solver(8, 8), LU) + for m, n in ((4, 8), (8, 4)): + with pytest.raises(ValueError, match="square"): + solver._resolved_ad_solver(m, n) + + +def test_square_implicit_tangent_uses_the_unwhitened_direct_solve(): + # The square rule solves J theta_dot = -dr/dp directly: the tangent is + # unique, so the metric selects nothing and the whitening round-trip the + # rectangular rules need is skipped. A non-identity metric must therefore + # leave the square tangent unchanged. + A_sq = jnp.asarray(RNG.normal(size=(N, N)), jnp.float32) + p0 = jnp.asarray(RNG.normal(size=N), jnp.float32) + direction = jnp.asarray(RNG.normal(size=N), jnp.float32) + + def tangent(metric): + solver = LevenbergMarquardt( + lambda x, args, p: A_sq @ x - p, + metric=metric, + cache_jacobian=False, + geodesic_acceleration=False, + ) + + def run(p_value): + return solver.solve(jnp.zeros(N), p=p_value, max_steps=200, atol=1e-6).x + + return jax.jvp(run, (p0,), (direction,))[1] + + np.testing.assert_allclose( + np.asarray(tangent(None)), + np.asarray(tangent(CholeskyMetric(L_W))), + rtol=1e-4, + atol=1e-5, + ) + + def test_free_scale_changes_the_step_and_its_tangent(): # free_scale is the free block's damping weight, so it must move both the # forward step and the implicit tangent -- not be quietly ignored. From cd471a9f374e5fefdf478647bb4eb96157af9d24 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 16:25:25 -0700 Subject: [PATCH 19/22] test: float32 coverage for solvers, implicit AD, and preconditioners nlls-gram has no ad/metric solve-dtype knob -- the 2.6/2.7 refactor removed linear_solve_dtype, metric_solve_dtype and ad_dtype -- so a float32 problem must stay float32 end to end, at float32 accuracy, with no promotion to recover conditioning. Nothing pinned that. tests/test_float32.py runs at default precision and covers, for each config, both dtype purity and accuracy against a float64 reference, so a silently promoted solve and a silently wrong one each fail: dense forward solvers (Cholesky auto/gram/normal, QR), matrix-free (CG, GramCG), the implicit-AD rules on a rectangular system (auto->SVD, SVD, Cholesky, GramCG) and on a square one (auto->LU, LU, SVD), the metrics, and every preconditioner. test_float64_subprocess.py gains the harder direction: x64 ENABLED with float32 inputs, where Python scalars default to f64 and can promote the whole compute silently. Across 18 configurations no primal, jvp or vjp jaxpr contains an f64 compute op; f64 appears only in explicit convert_element_type at the call boundary. This also gives NystromPreconditioner, WoodburyPreconditioner, ShermanMorrisonPreconditioner and PaddedPreconditioner their first tests -- only BlockEigen and Identity had any. The apply contract is checked for float32, finiteness and SPD (v'Mv > 0 plus symmetry on a random pair), and GramCG is run end to end under each dual preconditioner to confirm a preconditioner changes the CG path but not the converged step. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- tests/test_float32.py | 231 +++++++++++++++++++++++++++++++ tests/test_float64_subprocess.py | 152 ++++++++++++++++++++ 2 files changed, 383 insertions(+) create mode 100644 tests/test_float32.py diff --git a/tests/test_float32.py b/tests/test_float32.py new file mode 100644 index 0000000..76a8fa1 --- /dev/null +++ b/tests/test_float32.py @@ -0,0 +1,231 @@ +"""float32 coverage: dtype purity and accuracy across the config matrix. + +This module runs at JAX's default precision (x64 OFF), so every array is +float32 unless something promotes it. The x64-ENABLED-with-float32-inputs +case -- where Python scalars default to f64 and can silently promote the whole +compute -- is the more dangerous one and lives in test_float64_subprocess.py, +which needs a subprocess to set the flag before JAX initializes. + +Nothing here promotes a solve to float64: nlls-gram has no ad/metric solve +dtype knob, so float32 in must mean float32 out, at float32 accuracy. +""" + +import jax +import jax.numpy as jnp +import numpy as np +import pytest + +from nlls_gram import ( + CG, + LU, + QR, + SVD, + BlockEigenPreconditioner, + Cholesky, + CholeskyMetric, + DiagonalMetric, + GramCG, + IdentityPreconditioner, + LevenbergMarquardt, + LMState, + LMStatus, + NystromPreconditioner, + PaddedPreconditioner, + ShermanMorrisonPreconditioner, + SolverContext, + WoodburyPreconditioner, +) + +RNG = np.random.default_rng(5) +M, N = 4, 7 # underdetermined: the package's target regime +A_NP = RNG.normal(size=(M, N)) +B_NP = RNG.normal(size=M) +A = jnp.asarray(A_NP, jnp.float32) +B = jnp.asarray(B_NP, jnp.float32) +X0 = jnp.zeros(N, jnp.float32) + +A_SQ_NP = RNG.normal(size=(N, N)) + N * np.eye(N) # square and well conditioned +A_SQ = jnp.asarray(A_SQ_NP, jnp.float32) +P_SQ = jnp.asarray(RNG.normal(size=N), jnp.float32) +X0_SQ = jnp.zeros(N, jnp.float32) + + +def fat_residual(x, args, p): + return A @ x - p + + +def square_residual(x, args, p): + return A_SQ @ x - p + + +def min_norm(b): + return A_NP.T @ np.linalg.solve(A_NP @ A_NP.T, np.asarray(b, np.float64)) + + +FORWARD = { + "cholesky_auto": Cholesky(), + "cholesky_gram": Cholesky(form="gram"), + "cholesky_normal": Cholesky(form="normal"), + "qr": QR(), + "cg": CG(IdentityPreconditioner(), tol=1e-7, maxiter=200), + "gram_cg": GramCG(IdentityPreconditioner(), tol=1e-7, maxiter=200), +} + + +@pytest.mark.parametrize("name", list(FORWARD)) +def test_float32_forward_solvers_stay_float32_and_hit_the_min_norm_root(name): + solver = LevenbergMarquardt(fat_residual, linear_solver=FORWARD[name]) + result = solver.solve(X0, None, p=B, max_steps=200, atol=1e-5) + assert int(result.status) == int(LMStatus.CONVERGED) + assert result.x.dtype == jnp.float32 + assert result.lm_state.damping.dtype == jnp.float32 + assert result.info.loss.dtype == jnp.float32 + np.testing.assert_allclose(np.asarray(result.x), min_norm(B), rtol=2e-3, atol=2e-4) + + +AD_RULES_FAT = { + "auto": None, # -> SVD for a rectangular system + "svd": SVD(), + "cholesky": Cholesky(), + "gram_cg": GramCG(IdentityPreconditioner(), tol=1e-7, maxiter=200), +} + + +@pytest.mark.parametrize("name", list(AD_RULES_FAT)) +def test_float32_implicit_tangent_is_float32_and_matches_the_min_norm_map(name): + # x*(b) is linear in b here, so the tangent is the same map applied to b_dot. + solver = LevenbergMarquardt(fat_residual, ad_solver=AD_RULES_FAT[name]) + b_dot = jnp.asarray(RNG.normal(size=M), jnp.float32) + + def run(p): + return solver.solve(X0, None, p=p, max_steps=200, atol=1e-6).x + + tangent = jax.jvp(run, (B,), (b_dot,))[1] + (cotangent,) = jax.vjp(run, B)[1](jnp.ones(N, jnp.float32)) + + assert tangent.dtype == jnp.float32 + assert cotangent.dtype == jnp.float32 + assert jnp.all(jnp.isfinite(tangent)) and jnp.all(jnp.isfinite(cotangent)) + np.testing.assert_allclose( + np.asarray(tangent), min_norm(b_dot), rtol=3e-3, atol=3e-4 + ) + + +AD_RULES_SQUARE = {"auto": None, "lu": LU(), "svd": SVD()} + + +@pytest.mark.parametrize("name", list(AD_RULES_SQUARE)) +def test_float32_square_tangent_is_float32_and_matches_the_direct_solve(name): + solver = LevenbergMarquardt(square_residual, ad_solver=AD_RULES_SQUARE[name]) + direction = jnp.asarray(RNG.normal(size=N), jnp.float32) + + def run(p): + return solver.solve(X0_SQ, None, p=p, max_steps=200, atol=1e-6).x + + tangent = jax.jvp(run, (P_SQ,), (direction,))[1] + expected = np.linalg.solve(A_SQ_NP, np.asarray(direction, np.float64)) + assert tangent.dtype == jnp.float32 + np.testing.assert_allclose(np.asarray(tangent), expected, rtol=3e-3, atol=3e-4) + + +@pytest.mark.parametrize( + "metric", + [ + None, + DiagonalMetric(jnp.linspace(0.5, 2.0, N, dtype=jnp.float32)), + CholeskyMetric(jnp.eye(N, dtype=jnp.float32) * 1.5), + ], + ids=["euclidean", "diagonal", "cholesky"], +) +def test_float32_metrics_keep_the_solve_and_its_tangent_float32(metric): + solver = LevenbergMarquardt(fat_residual, metric=metric) + + def run(p): + return solver.solve(X0, None, p=p, max_steps=200, atol=1e-5).x + + x = run(B) + tangent = jax.jvp(run, (B,), (jnp.ones(M, jnp.float32),))[1] + assert x.dtype == jnp.float32 + assert tangent.dtype == jnp.float32 + assert jnp.all(jnp.isfinite(x)) and jnp.all(jnp.isfinite(tangent)) + + +# --- preconditioners ------------------------------------------------------- +# Nystrom, Woodbury, Sherman-Morrison and Padded had no coverage at all; these +# check the apply contract in float32 against a dense reference. + +DUAL = A_NP @ A_NP.T + 0.5 * np.eye(M) # an SPD m x m dual operator + + +def dual_solve(v): + """Static hashable A^-1 for the low-rank-update preconditioners.""" + return jnp.linalg.solve(jnp.asarray(DUAL, jnp.float32), v) + + +def dual_matvec(X): + return jnp.asarray(DUAL, jnp.float32) @ X + + +def preconditioner_cases(): + u = jnp.asarray(RNG.normal(size=M), jnp.float32) + U = jnp.asarray(RNG.normal(size=(M, 2)), jnp.float32) + weights = jnp.asarray([0.4, 0.7], jnp.float32) + families = [(jnp.asarray(np.eye(2)[None] * 2.0, jnp.float32), 1.0)] + return { + "identity": (IdentityPreconditioner(), M), + "sherman_morrison": ( + ShermanMorrisonPreconditioner(dual_solve, u, jnp.asarray(0.3, jnp.float32)), + M, + ), + "woodbury": (WoodburyPreconditioner(dual_solve, U, weights), M), + "nystrom": ( + NystromPreconditioner( + dual_matvec, n=M, rank=2, key=jax.random.key(0), dtype=jnp.float32 + ), + M, + ), + "block_eigen": ( + BlockEigenPreconditioner(families, jnp.arange(2)), + 2, + ), + "padded": (PaddedPreconditioner(IdentityPreconditioner(), n_real=M - 1), M), + } + + +@pytest.mark.parametrize("name", list(preconditioner_cases())) +def test_float32_preconditioner_apply_is_float32_finite_and_spd(name): + preconditioner, size = preconditioner_cases()[name] + damping = jnp.asarray(0.1, jnp.float32) + # BlockEigen reads the carried ridge, so the state must be real; the metric + # solver carries ridge=None, which is the LevenbergMarquardt case. + ctx = SolverContext(x=None, lm_state=LMState(damping=damping), args=None, p=None) + v = jnp.asarray(RNG.normal(size=size), jnp.float32) + + out = preconditioner.apply(v, damping, ctx) + assert out.dtype == jnp.float32, out.dtype + assert jnp.all(jnp.isfinite(out)) + + # SPD: v'M v > 0, and the map is symmetric on a random pair. + assert float(jnp.dot(v, out)) > 0.0 + w = jnp.asarray(RNG.normal(size=size), jnp.float32) + left = float(jnp.dot(w, preconditioner.apply(v, damping, ctx))) + right = float(jnp.dot(v, preconditioner.apply(w, damping, ctx))) + np.testing.assert_allclose(left, right, rtol=2e-3, atol=2e-5) + + +DUAL_PRECONDITIONERS = ["identity", "sherman_morrison", "woodbury", "nystrom"] + + +@pytest.mark.parametrize("name", DUAL_PRECONDITIONERS) +def test_float32_gram_cg_converges_under_each_dual_preconditioner(name): + # A preconditioner may only change the CG path, never the converged step. + preconditioner, _ = preconditioner_cases()[name] + solver = LevenbergMarquardt( + fat_residual, + linear_solver=GramCG(preconditioner, tol=1e-7, maxiter=200), + ad_solver=SVD(), + ) + result = solver.solve(X0, None, p=B, max_steps=200, atol=1e-5) + assert int(result.status) == int(LMStatus.CONVERGED) + assert result.x.dtype == jnp.float32 + np.testing.assert_allclose(np.asarray(result.x), min_norm(B), rtol=3e-3, atol=3e-4) diff --git a/tests/test_float64_subprocess.py b/tests/test_float64_subprocess.py index 49e6dc0..103adfa 100644 --- a/tests/test_float64_subprocess.py +++ b/tests/test_float64_subprocess.py @@ -768,3 +768,155 @@ def run(p_value): text=True, ) assert result.returncode == 0, result.stderr + result.stdout + + +def test_float32_problem_under_x64_never_promotes_solvers_ad_or_preconditioners(): + # The dangerous direction: with x64 ENABLED, Python scalars default to f64 + # and can silently promote a float32 problem's whole compute. Every config + # must keep its arithmetic in f32, with f64 appearing only where a + # call-boundary scalar is explicitly converted. + script = r""" +import jax +jax.config.update("jax_enable_x64", True) +import jax.numpy as jnp +import numpy as np + +from nlls_gram import ( + CG, + LU, + QR, + SVD, + Cholesky, + CholeskyMetric, + DiagonalMetric, + GramCG, + IdentityPreconditioner, + LevenbergMarquardt, + NystromPreconditioner, + ShermanMorrisonPreconditioner, + WoodburyPreconditioner, +) + +rng = np.random.default_rng(3) +m, n = 4, 7 +A = jnp.asarray(rng.normal(size=(m, n)), jnp.float32) +b = jnp.asarray(rng.normal(size=m), jnp.float32) +x0 = jnp.zeros(n, jnp.float32) +A_sq = jnp.asarray(rng.normal(size=(n, n)) + n * np.eye(n), jnp.float32) +p_sq = jnp.asarray(rng.normal(size=n), jnp.float32) +x0_sq = jnp.zeros(n, jnp.float32) +dual = jnp.asarray(A) @ jnp.asarray(A).T + 0.5 * jnp.eye(m, dtype=jnp.float32) + + +def fat(x, args, p): + return A @ x - p + + +def square(x, args, p): + return A_sq @ x - p + + +def dual_solve(v): + return jnp.linalg.solve(dual, v) + + +def dual_matvec(X): + return dual @ X + + +def promotions(text): + bad = [] + for line in text.splitlines(): + s = line.strip() + if " = " in s and ":f64[" in s.split(" = ")[0]: + if "convert_element_type" not in s: + bad.append(s[:100]) + return bad + + +def check(label, solver, residual, start, p_value, cotangent_size): + def run(p): + return solver.solve(start, None, p=p, max_steps=6, atol=1e-5).x + + traces = { + "primal": jax.make_jaxpr(run)(p_value), + "jvp": jax.make_jaxpr( + lambda p: jax.jvp(run, (p,), (jnp.ones_like(p),))[1] + )(p_value), + "vjp": jax.make_jaxpr( + lambda p: jax.vjp(run, p)[1](jnp.ones(cotangent_size, jnp.float32))[0] + )(p_value), + } + for mode, jaxpr in traces.items(): + bad = promotions(str(jaxpr)) + assert not bad, f"{label} [{mode}] promoted to f64:\n" + "\n".join(bad[:4]) + assert run(p_value).dtype == jnp.float32, label + + +precond = IdentityPreconditioner() +for label, kwargs in [ + ("cholesky", dict(linear_solver=Cholesky())), + ("cholesky_gram", dict(linear_solver=Cholesky(form="gram"))), + ("cholesky_normal", dict(linear_solver=Cholesky(form="normal"))), + ("qr", dict(linear_solver=QR())), + ("cg", dict(linear_solver=CG(precond, maxiter=8), ad_solver=SVD())), + ("gram_cg", dict(linear_solver=GramCG(precond, maxiter=8))), + ("ad_auto_svd", dict()), + ("ad_svd", dict(ad_solver=SVD())), + ("ad_cholesky", dict(ad_solver=Cholesky())), + ("ad_gram_cg", dict(ad_solver=GramCG(precond, maxiter=8))), + ("metric_diagonal", dict(metric=DiagonalMetric(jnp.ones(n, jnp.float32) * 2))), + ("metric_cholesky", dict(metric=CholeskyMetric(jnp.eye(n, dtype=jnp.float32)))), + ( + "precond_sherman_morrison", + dict( + linear_solver=GramCG( + ShermanMorrisonPreconditioner( + dual_solve, + jnp.asarray(rng.normal(size=m), jnp.float32), + jnp.asarray(0.3, jnp.float32), + ), + maxiter=8, + ), + ad_solver=SVD(), + ), + ), + ( + "precond_woodbury", + dict( + linear_solver=GramCG( + WoodburyPreconditioner( + dual_solve, + jnp.asarray(rng.normal(size=(m, 2)), jnp.float32), + jnp.asarray([0.4, 0.7], jnp.float32), + ), + maxiter=8, + ), + ad_solver=SVD(), + ), + ), + ( + "precond_nystrom", + dict( + linear_solver=GramCG( + NystromPreconditioner( + dual_matvec, n=m, rank=2, key=jax.random.key(0), dtype=jnp.float32 + ), + maxiter=8, + ), + ad_solver=SVD(), + ), + ), +]: + check(label, LevenbergMarquardt(fat, **kwargs), fat, x0, b, n) + +for label, ad in [("square_auto_lu", None), ("square_lu", LU()), ("square_svd", SVD())]: + check(label, LevenbergMarquardt(square, ad_solver=ad), square, x0_sq, p_sq, n) +""" + result = subprocess.run( + [sys.executable, "-c", textwrap.dedent(script)], + check=False, + capture_output=True, + text=True, + ) + assert result.returncode == 0, result.stderr + result.stdout From 5a58142e94ba0b8f1cd0b2661479ff87d2623930 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 17:21:26 -0700 Subject: [PATCH 20/22] fix: pin internal matmuls to HIGHEST so float32 is not served from TF32 XLA:GPU serves float32 dot_general from TF32 tensor cores by default on Ampere and later: a 10-bit mantissa, so ~1e-3 relative where float32 is ~1e-7. Forming a Gram or normal matrix already squares the condition number, so paying TF32 on top spends about three decimal digits before the factorization starts. That is not a trade this package should be making silently on a user's behalf. It was doing exactly that. Eleven tests fail on an RTX 3090 and pass on CPU -- cross-solver step agreement, the metric factor round-trip, the block-eigen apply against its dense inverse, and the CG-vs-Cholesky implicit tangent -- every one of them a comparison routing through a product. They are not a regression: the same eleven fail at 0643a49, before any of this branch. They are also not tolerance problems. On the 3090: default (TF32) 11 failed, 20 passed JAX_DEFAULT_MATMUL_PRECISION=highest 31 passed Every product the package owns now goes through utilities.mm (or passes precision=HIGHEST to einsum): the Gram and normal assembly, the matrix-free CG operator, the QR back-substitution, the metric factor applications, all six preconditioners, the state-space metric scans, and the implicit-AD tangent solves. Unconditional, with no opt-out knob -- a float32 solve now answers the same on GPU as on CPU, where the setting is a no-op. The metric round-trip is the tell for why this is the right layer: factor_apply is a matmul and factor_solve is a triangular solve, so each op looked fine alone while the round-trip drifted. tests/conftest.py sets jax_default_matmul_precision globally, which the package's own pinning does NOT cover: the tests build dense references of their own, and without it those would stay TF32 and the comparison would fail on the reference side. To keep that from masking the library change, a new test traces a solve whose residual contains no matmul -- so every dot_general in the jaxpr is the solver's -- and asserts each carries HIGHEST. Asserting on the jaxpr rather than on numbers makes it device-independent, so CPU CI guards the GPU path; there is no GPU runner. The float32 tolerances are untouched. They sit above the TF32 floor, which is why all 26 float32 tests passed on GPU while the library was degraded -- they now pass for the right reason. docs/tuning_guide.md gains a section on the trap, what the package pins, what it cannot reach (matmuls in the caller's residual), and the failure signature: CPU and GPU agreeing to about three digits and no further, worst in the tangent. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/tuning_guide.md | 42 +++++++++++++++++ src/nlls_gram/experimental/quasiseparable.py | 36 +++++++------- src/nlls_gram/linear_solvers.py | 24 ++++++---- src/nlls_gram/metric_lm.py | 11 +++-- src/nlls_gram/metrics.py | 6 +-- src/nlls_gram/preconditioners.py | 28 ++++++----- src/nlls_gram/ridge_lm.py | 5 +- src/nlls_gram/utilities.py | 21 ++++++++- tests/conftest.py | 9 ++++ tests/test_float32.py | 49 ++++++++++++++++++++ 10 files changed, 181 insertions(+), 50 deletions(-) create mode 100644 tests/conftest.py diff --git a/docs/tuning_guide.md b/docs/tuning_guide.md index 8c32433..d5a928c 100644 --- a/docs/tuning_guide.md +++ b/docs/tuning_guide.md @@ -89,3 +89,45 @@ the callback, any shape, and any instance **static field** (a metric's | `CONVERGED` but the residual is large | `atol` fired on the wrong scale, or `gtol` alone stopped a ridge level | | tangent finite but wrong | the `ad_solver`'s operator is singular for this shape — see [Metric LM](metric_lm.md#rank-deficiency-and-implicit-ad) | | every solve recompiles | a metric, preconditioner, or callback rebuilt per call | + +## GPU matmul precision in float32 + +On an NVIDIA GPU from Ampere onward, XLA serves float32 `dot_general` from +TF32 tensor cores by default: a 10-bit mantissa, so about \(10^{-3}\) relative +error rather than float32's \(10^{-7}\). That is a poor trade here. Forming a +Gram or normal matrix already squares the condition number, so paying TF32 on +top spends roughly three decimal digits before the factorization starts — +enough to move a converged step and to leave an implicit tangent visibly +wrong. + +Every product **inside** this package is therefore pinned to +`jax.lax.Precision.HIGHEST`, unconditionally and with no opt-out: the Gram and +normal assembly, the matrix-free CG operator, the metric factor applications, +the preconditioner contractions, and the implicit-AD solves. A float32 solve +answers the same on GPU as on CPU, where the setting is a no-op. + +What the package cannot reach is **your** code — the matmuls inside your +residual function, and any dense reference you compare against. Set the +default near the top of a script: + +```python +import jax + +jax.config.update("jax_default_matmul_precision", "highest") +``` + +or export `JAX_DEFAULT_MATMUL_PRECISION=highest`. There is no reason not to +for this class of problem; TF32's speed only pays on large, well-conditioned +matmuls, which is not what a least-squares solve is doing. + +The failure signature, if it is ever missed: results that agree between CPU +and GPU to about three digits and no further, with the gap concentrated in +whichever quantity passed through the most products — typically the tangent +before the primal. + +CI has no GPU runner, so `tests/test_gpu.py` is skipped there. Run it on a +GPU box explicitly: + +```bash +uv run --group gpu pytest -q +``` diff --git a/src/nlls_gram/experimental/quasiseparable.py b/src/nlls_gram/experimental/quasiseparable.py index eedeb86..a051cbb 100644 --- a/src/nlls_gram/experimental/quasiseparable.py +++ b/src/nlls_gram/experimental/quasiseparable.py @@ -31,6 +31,8 @@ import jax import jax.numpy as jnp +from nlls_gram.utilities import HIGHEST, mm + def matern_state_space(sigma, ell, nu): """Return the ``(h, Pinf, transition)`` state-space model of a Matern kernel. @@ -144,10 +146,10 @@ def _state_space_generators(points, h, Pinf, transition): # The dt=0 shift trick makes A[0] = transition(0) = I. dt = points - jnp.concatenate([points[:1], points[:-1]]) A = transition(dt) - hP = h @ Pinf - d = jnp.full((n,), hP @ h) + hP = mm(h, Pinf) + d = jnp.full((n,), mm(hP, h)) q = jnp.broadcast_to(h, (n, h.shape[0])) - p = jnp.einsum("i,kij->kj", hP, A) + p = jnp.einsum("i,kij->kj", hP, A, precision=HIGHEST) return d, p, q, A @@ -157,10 +159,10 @@ def _cholesky(d, p, q, A): def step(F, inputs): d_k, p_k, q_k, A_k = inputs - c_k = jnp.sqrt(d_k - p_k @ F @ p_k) - tmp = F @ A_k.T - w_k = (q_k - p_k @ tmp) / c_k - F_next = A_k @ tmp + jnp.outer(w_k, w_k) + c_k = jnp.sqrt(d_k - mm(p_k, mm(F, p_k))) + tmp = mm(F, A_k.T) + w_k = (q_k - mm(p_k, tmp)) / c_k + F_next = mm(A_k, tmp) + jnp.outer(w_k, w_k) return F_next, (c_k, w_k) F0 = jnp.zeros((m, m), dtype=d.dtype) @@ -174,7 +176,7 @@ def _scan_affine(M, b, reverse=False): def combine(earlier, later): M1, b1 = earlier M2, b2 = later - return M2 @ M1, M2 @ b1 + b2 + return mm(M2, M1), mm(M2, b1) + b2 if reverse: M = M[::-1] @@ -193,12 +195,12 @@ def _forward_substitution(c, p, w, A, y, parallel): M = A - w[:, :, None] * (p / c[:, None])[:, None, :] b = w[:, :, None] * (y / c[:, None])[:, None, :] G = _scan_affine(M, b) - return (y - jnp.einsum("km,kmr->kr", p, G)) / c[:, None] + return (y - jnp.einsum("km,kmr->kr", p, G, precision=HIGHEST)) / c[:, None] def step(G, inputs): c_k, p_k, w_k, A_k, y_k = inputs - x_k = (y_k - p_k @ G) / c_k - return A_k @ G + jnp.outer(w_k, x_k), x_k + x_k = (y_k - mm(p_k, G)) / c_k + return mm(A_k, G) + jnp.outer(w_k, x_k), x_k G0 = jnp.zeros((p.shape[1], y.shape[1]), dtype=y.dtype) _, x = jax.lax.scan(step, G0, (c, p, w, A, y)) @@ -212,12 +214,12 @@ def _backward_substitution(c, p, w, A, y, parallel): M = jnp.swapaxes(A, -1, -2) - p[:, :, None] * (w / c[:, None])[:, None, :] b = p[:, :, None] * (y / c[:, None])[:, None, :] G = _scan_affine(M, b, reverse=True) - return (y - jnp.einsum("km,kmr->kr", w, G)) / c[:, None] + return (y - jnp.einsum("km,kmr->kr", w, G, precision=HIGHEST)) / c[:, None] def step(G, inputs): c_k, p_k, w_k, A_k, y_k = inputs - x_k = (y_k - w_k @ G) / c_k - return A_k.T @ G + jnp.outer(p_k, x_k), x_k + x_k = (y_k - mm(w_k, G)) / c_k + return mm(A_k.T, G) + jnp.outer(p_k, x_k), x_k G0 = jnp.zeros((p.shape[1], y.shape[1]), dtype=y.dtype) _, x = jax.lax.scan(step, G0, (c, p, w, A, y), reverse=True) @@ -233,12 +235,12 @@ def _cholesky_transpose_matvec(c, p, w, A, x, parallel): p[:, :, None] * x[:, None, :], reverse=True, ) - return c[:, None] * x + jnp.einsum("km,kmr->kr", w, H) + return c[:, None] * x + jnp.einsum("km,kmr->kr", w, H, precision=HIGHEST) def step(H, inputs): c_k, p_k, w_k, A_k, x_k = inputs - z_k = c_k * x_k + w_k @ H - return A_k.T @ H + jnp.outer(p_k, x_k), z_k + z_k = c_k * x_k + mm(w_k, H) + return mm(A_k.T, H) + jnp.outer(p_k, x_k), z_k H0 = jnp.zeros((p.shape[1], x.shape[1]), dtype=x.dtype) _, z = jax.lax.scan(step, H0, (c, p, w, A, x), reverse=True) diff --git a/src/nlls_gram/linear_solvers.py b/src/nlls_gram/linear_solvers.py index 15d60dd..d16ea21 100644 --- a/src/nlls_gram/linear_solvers.py +++ b/src/nlls_gram/linear_solvers.py @@ -32,7 +32,7 @@ import jax.scipy.sparse.linalg as jsp_sparse_linalg from nlls_gram.preconditioners import Preconditioner -from nlls_gram.utilities import _IdentityKey +from nlls_gram.utilities import _IdentityKey, mm __all__ = [ "CG", @@ -295,7 +295,7 @@ def new_cache(self, m, n, n_m, dtype, penalized): def prepare(self, sub): n_m, ridge = sub.n_m, sub.ridge # B' = F_bar^{-T} J', shape (n, m). Every form below is built from it. - grad = sub.whitened_transpose(sub.Jt @ sub.resid) + grad = sub.whitened_transpose(mm(sub.Jt, sub.resid)) if sub.penalized: grad = grad + ridge * sub.penalty_gradient gram = self._resolved_form(sub.m, sub.n, sub.penalized) == "gram" @@ -303,8 +303,8 @@ def prepare(self, sub): def assemble(): Bt = sub.whitened_transpose(sub.Jt) if gram: - return Bt.T @ Bt - normal = Bt @ Bt.T + return mm(Bt.T, Bt) + normal = mm(Bt, Bt.T) if not sub.penalized: return normal diagonal = jnp.arange(n_m) @@ -317,7 +317,9 @@ def assemble(): if gram: # u = -B'(D + damping I)^{-1} c on residual-space right-hand sides. def dual_step(c): - return -sub.whitened_transpose(sub.Jt @ jsp_linalg.cho_solve(factor, c)) + return -sub.whitened_transpose( + mm(sub.Jt, jsp_linalg.cho_solve(factor, c)) + ) velocity, correction = (lambda: dual_step(sub.resid)), dual_step else: @@ -327,7 +329,7 @@ def normal_step(c): velocity = lambda: normal_step(grad) # noqa: E731 correction = lambda f_vv: normal_step( # noqa: E731 - sub.whitened_transpose(sub.Jt @ f_vv) + sub.whitened_transpose(mm(sub.Jt, f_vv)) ) return StepSolver( grad=grad, @@ -369,7 +371,7 @@ def new_cache(self, m, n, n_m, dtype, penalized): def prepare(self, sub): n, n_m, ridge, dtype = sub.n, sub.n_m, sub.ridge, sub.dtype sqrt_ridge = jnp.sqrt(ridge) - grad = sub.whitened_transpose(sub.Jt @ sub.resid) + grad = sub.whitened_transpose(mm(sub.Jt, sub.resid)) if sub.penalized: grad = grad + ridge * sub.penalty_gradient @@ -397,7 +399,9 @@ def assemble(): Q_mu, R_mu = jnp.linalg.qr(damped_stack, mode="reduced") def damped_normal_matvec(v): - gauss_newton = sub.whitened_transpose(sub.Jt @ (sub.Jt.T @ sub.whitened(v))) + gauss_newton = sub.whitened_transpose( + mm(sub.Jt, mm(sub.Jt.T, sub.whitened(v))) + ) shift = sub.damping * v if sub.penalized: shift = shift + ridge * jnp.concatenate( @@ -410,7 +414,7 @@ def correction(f_vv): # against R_mu, then ONE fixed iterative-refinement pass through # matvecs (Bjorck 1996 Sec. 6.6.5). The second-order correction # tolerates the squared conditioning; accept/reject guards it. - b = -sub.whitened_transpose(sub.Jt @ f_vv) + b = -sub.whitened_transpose(mm(sub.Jt, f_vv)) half = jsp_linalg.solve_triangular(R_mu.T, b, lower=True) delta = jsp_linalg.solve_triangular(R_mu, half, lower=False) correction_rhs = b - damped_normal_matvec(delta) @@ -421,7 +425,7 @@ def velocity(): # min ||[R; sqrt(damping) I] delta + [Q'b; 0]||^2 solved through # Q2: exact and backward stable at cond(A), never cond(A)^2. rhs = jnp.concatenate([transformed_rhs, jnp.zeros(n, dtype=dtype)]) - return -jsp_linalg.solve_triangular(R_mu, Q_mu.T @ rhs, lower=False) + return -jsp_linalg.solve_triangular(R_mu, mm(Q_mu.T, rhs), lower=False) return StepSolver( grad=grad, diff --git a/src/nlls_gram/metric_lm.py b/src/nlls_gram/metric_lm.py index e011ded..5b439af 100644 --- a/src/nlls_gram/metric_lm.py +++ b/src/nlls_gram/metric_lm.py @@ -46,6 +46,7 @@ _where_tree, _zero_tangent_leaf, canonicalize_residual, + mm, register_pytree_dataclass, ) @@ -628,10 +629,10 @@ def _ad_tangent_dense(self, Bt, residual_p_dot): # deficient B needs SVD(), which selects the minimum-norm tangent. n, m = Bt.shape if n > m: - factor = jsp_linalg.cho_factor(Bt.T @ Bt) - return -Bt @ jsp_linalg.cho_solve(factor, residual_p_dot) - factor = jsp_linalg.cho_factor(Bt @ Bt.T) - return -jsp_linalg.cho_solve(factor, Bt @ residual_p_dot) + factor = jsp_linalg.cho_factor(mm(Bt.T, Bt)) + return -mm(Bt, jsp_linalg.cho_solve(factor, residual_p_dot)) + factor = jsp_linalg.cho_factor(mm(Bt, Bt.T)) + return -jsp_linalg.cho_solve(factor, mm(Bt, residual_p_dot)) def _ad_tangent_lu(self, Bt, residual_p_dot): # Square B: u = -B^{-1} (dr/dp) p_dot, factored directly. The normal @@ -649,7 +650,7 @@ def _ad_tangent_svd(self, Bt, residual_p_dot): U, sigma, Vt = jnp.linalg.svd(Bt.T, full_matrices=False) cutoff = max(Bt.shape) * jnp.finfo(Bt.dtype).eps * sigma[0] inverted = jnp.where(sigma > cutoff, 1.0 / jnp.maximum(sigma, cutoff), 0.0) - return -Vt.T @ (inverted * (U.T @ residual_p_dot)) + return -mm(Vt.T, inverted * mm(U.T, residual_p_dot)) def _ad_tangent_krylov( self, config, theta, theta_jvp, residual_p_dot, whiten, whiten_transpose, ctx diff --git a/src/nlls_gram/metrics.py b/src/nlls_gram/metrics.py index 376dd8b..3565a74 100644 --- a/src/nlls_gram/metrics.py +++ b/src/nlls_gram/metrics.py @@ -17,7 +17,7 @@ import jax.scipy.linalg as jsp_linalg from nlls_gram.lm_types import SolverContext -from nlls_gram.utilities import register_pytree_dataclass +from nlls_gram.utilities import mm, register_pytree_dataclass __all__ = [ "CholeskyMetric", @@ -192,7 +192,7 @@ def __post_init__(self): def factor_apply(self, v, ctx): _check_leading_size(v, self.size) - return self.L.T @ v + return mm(self.L.T, v) def factor_solve(self, v, ctx): _check_leading_size(v, self.size) @@ -303,7 +303,7 @@ def _map_blocks(self, block_op, v): ).reshape((self.size,) + trailing_shape) def factor_apply(self, v, ctx): - return self._map_blocks(lambda m: self.F @ m, v) + return self._map_blocks(lambda m: mm(self.F, m), v) def factor_solve(self, v, ctx): return self._map_blocks( diff --git a/src/nlls_gram/preconditioners.py b/src/nlls_gram/preconditioners.py index a0c6f3b..f0f23bc 100644 --- a/src/nlls_gram/preconditioners.py +++ b/src/nlls_gram/preconditioners.py @@ -17,7 +17,7 @@ import jax.numpy as jnp import jax.scipy.linalg as jsp_linalg -from nlls_gram.utilities import register_pytree_dataclass +from nlls_gram.utilities import HIGHEST, mm, register_pytree_dataclass class Preconditioner: @@ -184,9 +184,13 @@ def apply(self, v, damping, ctx): segment = permuted[offset : offset + groups * size] offset += groups * size shift = ridge_weight * ridge + damping - coefficients = jnp.einsum("gab,ga->gb", V, segment.reshape(groups, size)) + coefficients = jnp.einsum( + "gab,ga->gb", V, segment.reshape(groups, size), precision=HIGHEST + ) pieces.append( - jnp.einsum("gab,gb->ga", V, coefficients / (values + shift)).reshape(-1) + jnp.einsum( + "gab,gb->ga", V, coefficients / (values + shift), precision=HIGHEST + ).reshape(-1) ) return jnp.concatenate(pieces)[self.inverse_permutation].astype(v.dtype) @@ -236,11 +240,11 @@ def __post_init__(self): object.__setattr__(self, "u", u) object.__setattr__(self, "weight", weight) object.__setattr__(self, "solve_u", solve_u) - object.__setattr__(self, "denominator", 1.0 / weight + u @ solve_u) + object.__setattr__(self, "denominator", 1.0 / weight + mm(u, solve_u)) def apply(self, v, damping, ctx): y = self.solve(v) - return y - self.solve_u * ((self.u @ y) / self.denominator) + return y - self.solve_u * (mm(self.u, y) / self.denominator) register_pytree_dataclass( @@ -277,7 +281,7 @@ def __post_init__(self): object.__setattr__(self, "weights", weights) solve_U = self.solve(U) object.__setattr__(self, "solve_U", solve_U) - capacitance = jnp.diag(1.0 / weights) + U.T @ solve_U + capacitance = jnp.diag(1.0 / weights) + mm(U.T, solve_U) object.__setattr__( self, "capacitance_factor", jsp_linalg.cho_factor(capacitance)[0] ) @@ -285,9 +289,9 @@ def __post_init__(self): def apply(self, v, damping, ctx): y = self.solve(v) correction = jsp_linalg.cho_solve( - (self.capacitance_factor, False), self.U.T @ y + (self.capacitance_factor, False), mm(self.U.T, y) ) - return y - self.solve_U @ correction + return y - mm(self.solve_U, correction) register_pytree_dataclass( @@ -400,7 +404,7 @@ def __post_init__(self, matvec, key, dtype): finfo = jnp.finfo(dtype) nu = jnp.maximum(finfo.eps * jnp.linalg.norm(Y), finfo.tiny / finfo.eps) Y_nu = Y + nu * Omega - core = Omega.T @ Y_nu + core = mm(Omega.T, Y_nu) L = jnp.linalg.cholesky(0.5 * (core + core.T)) B = jsp_linalg.solve_triangular(L, Y_nu.T, lower=True).T U, sigma, _ = jnp.linalg.svd(B, full_matrices=False) @@ -411,8 +415,10 @@ def apply(self, v, damping, ctx): # Regrouped so the apply is two (n, rank) matvecs instead of three. U, lam = self.basis, self.eigenvalues rho = lam[-1] - Utv = U.T @ v - return U @ (Utv / (lam + damping) - Utv / (rho + damping)) + v / (rho + damping) + Utv = mm(U.T, v) + return mm(U, Utv / (lam + damping) - Utv / (rho + damping)) + v / ( + rho + damping + ) register_pytree_dataclass( diff --git a/src/nlls_gram/ridge_lm.py b/src/nlls_gram/ridge_lm.py index c829307..08b8df5 100644 --- a/src/nlls_gram/ridge_lm.py +++ b/src/nlls_gram/ridge_lm.py @@ -51,6 +51,7 @@ _where_tree, _zero_tangent_leaf, canonicalize_residual, + mm, ) __all__ = [ @@ -1044,9 +1045,9 @@ def _ad_tangent_cholesky(self, x, args, p, p_dot, ridge, lm_state): self._extended_solve_transpose(Jt, ctx), dtype=residual.dtype ) diag = jnp.arange(n_m) - normal_matrix = (Jt_sub @ Jt_sub.T).at[diag, diag].add(ridge_typed) + normal_matrix = mm(Jt_sub, Jt_sub.T).at[diag, diag].add(ridge_typed) factor = jsp_linalg.cho_factor(normal_matrix) - y_dot = jsp_linalg.cho_solve(factor, -(Jt_sub @ residual_p_dot)) + y_dot = jsp_linalg.cho_solve(factor, -mm(Jt_sub, residual_p_dot)) theta_dot = jnp.asarray(self._extended_solve(y_dot, ctx), residual.dtype) return unravel(theta_dot) diff --git a/src/nlls_gram/utilities.py b/src/nlls_gram/utilities.py index 8de4ef4..f11a143 100644 --- a/src/nlls_gram/utilities.py +++ b/src/nlls_gram/utilities.py @@ -1,7 +1,7 @@ """Solver-agnostic helpers: pytree selection/masking, jit static-key hashing, -and residual-signature canonicalization. +residual-signature canonicalization, and the pinned-precision matrix product. -No solver, metric, or linear-algebra code lives here -- only plumbing both +No solver or metric code lives here -- only plumbing both ``LevenbergMarquardt`` and ``RidgeLevenbergMarquardt`` share. """ @@ -11,6 +11,23 @@ import jax import jax.numpy as jnp +# XLA:GPU serves float32 dot_general from TF32 tensor cores by default: a +# 10-bit mantissa, so ~1e-3 relative error. Forming a Gram or normal matrix +# already squares the condition number, and doing that at TF32 spends about +# three decimal digits before the factorization starts -- enough to move a +# converged step and to put an implicit tangent visibly off. Every product +# inside the package goes through `mm` (or passes `precision=HIGHEST` to +# einsum) so a float32 solve answers the same on GPU as on CPU, where the +# setting is a no-op. Callers should also set +# `jax.config.update("jax_default_matmul_precision", "highest")` near the top +# of a script: that covers matmuls in their own residual functions, which the +# package cannot reach from here. +HIGHEST = jax.lax.Precision.HIGHEST + + +def mm(a, b): + return jnp.matmul(a, b, precision=HIGHEST) + def register_pytree_dataclass(cls, *, data_fields, meta_fields=()): """Register a frozen dataclass as a pytree whose unflatten bypasses diff --git a/tests/conftest.py b/tests/conftest.py new file mode 100644 index 0000000..38c5e21 --- /dev/null +++ b/tests/conftest.py @@ -0,0 +1,9 @@ +import jax + +# The tests build their own dense references (`selection.T @ shifted @ +# selection`, `F_bar @ v`) and compare them against solver output. The package +# pins its own products to HIGHEST, so without this the reference side would +# still come from TF32 tensor cores on an Ampere GPU and the two would disagree +# at ~1e-3 -- a comparison failing on the reference, not on the solver. +# A no-op on CPU. +jax.config.update("jax_default_matmul_precision", "highest") diff --git a/tests/test_float32.py b/tests/test_float32.py index 76a8fa1..ac16eb4 100644 --- a/tests/test_float32.py +++ b/tests/test_float32.py @@ -8,6 +8,11 @@ Nothing here promotes a solve to float64: nlls-gram has no ad/metric solve dtype knob, so float32 in must mean float32 out, at float32 accuracy. + +float32 is also where matmul precision bites: XLA:GPU serves float32 +``dot_general`` from TF32 tensor cores by default, at a 10-bit mantissa. The +package pins every product it owns to HIGHEST, which the last test here +asserts on the jaxpr -- device-independently, so CPU CI protects the GPU path. """ import jax @@ -229,3 +234,47 @@ def test_float32_gram_cg_converges_under_each_dual_preconditioner(name): assert int(result.status) == int(LMStatus.CONVERGED) assert result.x.dtype == jnp.float32 np.testing.assert_allclose(np.asarray(result.x), min_norm(B), rtol=3e-3, atol=3e-4) + + +def test_internal_matmuls_are_pinned_to_highest_precision(): + # TF32 tensor cores serve float32 dot_general on Ampere by default, at a + # 10-bit mantissa (~1e-3). Forming a Gram matrix already squares the + # condition number, so every product the package owns is pinned. The + # residual below has no matmul of its own, so every dot_general in the + # trace belongs to the solver. Asserted on the jaxpr rather than on + # numbers: that holds on CPU, where the setting is a no-op, and so guards + # the GPU path from CI. tests/conftest.py sets the global default too, but + # only for the tests' own reference matmuls -- this must pass without it. + def elementwise_residual(x, args, p): + return x - p + + solver = LevenbergMarquardt( + elementwise_residual, cache_jacobian=False, geodesic_acceleration=False + ) + p0 = jnp.linspace(0.5, 1.5, N, dtype=jnp.float32) + + def run(p): + return solver.solve(jnp.zeros(N, jnp.float32), None, p=p, max_steps=4).x + + stack = [jax.make_jaxpr(run)(p0).jaxpr] + dots = [] + while stack: + current = stack.pop() + for equation in current.eqns: + if equation.primitive.name == "dot_general": + dots.append(equation) + for value in equation.params.values(): + if hasattr(value, "eqns"): + stack.append(value) + elif hasattr(value, "jaxpr"): + inner = value.jaxpr + stack.append(inner.jaxpr if hasattr(inner, "jaxpr") else inner) + + assert dots, "no dot_general in the trace; the assertion below is vacuous" + unpinned = [ + equation + for equation in dots + if equation.params.get("precision") + != (jax.lax.Precision.HIGHEST, jax.lax.Precision.HIGHEST) + ] + assert not unpinned, "\n".join(str(equation)[:110] for equation in unpinned[:5]) From 791fafacc31df2b8429d72e1e28baaaa787be575 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 17:28:58 -0700 Subject: [PATCH 21/22] docs: the GPU matmul setting is required, not advisory Measured on the 3090: the package pinning its own products leaves a dense float32 solve at 3.3e-4 relative, because the Jacobian is differentiated through the caller's residual matmuls and arrives already carrying TF32 error. Setting jax_default_matmul_precision=highest takes the same solve to 1.6e-7. Since a residual here is usually a network or a kernel evaluation, that is the normal case. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- docs/tuning_guide.md | 23 +++++++++++++++++------ 1 file changed, 17 insertions(+), 6 deletions(-) diff --git a/docs/tuning_guide.md b/docs/tuning_guide.md index d5a928c..7858d02 100644 --- a/docs/tuning_guide.md +++ b/docs/tuning_guide.md @@ -106,9 +106,20 @@ normal assembly, the matrix-free CG operator, the metric factor applications, the preconditioner contractions, and the implicit-AD solves. A float32 solve answers the same on GPU as on CPU, where the setting is a no-op. -What the package cannot reach is **your** code — the matmuls inside your -residual function, and any dense reference you compare against. Set the -default near the top of a script: +That is necessary but **not sufficient**, and on a GPU you must do one more +thing. The package cannot reach the matmuls inside **your** residual, and the +Jacobian is differentiated through those — so a TF32 residual hands the solver +a Jacobian that is already wrong, and pinning everything downstream cannot +recover it. Since a residual here is usually a neural network or a kernel +evaluation, that is the normal case, not the exception. Measured on a dense +underdetermined float32 problem on an RTX 3090: + +| | relative error | +|---|---| +| default | \(3.3 \times 10^{-4}\) | +| `jax_default_matmul_precision="highest"` | \(1.6 \times 10^{-7}\) | + +So set it near the top of any script that will run on a GPU: ```python import jax @@ -116,9 +127,9 @@ import jax jax.config.update("jax_default_matmul_precision", "highest") ``` -or export `JAX_DEFAULT_MATMUL_PRECISION=highest`. There is no reason not to -for this class of problem; TF32's speed only pays on large, well-conditioned -matmuls, which is not what a least-squares solve is doing. +or export `JAX_DEFAULT_MATMUL_PRECISION=highest`. TF32's speed only pays on +large well-conditioned matmuls, which is not what a least-squares solve is +doing, so there is no reason to leave it off. The failure signature, if it is ever missed: results that agree between CPU and GPU to about three digits and no further, with the gap concentrated in From 11246e27b019e20913f7e367351c1e07b1f8a203 Mon Sep 17 00:00:00 2001 From: Jesse Perla Date: Sat, 25 Jul 2026 19:08:44 -0700 Subject: [PATCH 22/22] test: assert the carried-instance contract directly, not through convergence test_callback_refresh_reaches_the_next_inner_solve failed in CI on x86 while passing on ARM. It is not a regression -- it fails identically at 0643a49 -- and it was never visible before because the test is branch-only (added by c8e11e2) and CI runs only on main and PRs, so this branch's 21 commits had never been through it. The mechanism is fine. Swapping a preconditioner into the carried state produces a BIT-IDENTICAL step to a solver built with that instance, on both x86 and ARM (measured: ||swapped - exact|| = 0.0). What the old assertion actually measured was the float32 endgame. The residual is linear, so with a starved maxiter=3 budget the solve reaches the float32 loss floor, no trial step strictly improves the loss any more, every step is rejected, and damping ratchets to ~3e4. Whether gtol=1e-5 sits above or below that floor is platform arithmetic: ARM reached 4.5e-6, x86 stopped at 6.0e-5 and stayed there at 60, 200 and 600 steps. Exact-from-start converges to ~1e-6 on both, which is what made the difference look like a mechanism failure rather than a stalled endgame. So the convergence assertion is replaced by the contract it was standing in for: the step taken with a swapped-in instance equals the step a solver built with it takes from the same state, and differs materially from the stale one so the check is not vacuous. The end-to-end callback path still asserts the refreshed instance is the one carried out, that a starved scrambled run does not converge, and that refreshing strictly improves stationarity -- which holds on both platforms without depending on where the float32 floor lands. Co-Authored-By: Mecha Perla (Claude) Claude-Session: https://claude.ai/code/session_014og23CSBQfdHGNCfA21F8x --- tests/test_ridge_preconditioners.py | 58 ++++++++++++++++++++++------- 1 file changed, 44 insertions(+), 14 deletions(-) diff --git a/tests/test_ridge_preconditioners.py b/tests/test_ridge_preconditioners.py index ff38c20..e400a01 100644 --- a/tests/test_ridge_preconditioners.py +++ b/tests/test_ridge_preconditioners.py @@ -145,24 +145,54 @@ def test_cg_solve_matches_cholesky(): def test_callback_refresh_reaches_the_next_inner_solve(): - # A callback-constructed instance replaces the carried one and drives the - # very next CG solve: with a starved inner budget, a scrambled - # preconditioner cannot reach gtol within the step cap, while refreshing - # to the exact one at step 1 converges almost as fast as exact-from-start - # -- and the swap is not a problem change, so convergence fires normally. + # The contract: an instance a callback puts in the carried state is what + # the NEXT inner solve uses. Asserted on the step itself -- swapping the + # exact preconditioner into a scrambled solver's state must produce the + # step a solver BUILT with the exact one takes from the same state -- and + # that holds bit-for-bit on both x86 and ARM. + # + # It used to be asserted through "the refreshed solve reaches gtol", which + # measured something else. The residual here is linear, so with a starved + # maxiter=3 budget the endgame stalls at the float32 loss floor: once no + # trial strictly improves the loss, every step is rejected and damping + # ratchets to ~3e4. Whether gtol=1e-5 lands above or below that floor is + # platform arithmetic -- ARM reached 4.5e-6 and x86 stopped at 6.0e-5 -- + # so the old assertion passed on the author's machine and failed in CI + # while the mechanism it was meant to check was working identically on + # both. metric, residual, G = build_problem() p = {"scale": jnp.asarray(1.0)} x0 = jnp.zeros(P_DIM) - def build(callback=None): - solver = RidgeLevenbergMarquardt( + def solver_with(preconditioner): + return RidgeLevenbergMarquardt( residual, metric=metric, ridge=RIDGE, - linear_solver=CG(scrambled_preconditioner(), tol=0.0, maxiter=3), + linear_solver=CG(preconditioner, tol=0.0, maxiter=3), ) - return solver.solve(x0, p=p, max_steps=60, gtol=1e-5, callback=callback) + scrambled = solver_with(scrambled_preconditioner()) + exact = solver_with(exact_preconditioner(G)) + + stale_state = scrambled.init(x0, p=p) + swapped_state = dataclasses.replace( + stale_state, preconditioner=exact_preconditioner(G) + ) + x_stale = scrambled.update(x0, stale_state, p=p)[0] + x_exact = exact.update(x0, exact.init(x0, p=p), p=p)[0] + x_swapped = scrambled.update(x0, swapped_state, p=p)[0] + + # The carried instance drives the solve... + np.testing.assert_allclose( + np.asarray(x_swapped), np.asarray(x_exact), rtol=1e-6, atol=1e-7 + ) + # ...and the scrambled one it replaced gives a materially different step, + # so the check above is not vacuous. + assert float(jnp.linalg.norm(x_swapped - x_stale)) > 1.0 + + # End to end through a callback: the refreshed instance is the one carried + # out of the solve, and a starved scrambled run does not converge. def refresh(ctx): fresh = jax.lax.cond( ctx.step == 1, @@ -173,17 +203,17 @@ def refresh(ctx): lm_state=dataclasses.replace(ctx.lm_state, preconditioner=fresh) ) - stale = build() - refreshed = build(refresh) + refreshed = scrambled.solve(x0, p=p, max_steps=60, gtol=1e-5, callback=refresh) + stale = scrambled.solve(x0, p=p, max_steps=60, gtol=1e-5) assert int(stale.status) == int(LMStatus.MAX_STEPS) - assert int(refreshed.status) == int(LMStatus.CONVERGED) - assert int(refreshed.steps) <= 12 - # The carried instance in the result is the refreshed one. np.testing.assert_allclose( refreshed.lm_state.preconditioner.eigenvalues[0], exact_preconditioner(G).eigenvalues[0], rtol=1e-6, ) + # The refresh has to help, even where the float32 floor stops it short of + # gtol: a strictly better stationarity than the run that never refreshed. + assert float(refreshed.info.grad_norm) < float(stale.info.grad_norm) @pytest.mark.parametrize("ad_mode", ["explicit", "inherit", "inherit_knobs"])