From a7f6897003e587950e6326a55a97b74b0cb735c7 Mon Sep 17 00:00:00 2001 From: tlopex <820958424@qq.com> Date: Tue, 11 Aug 2026 16:56:31 -0400 Subject: [PATCH 1/5] Add FlashMLA tutorial and diagrams --- README.md | 5 +- chapter_flashmla/index.md | 1044 +++ img/flashmla_cache_story.png | Bin 0 -> 251236 bytes img/flashmla_cache_story_zh.svg | 5311 +++++++++++++++ img/flashmla_cta_ownership.png | Bin 0 -> 199760 bytes img/flashmla_cta_ownership_zh.svg | 4719 +++++++++++++ img/flashmla_dataflow.png | Bin 0 -> 331547 bytes img/flashmla_dataflow_zh.svg | 6678 ++++++++++++++++++ img/flashmla_mla_modes.png | Bin 0 -> 278042 bytes img/flashmla_mla_modes_zh.svg | 5780 ++++++++++++++++ img/flashmla_pipeline.png | Bin 0 -> 315386 bytes img/flashmla_pipeline_stages.png | Bin 0 -> 266127 bytes img/flashmla_pipeline_stages_zh.svg | 6055 +++++++++++++++++ img/flashmla_pipeline_zh.svg | 6521 ++++++++++++++++++ img/flashmla_sparse_story.png | Bin 0 -> 266548 bytes img/flashmla_sparse_story_zh.svg | 6683 +++++++++++++++++++ img/scripts/flashmla_diagram_common.py | 228 + img/scripts/gen_flashmla_cache_story.py | 390 ++ img/scripts/gen_flashmla_cta_ownership.py | 321 + img/scripts/gen_flashmla_dataflow.py | 484 ++ img/scripts/gen_flashmla_mla_modes.py | 384 ++ img/scripts/gen_flashmla_pipeline.py | 448 ++ img/scripts/gen_flashmla_pipeline_stages.py | 478 ++ img/scripts/gen_flashmla_sparse_story.py | 467 ++ index.md | 14 +- zh/chapter_flashmla/index.md | 1000 +++ zh/index.md | 7 +- 27 files changed, 47006 insertions(+), 11 deletions(-) create mode 100644 chapter_flashmla/index.md create mode 100644 img/flashmla_cache_story.png create mode 100644 img/flashmla_cache_story_zh.svg create mode 100644 img/flashmla_cta_ownership.png create mode 100644 img/flashmla_cta_ownership_zh.svg create mode 100644 img/flashmla_dataflow.png create mode 100644 img/flashmla_dataflow_zh.svg create mode 100644 img/flashmla_mla_modes.png create mode 100644 img/flashmla_mla_modes_zh.svg create mode 100644 img/flashmla_pipeline.png create mode 100644 img/flashmla_pipeline_stages.png create mode 100644 img/flashmla_pipeline_stages_zh.svg create mode 100644 img/flashmla_pipeline_zh.svg create mode 100644 img/flashmla_sparse_story.png create mode 100644 img/flashmla_sparse_story_zh.svg create mode 100644 img/scripts/flashmla_diagram_common.py create mode 100644 img/scripts/gen_flashmla_cache_story.py create mode 100644 img/scripts/gen_flashmla_cta_ownership.py create mode 100644 img/scripts/gen_flashmla_dataflow.py create mode 100644 img/scripts/gen_flashmla_mla_modes.py create mode 100644 img/scripts/gen_flashmla_pipeline.py create mode 100644 img/scripts/gen_flashmla_pipeline_stages.py create mode 100644 img/scripts/gen_flashmla_sparse_story.py create mode 100644 zh/chapter_flashmla/index.md diff --git a/README.md b/README.md index aaedf18e..70225611 100644 --- a/README.md +++ b/README.md @@ -23,8 +23,9 @@ vehicle is **TIRx** (Tensor IR next), a Python DSL for writing GPU kernels at th layout model (`TileLayout`, named axes, swizzle). - **Part III — GEMM: Tiled to SOTA.** A tiled GEMM built up through TMA pipelining, persistent scheduling, warp specialization, and 2-CTA clusters. -- **Part IV — Flash Attention 4.** A complete attention kernel built from the Part III techniques: - two MMAs with softmax between them, online-softmax rescaling, causal masking, and GQA. +- **Part IV — Attention Kernels.** Flash Attention 4 and FlashMLA connect the Part III techniques + into complete attention pipelines, including online softmax, latent KV representations, sparse + gathers, warp specialization, and cooperative two-CTA execution. - **Appendices.** TIRx language reference, [reproducible GPU benchmarking and profiling](appendix/benchmarking_gpu_kernels.md), compiler internals, and asynchronous-kernel debugging. diff --git a/chapter_flashmla/index.md b/chapter_flashmla/index.md new file mode 100644 index 00000000..b691f24b --- /dev/null +++ b/chapter_flashmla/index.md @@ -0,0 +1,1044 @@ +(chap_flashmla)= +# FlashMLA + +Start with an apparent contradiction. The Blackwell kernel studied in this +chapter accepts 128 query heads, but its KV tensor has only one head. One cached +KV entry must somehow serve all 128 heads, preserve head-specific attention, and +produce 128 different 512-coordinate outputs. + +That puzzle has three layers. MLA explains why the cache can be shared. +Weight absorption explains where the per-head projections went. The FlashMLA +kernel explains how a sparse list of shared cache rows becomes a dense, +two-CTA tensor-core computation. + +```{figure} ../img/flashmla_cache_story.png +:width: 100% +:alt: One latent KV cache entry serving 128 query heads through absorbed projections + +The cache stores one latent content vector and one shared RoPE key per token. +Per-head behavior survives on the query and output sides rather than as 128 +materialized K/V cache entries. +``` + +:::{admonition} Overview +:class: overview + +- Derive MLA's shared latent cache, MHA/MQA execution modes, and weight absorption. +- Turn the sparse-attention contract into a 2-CTA Blackwell dataflow program. +- Run executable references, then compile and verify the pinned kernel on B200. +::: + +The name *FlashMLA* combines two ideas that are easy to conflate. MLA is an +attention architecture that compresses key-value state into a latent vector. +FlashMLA is DeepSeek's library of optimized attention kernels, spanning dense +and sparse operators across prefill and decoding. + +We will derive the architecture, make the sparse contract executable, and then +read one specific library path with the same algorithm-to-schedule depth used +for FA4: the regular 128-query-head sparse-prefill forward kernel on Blackwell. + +Our implementation reference is pinned to +[`mlc-ai/tirx-kernels@5be39749`](https://github.com/mlc-ai/tirx-kernels/tree/5be39749e7dfd2c4bdae9b4d396f8ec35af07126). +All TIRx API spellings and excerpts below come from that revision. This matters: +the compiler APIs are evolving, while a textbook example must be reproducible. + +## Why does MHA cache separate K/V for every head? + +Let $h_t\in\mathbb{R}^{d_{model}}$ be the hidden state of token $t$. Ordinary +multi-head attention (MHA) projects it independently for every head $i$: + +$$ +q_{t,i}=W_i^Q h_t,\qquad +k_{t,i}=W_i^K h_t,\qquad +v_{t,i}=W_i^V h_t. +$$ + +For a query at position $t$, head $i$ computes + +$$ +p_{t,s,i}=\operatorname{softmax}_s +\left(\frac{q_{t,i}^{\mathsf T}k_{s,i}}{\sqrt{d_h}}\right), +\qquad +o_{t,i}=\sum_s p_{t,s,i}v_{s,i}. +$$ + +The output projection mixes the per-head results. During autoregressive +generation, however, every earlier $k_{s,i}$ and $v_{s,i}$ must remain available. +The cache therefore stores $2n_h d_h$ elements per token per layer: one K slice +and one V slice for every head. + +For a fixed $d_{model}=n_h d_h$, changing only the head count need not change +that total width. The structural cost is that the cache still materializes +separate per-head state. + +During a long decode, reading those slices for the growing token history can +dominate the step. + +Multi-query attention (MQA) reduces the cache by sharing one K/V head across all +query heads. Grouped-query attention shares within groups. Those are useful model +architectures, but MLA takes a different route: retain the expressive per-head +projections while caching a shared low-dimensional source from which they can be +recovered. + +### How does MLA cache once and recover per-head behavior? + +The original [DeepSeek-V2 MLA derivation](https://arxiv.org/abs/2405.04434) +introduces a joint latent KV vector + +$$ +c_t^{KV}=W^{DKV}h_t, +$$ + +followed by separate up-projections + +$$ +k_{t,i}^{C}=W_i^{UK}c_t^{KV},\qquad +v_{t,i}^{C}=W_i^{UV}c_t^{KV}. +$$ + +The superscript $C$ denotes the non-positional, or *content*, channel. The key +observation is that the cache need not store the expanded $k^C$ and $v^C$ for +every head. It stores one $c^{KV}$ per token instead. + +MLA may also factor the query projection through a separate low-rank latent, + +$$ +c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +$$ + +This query-side factorization reduces activation memory during training, but it +does not reduce the KV cache. + +It also happens before the core-attention API: the `q` tensor passed to FlashMLA +already contains the projected query. We therefore treat $q^C$ as an input and +focus on the KV-side compression that determines the cache and kernel operands. + +RoPE complicates this simple picture. A position-dependent rotation between +$W^{UK}$ and a dot product would prevent the matrices from being reassociated. +MLA therefore uses a decoupled positional channel: each query head has +$q_{t,i}^{R}$, while all heads share a cached $k_t^R$. The actual MHA-form score +uses + +$$ +q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad +k_{s,i}=[k_{s,i}^{C};k_s^R]. +$$ + +The cache is now $[c_s^{KV};k_s^R]$, still shared across heads. The positional +channel remains explicit; weight absorption applies to the content channel. + +### Where do the per-head up-projections go? + +MLA admits two algebraically related core-attention modes. This should not be +taken to mean that every MLA model is an ordinary MQA model. + +| MLA execution mode | Core-attention K/V presented to the kernel | Where up-projection occurs | +| --- | --- | --- | +| MHA mode | Per-head $[W_i^{UK}c^{KV};k^R]$ and $W_i^{UV}c^{KV}$ | Before core attention | +| MQA mode | Shared $[c^{KV};k^R]$ and shared latent values $c^{KV}$ | Absorbed into the query and output paths | + +```{figure} ../img/flashmla_mla_modes.png +:width: 100% +:alt: MHA and MQA execution modes of MLA and the two weight-absorption paths + +MLA's MHA mode expands latent KV before core attention. Its MQA mode moves the key +up-projection to the query path and the value up-projection to the output path. +The shared RoPE key stays explicit in both modes. +``` + +The picture suggests the answer; the following two identities prove it. On the +key side, reassociate the matrix multiplication: + +$$ +(q_{t,i}^{C})^{\mathsf T}W_i^{UK}c_s^{KV} +=\left((W_i^{UK})^{\mathsf T}q_{t,i}^{C}\right)^{\mathsf T}c_s^{KV}. +$$ + +Define the absorbed query $q_{t,i}^{A}=(W_i^{UK})^{\mathsf T}q_{t,i}^{C}$. +The content score can now be computed directly against the cached latent. On the +value side, linearity gives + +$$ +\sum_s p_{t,s,i}W_i^{UV}c_s^{KV} +=W_i^{UV}\left(\sum_s p_{t,s,i}c_s^{KV}\right). +$$ + +Consequently, $W_i^{UV}$ can be composed with the model's output projection. +Neither expanded per-head K nor expanded per-head V needs to be materialized by +the attention kernel. + +The distinction is operational, not merely notational. Appendix A of the +[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) +states that DeepSeek-V3.1-Terminus used MHA mode for training and prefill and MQA +mode for decoding. + +DeepSeek Sparse Attention (DSA), by contrast, instantiates MLA in MQA mode even +for sparse prefill because each selected latent KV entry is shared by all query +heads. + +Thus the $d_{qk}=576$, $d_v=512$ contract commonly seen in this sparse-prefill +path is an absorbed MQA representation: 512 latent content coordinates plus a +64-coordinate RoPE channel. It is not a universal shape for MLA or every +FlashMLA operator. The implementation also supports a $d_{qk}=512$ variant. + +### Can a small program prove the two modes agree? + +The following CPU program constructs both executions. It includes a shared RoPE +score term, expands K/V in the MHA path, and absorbs the same matrices in the MQA +path. Float64 makes the equality check sensitive enough to catch a transposed +index or an incorrect contraction. + +```python +import math +import torch + +torch.manual_seed(0) +Q, K, H = 3, 5, 4 +D_CONTENT, D_LATENT, D_VALUE, D_ROPE, D_MODEL = 7, 6, 8, 3, 11 + +# Per-head queries, one shared latent KV per key token, and shared RoPE keys. +q_content = torch.randn(Q, H, D_CONTENT, dtype=torch.float64) +q_rope = torch.randn(Q, H, D_ROPE, dtype=torch.float64) +c_kv = torch.randn(K, D_LATENT, dtype=torch.float64) +k_rope = torch.randn(K, D_ROPE, dtype=torch.float64) + +W_UK = torch.randn(H, D_CONTENT, D_LATENT, dtype=torch.float64) +W_UV = torch.randn(H, D_VALUE, D_LATENT, dtype=torch.float64) +W_O = torch.randn(D_MODEL, H, D_VALUE, dtype=torch.float64) + +# MHA mode: explicitly expand a key and value for every head. +k_content = torch.einsum("hdc,kc->khd", W_UK, c_kv) +v_content = torch.einsum("hvc,kc->khv", W_UV, c_kv) +scale = 1.0 / math.sqrt(D_CONTENT + D_ROPE) +scores_mha = ( + torch.einsum("qhd,khd->qhk", q_content, k_content) + + torch.einsum("qhr,kr->qhk", q_rope, k_rope) +) * scale +prob = torch.softmax(scores_mha, dim=-1) +head_out_mha = torch.einsum("qhk,khv->qhv", prob, v_content) +model_out_mha = torch.einsum("mhv,qhv->qm", W_O, head_out_mha) + +# MQA mode: move W_UK to Q, attend to c_kv, then move W_UV to output. +q_absorbed = torch.einsum("qhd,hdc->qhc", q_content, W_UK) +scores_mqa = ( + torch.einsum("qhc,kc->qhk", q_absorbed, c_kv) + + torch.einsum("qhr,kr->qhk", q_rope, k_rope) +) * scale +latent_out = torch.einsum("qhk,kc->qhc", torch.softmax(scores_mqa, -1), c_kv) +W_O_absorbed = torch.einsum("mhv,hvc->mhc", W_O, W_UV) +model_out_mqa = torch.einsum("mhc,qhc->qm", W_O_absorbed, latent_out) + +torch.testing.assert_close(scores_mha, scores_mqa, rtol=1e-12, atol=1e-12) +torch.testing.assert_close(model_out_mha, model_out_mqa, rtol=1e-12, atol=1e-12) +print("weight absorption: exact up to float64 roundoff") +``` + +Notice that the scale remains the scale of the model's semantic QK head, not +$1/\sqrt{D_{latent}}$ merely because the absorbed dot product happens to have +$D_{latent}$ coordinates. + +## Does the sparse kernel choose the tokens? + +Dense attention visits every eligible KV token. DSA first uses a lightweight +*lightning indexer* to score candidate tokens and chooses a top-$k$ set for each +query. The sparse core attention then reads only those latent KV entries. If the +original context length is $L$, this changes the core-attention work from +$O(L^2)$ to $O(Lk)$ for prefill, although the indexer has its own cost. + +```{figure} ../img/flashmla_sparse_story.png +:width: 100% +:alt: A lightning indexer selecting token rows before the sparse FlashMLA attention kernel + +Selection and attention are separate operators. The indexer produces row +addresses; the sparse-prefill kernel gathers those rows and performs the +QK--softmax--PV computation. +``` + +The sparse-prefill operator studied here does not compute the index scores and +does not run top-k selection. It receives an `indices` tensor. Therefore its +semantic contract is: + +1. gather the requested KV rows; +2. mark out-of-range and length-masked positions invalid; +3. compute attention over the remaining rows, including duplicates if the caller + supplied duplicates; +4. return the output, maximum logit, and log-sum-exp. + +There is no causal flag in this interface. A caller that requires causal +attention must produce an index list containing only allowed keys. Sparsity is +not itself a causal mask. + +When `topk_length` is present, every query must satisfy +`0 <= topk_length[q] <= topk`. This is a caller precondition, not a value that +the kernel clips automatically: a value above `topk` makes the pinned kernel +walk beyond the logical `indices` storage. + +This prefill interface also has no batch dimension. In the port studied below, +`h_kv=1`, so `indices` has shape `[s_q, 1, topk]`: each query token supplies one +selected-token list, and all 128 of its query heads share that list. A serving +system must flatten or otherwise map batches before making this call. + +### Is FlashMLA one kernel or an operator family? + +*Prefill* processes the prompt's query tokens in parallel; *decoding* adds a new +query (or a small speculative group) step by step while reusing the KV cache. +The [official FlashMLA repository](https://github.com/deepseek-ai/FlashMLA) +organizes its kernels into four broad families: + +| Selection | Sequence stage | Representative purpose | +| --- | --- | --- | +| dense | prefill | MHA forward and backward | +| dense | decoding | read an MLA KV cache for newly generated queries | +| token-sparse | prefill | DSA core attention over a selected token list | +| token-sparse | decoding | DSA inference over a selected FP8 KV cache | + +FlashMLA is therefore neither synonymous with sparse attention nor with the +kernel in this chapter. + +We use its sparse prefill operator because it makes one systems question +especially visible: how can irregular TMA gathers feed regular tensor-core +tiles? Sparse decode has a different paged-cache, scheduling, and reduction +contract and is outside this chapter's boundary. + +The public upstream sparse-prefill call is conceptually + +```text +out, max_logits, lse = flash_mla_sparse_fwd( + q, kv, indices, sm_scale, + d_v=512, + attn_sink=attn_sink, # optional [h_q], float32 + topk_length=topk_length, # optional [s_q], int32 +) +``` + +The pinned TIRx repository reuses the public name in its unified +`flash_mla_sparse_fwd` registry entry, then dispatches to one of three SM100 +phase-1 modules by shape. + +:::{admonition} Port scope: `sm_scale` is fixed +:class: warning + +The upstream call above accepts `sm_scale` at runtime. The pinned TIRx entry +preserves the registry name and shape dispatch, **not** the complete call +signature. All three prefill modules specialize the scale to `1 / sqrt(d_qk)`, +and the launch ABI has no scale argument. + +In this revision, passing `sm_scale=...` through the `**kwargs` wrappers is +silently ignored. The B200 examples below therefore validate a fixed-scale +teaching port, not a drop-in replacement for upstream `flash_mla_sparse_fwd`. + +A model whose semantic QK scale differs must expose or specialize the correct +value. Weight absorption does not justify changing that scale. +::: + +## Can we make the sparse contract executable first? + +Before reading the kernel, we need a reference that makes edge cases explicit. +For the absorbed MQA contract, `kv[:, 0, :]` supplies both K and V: all `d_qk` +coordinates participate in QK, while the first `d_v` coordinates are the latent +value. + +Invalid indices must be clamped *before* a PyTorch gather and then masked out. +Directly indexing with `-1` would incorrectly select the last row. + +The gathered V row for an out-of-range address is also cleared before PV, +because a zero softmax weight does not neutralize a NaN under IEEE arithmetic. +We deliberately leave an in-range row masked only by `topk_length` unsanitized +to match the pinned kernel behavior discussed below. + +The complete CPU block answers whether those rules, the attention sink, and the +all-invalid convention can coexist in one executable oracle: + +```python +import math +import torch + +def sparse_prefill_reference( + q, kv, indices, sm_scale, d_v, *, attn_sink=None, topk_length=None +): + """Reference for q[SQ,H,D], kv[SKV,1,D], indices[SQ,1,TOPK].""" + s_q, h_q, d_qk = q.shape + s_kv, h_kv, kv_width = kv.shape + assert h_kv == 1 and kv_width == d_qk and d_v <= d_qk + assert indices.shape[:2] == (s_q, 1) + + idx = indices[:, 0].to(torch.long) # [SQ, TOPK] + topk = idx.shape[1] + assert topk > 0 + in_range = (idx >= 0) & (idx < s_kv) + safe_idx = idx.clamp(0, s_kv - 1) + focused_kv = kv[:, 0].float()[safe_idx] # [SQ, TOPK, D] + + # OOB indices use a clamped boundary row only as a safe gather address. Clear + # their V rows before PV so that 0 * NaN cannot leak from that sentinel row. + # Deliberately keep in-range rows beyond topk_length unchanged to match the + # kernel's documented exceptional NaN behavior. + focused_v = torch.where( + in_range[:, :, None], + focused_kv[:, :, :d_v], + torch.zeros_like(focused_kv[:, :, :d_v]), + ) + + position = torch.arange(topk, device=q.device)[None, :] + if topk_length is not None: + assert topk_length.shape == (s_q,) + assert bool(((0 <= topk_length) & (topk_length <= topk)).all()) + length = ( + topk_length.to(torch.long)[:, None] + if topk_length is not None + else torch.full((s_q, 1), topk, device=q.device) + ) + valid = in_range & (position < length) + + logits = torch.einsum("qhd,qkd->qhk", q.float(), focused_kv) * sm_scale + logits = logits.masked_fill(~valid[:, None, :], -torch.inf) + max_logits = logits.amax(dim=-1) + have_valid = valid.any(dim=-1)[:, None] + + # Avoid (-inf)-(-inf) on rows for which every selected index is invalid. + softmax_origin = torch.where(have_valid, max_logits, torch.zeros_like(max_logits)) + weight = torch.exp(logits - softmax_origin[:, :, None]) + weight = torch.where(valid[:, None, :], weight, torch.zeros_like(weight)) + denominator = weight.sum(dim=-1) + numerator = torch.einsum("qhk,qkv->qhv", weight, focused_v) + + if attn_sink is None: + sink_term = torch.zeros_like(denominator) + else: + sink_term = torch.exp(attn_sink.float()[None, :] - softmax_origin) + out = numerator / (denominator + sink_term).clamp_min(torch.finfo(torch.float32).tiny)[ + :, :, None + ] + out = torch.where(have_valid[:, :, None], out, torch.zeros_like(out)) + + # FlashMLA's reported LSE excludes the attention sink. Its all-invalid + # convention is max_logits=-inf, lse=+inf, output=0. + lse = torch.where( + have_valid, + max_logits + torch.log(denominator), + torch.full_like(max_logits, torch.inf), + ) + return out, max_logits, lse + + +torch.manual_seed(1) +q = torch.randn(2, 3, 6) +kv = torch.randn(9, 1, 6) +indices = torch.tensor([[[0, 3, -1, 12]], [[8, 1, 4, 2]]], dtype=torch.int32) +topk_length = torch.tensor([3, 2], dtype=torch.int32) +attn_sink = torch.randn(3) +out, max_logits, lse = sparse_prefill_reference( + q, kv, indices, 1 / math.sqrt(6), 4, + attn_sink=attn_sink, + topk_length=topk_length, +) +assert out.shape == (2, 3, 4) +assert max_logits.shape == lse.shape == (2, 3) +assert torch.isfinite(out).all() + +# An OOB sentinel must not inherit NaNs from the row used as its safe address. +nan_q = torch.ones(1, 1, 2) +nan_kv = torch.tensor([[[torch.nan, torch.nan]], [[2.0, 3.0]]]) +nan_indices = torch.tensor([[[-1, 1]]], dtype=torch.int32) +nan_out, _, _ = sparse_prefill_reference(nan_q, nan_kv, nan_indices, 1.0, 2) +torch.testing.assert_close(nan_out, torch.tensor([[[2.0, 3.0]]])) +print(out.shape, max_logits.shape, lse.shape) +``` + +An attention sink is equivalent to adding a logit whose value vector is zero. +It changes only the output denominator: + +$$ +O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} +{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. +$$ + +Here $a_i$ is the per-head sink logit. It has no effect on `max_logits` or the +returned `lse`, a detail that is easy to miss when writing an independent +oracle. + +## Which Blackwell case are we studying? + +We now focus on +[`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py). +Despite the internal `phase1` name inherited from upstream FlashMLA, this +prefill path produces the complete `(out, max_logits, lse)` result in one kernel; +it is not a partial split-KV output awaiting a combine kernel. + +This regular head-128 case is a useful bridge from the preceding FlashAttention +chapter. It retains the familiar QK--softmax--PV chain, then adds irregular +gather, absorbed latent KV, and cooperative 2-CTA ownership. + +One naming warning prevents confusion later. In the mathematical introduction, +$p$ denotes a normalized softmax probability. In the pinned source, however, +`tmem_p` and the register variable `p` hold **raw QK logits**. In the schedule +discussion we will call those logits $L$. + +The source's `s_frag` and `s_smem_gemm` hold BF16 **unnormalized exponential +weights**, which we will call $W$. + +The weights are not normalized in place. The final output becomes normalized +only when the accumulated output is divided by `li` plus the optional sink term +in the epilogue. + +All shorter TIRx code blocks below are contextual excerpts from the pinned +kernel, not standalone programs. The complete module is compiled and +numerically verified in the final section. Blocks intended to run independently +are called out explicitly. + +### Which shapes reach the regular head-128 path? + +The regular head-128 module fixes the following tile constants: + +```python +B_H = 128 +B_TOPK = 128 +D_V = 512 +NUM_BUFS = 2 +NUM_THREADS = 512 +D_TQ = 384 +``` + +Its input and output contract is: + +| Tensor | Shape | Type | Meaning | +| --- | --- | --- | --- | +| `q` | `[s_q, 128, d_qk]` | BF16 | absorbed queries | +| `kv` | `[s_kv, 1, d_qk]` | BF16 | shared latent/positional KV rows | +| `indices` | `[s_q, 1, topk]` | int32 | direct KV row indices | +| `attn_sink` | `[128]` | FP32 | optional per-head sink logits | +| `topk_length` | `[s_q]` | int32 | optional valid prefix length; every entry is in `[0, topk]` | +| `out` | `[s_q, 128, 512]` | BF16 | sparse-attention result | +| `max_logits` | `[s_q, 128]` | FP32 | maximum scaled logit | +| `lse` | `[s_q, 128]` | FP32 | natural-log sum-exp, without sink | + +The module accepts `d_qk` 512 or 576, requires `h_kv=1`, `d_v=512`, and requires +the regular path's `topk` to be a positive multiple of 128. The unified front +door makes one additional choice for 128 heads: `d_qk=512` with `topk<=1280` goes to the +small-top-k implementation; other supported head-128 shapes go to this regular +implementation. Head-64 shapes use a separate kernel. + +The positive-`topk` condition is a required caller precondition. The unified front +door rejects `topk<=0`, but the pinned per-implementation `_cfg().validate()` +methods check divisibility without checking positivity. A direct import of one +specialization must therefore still reject or avoid nonpositive `topk`; acceptance +by that local validator does not make such a launch valid. + +This dispatch can be inspected without launching a GPU kernel: + +```python +from tirx_kernels.flashmla.flash_mla_sparse_fwd import ( + dispatch_reason, + select_kernel, +) + +shape = dict(h_q=128, h_kv=1, d_qk=576, d_v=512, topk=2048) +assert select_kernel(**shape) == "sparse_flashmla_prefill_head128_phase1" +print(dispatch_reason(**shape)) +# sm100 h_q=128 dispatches to regular head128 phase1 +``` + +The dispatch itself is documented in the pinned +[`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120). +Keeping dispatch separate from the device schedule prevents a tutorial from +mistaking one specialization for the entire operator. + +### Why does one query row need two CTAs? + +The launch grid contains `2 * s_q` CTAs and clusters adjacent CTAs in pairs: + +```python +block_idx = T.cta_id([2 * s_q]) +T.cta_id_in_cluster([2]) +cta_idx: T.let = block_idx % 2 +s_q_idx: T.let = block_idx // 2 +thread_idx = T.thread_id([512]) +T.warpgroup_id([4]) +``` + +One cluster therefore owns one query row, and each CTA has four warpgroups. +Start with the ownership map: the unusual point is that the partition axis +changes between QK and PV. + +```{figure} ../img/flashmla_cta_ownership.png +:width: 100% +:alt: Two-CTA ownership of query heads, selected K rows, and V feature columns + +For each query row, the CTA pair changes its logical partition between QK and +PV. Each CTA ultimately writes 64 complete output-head vectors, each with 512 +coordinates. +``` + +The pair divides three different axes in three different ways: + +| Resource within a 128-token top-k tile | CTA 0 | CTA 1 | +| --- | --- | --- | +| query/output head ownership | heads 0--63 | heads 64--127 | +| K-row gather ownership | selected tokens 0--63 | selected tokens 64--127 | +| V-feature gather ownership | value columns 0--255 | value columns 256--511 | + +This is why a 2-CTA tensor-core operation is more than “two CTAs doing half the +same loop.” QK needs the cross-product of 128 heads and 128 selected tokens; PV +then contracts those tokens into 512 value coordinates. The partition rotates +between the two GEMMs. Collective `cta_group=2` MMA, paired SMEM/TMEM layouts, +and cross-CTA barriers together form the logical tile. + +The division follows directly from the pinned source: Q is chunked by +`cta_idx`, the K producer selects the `cta_idx` half of every top-k block, and +the V producer starts at `cta_idx * 256`. + +## Where do the tiles live? + +Blackwell's tensor memory (TMEM) lets `tcgen05` keep large accumulators close to +the tensor cores. It does not replace shared memory (SMEM). TMA gathers arrive in +SMEM, and the softmax warpgroup must materialize BF16 unnormalized weights in +SMEM for the PV GEMM. + +```{figure} ../img/flashmla_dataflow.png +:width: 100% +:alt: Data movement between global memory, shared memory, tensor memory, and registers + +Q is split between an SMEM prefix and a TMEM suffix. Gathered K/V enter SMEM, +raw QK logits and the output accumulate in TMEM, and unnormalized softmax +weights cross back through SMEM for PV. +``` + +For one CTA, the important logical views are: + +| Storage | Logical tile | Lifetime and purpose | +| --- | --- | --- | +| SMEM `q_full` | `64 x d_qk` BF16 | Q prologue; its prefix remains for SS QK | +| TMEM `q_tmem` | `64 x 384` BF16 | suffix of Q used by TS QK | +| SMEM `k_smem` | `64 x d_qk` BF16 | this CTA's gathered half of a 128-row K tile | +| TMEM `tmem_p` | `64 x 128` FP32 logical view | raw QK logits $L$ consumed by softmax | +| SMEM `s_smem_gemm` | `64 x 128` BF16 | unnormalized exponential weights $W$ for PV | +| SMEM `v_smem_gemm` | `128 x 256` BF16 logical view | rearranged view of `v_smem`: all tile rows, this CTA's V columns | +| TMEM `o_tmem` | `64 x 512` FP32 logical view | running unnormalized output | +| SMEM `o_smem` | `64 x 512` BF16 | epilogue staging before TMA store | + +These are logical views; CTA-group TMEM layouts and rearrangements give the MMA +and load/store instructions their physical lane mapping. The source allocates +one 512-column CTA-group TMEM pool, then carves out O, raw-logit, and Q views. + +SMEM is aggressively aliased. `q_full`, the gathered K/V region, and the output +epilogue reuse a union-like base when their lifetimes permit. + +After the final 384 Q columns have moved to TMEM, only the +$d_{sq}=d_{qk}-384$ prefix must stay live for the first QK part. For +`d_qk=512`, $d_{sq}=128$; for 576, it is 192. + +The allocation plan is visible in +[`sparse_prefill_head128_phase1.py` lines 302--365](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L302-L365). + +One important caveat is that `NUM_BUFS = 2` does **not** allocate two complete K, +V, $L$, or $W$ tiles. Those arrays have no stage axis. `NUM_BUFS` drives the +two-slot barrier/phase ring and also gives the small packed-validity mask two +slots; completion barriers make it safe to overwrite parts of the single large +tile storage. Calling this layout “double-buffered K/V” would describe storage +that does not exist. + +## Which warpgroup owns each transition? + +The four warpgroups do different jobs rather than advancing in lockstep: + +| Warpgroup | Warps | Responsibility | +| --- | --- | --- | +| WG0 | 0--3 | load raw logits $L$ from TMEM, mask, online softmax, write weights $W$, rescale O, epilogue | +| WG1 | 4--7 | load index fragments and issue gather4 TMA for K | +| WG2 | 8--11 | load index fragments and issue gather4 TMA for V | +| WG3 | 12--15 | warp 12 of CTA 0 issues CTA-group QK/PV MMA; warp 13 in each CTA builds validity masks | + +The remaining WG3 warps do not acquire another hidden stage. This asymmetric +role assignment is deliberate: one elected lane can issue asynchronous MMA for +the CTA pair, while many lanes are useful for exponentiation, row reductions, +packing, and epilogue conversion. + +The register budgets match the roles. WG0 raises its limit to 144 registers and +WG3 to 168; producer groups lower theirs to 96. The pinned API spells these calls +as `T.ptx.setmaxnreg(True, ...)` for an increase and +`T.ptx.setmaxnreg(False, ...)` for a decrease. + +### How do irregular rows become regular tiles? + +Sparse row addresses destroy the contiguous 2-D copy pattern used by dense +attention. WG1 and WG2 use explicit TMA `gather4`: one issue supplies exactly +four row coordinates, so a warp can bring noncontiguous KV rows into a regular +SMEM tile. + +The next contextual excerpt answers which addresses one `gather4` issue reads +and which barrier receives its completion. Its index names and slices are kept +exactly as they appear at the pinned revision: + +```python +_kv_gather_tma = partial( + tma_config, + dispatch="tma_explicit", + cta_group=2, + cta_mask=T.uint16(1), + cache_hint=T.uint64(0x14F0000000000000), +) + +for row_group in T.unroll(WG1_ROWS_PER_WARP): + for col_atom in T.unroll(col_count): + col = T.meta_var((col_start + col_atom) * 64) + Tx.copy_async( + k_gather_tile[ + row_group * 4 : row_group * 4 + 4, + col_atom * 64 : col_atom * 64 + 64, + ], + kv_tma[0:1, col : col + 64], + **_kv_gather_tma( + mbar=leader_mbar(bar.ptr_to([cur_buf])), + gather4=[indices_int4[row_group, lane] for lane in range(4)], + ), + ) +``` + +Gathering and validity are related but separate. Warp 13 loads eight indices per +active lane and calls `pack_valid_mask8`. Bit $i$ is one only if + +$$ +0\leq\text{index}_i 0: + sq_smem = q_full.sub[:, :d_sq] + Tx.gemm_async( + tmem_p[:, :], + sq_smem[:, :d_sq], + k_smem[:, :d_sq], + **_mma_config(accum=mma_p_accumulate, smem_desc=mma_smem_desc), + ) + mma_p_accumulate = T.uint32(1) + +Tx.gemm_async( + tmem_p[:, :], + q_tmem[:, :D_TQ], + k_smem[:, d_sq : d_sq + D_TQ], + **_mma_config(accum=mma_p_accumulate, smem_desc=mma_smem_desc), +) +``` + +The first operation is SS: both Q and K operands are described from SMEM. The +second is TS: Q's 384-column suffix comes from TMEM while K remains in SMEM. Both +write the same FP32 raw-logit accumulator (`tmem_p` in the source); the first +clears it and the second accumulates. Splitting Q this way preserves only the +smaller Q prefix in SMEM, making the union allocation possible without giving +up the TS path for the larger suffix. + +After softmax, PV is an SS GEMM: BF16 $W$ and V are both in SMEM, while the FP32 O +accumulator stays in TMEM. The kernel splits the V rows and output columns into +two halves each; the four combinations collectively update all 512 value +coordinates. + +## How does online softmax avoid needless O rescaling? + +For a stream of score tiles, the usual online-softmax recurrence stores a row +origin $m$, denominator $\ell$, and unnormalized output $\widetilde O$. In base +2, when the next tile has scaled scores $r$, + +$$ +m'=\max(m,\max r),\qquad +\alpha=2^{m-m'}, +$$ + +$$ +\ell'=\alpha\ell+\sum_j2^{r_j-m'},\qquad +\widetilde O'=\alpha\widetilde O+\sum_j2^{r_j-m'}v_j. +$$ + +Conceptually, the implementation multiplies natural-unit logits by the model's +semantic QK scale and `log2(e)`, then uses `exp2`. In this fixed-scale port, the +compile-time `sm_scale_div_log2` is +`(1 / sqrt(d_qk)) * log2(e)`. This is the same softmax in a form that maps +directly to fast base-2 exponent instructions. + +Rescaling the full 512-coordinate O tile whenever the row maximum increases +would be expensive. The head-128 kernel uses a lazy threshold: + +```python +should_scale_o: T.bool = ( + T.ptx.any_sync(T.uint32(0xFFFFFFFF), cur_pi_max - mi > 6.0) != 0 +) + +if not should_scale_o: + scale_for_old = 1.0 + new_max = mi +else: + new_max = T.max(cur_pi_max, mi) + scale_for_old = T.ptx.exp2(mi - new_max) +``` + +If the new tile maximum is at most 6 base-2 units above the stored origin, the +kernel keeps the old origin. New exponentials may then be as large as $2^6=64$, +but the accumulated O does not need a rescale. Once the difference exceeds 6, +it rebases and rescales both $\ell$ and, when it already exists, O. The warp-wide +`any_sync` keeps the decision uniform for the participating rows. + +`real_mi` is maintained separately as the exact maximum seen so far. Therefore +the optimization does not change `max_logits`; `mi` is the numerical origin for +the recurrence, while `real_mi` is the reported statistic. At the end, the two +64-token contributions to each logical row are combined, and the kernel emits + +$$ +\mathrm{lse}=m\ln 2+\ln\ell. +$$ + +The optional attention sink changes the final output scale to + +```python +output_scale: T.float32 = T.cuda.fdividef( + T.float32(1.0), li + T.ptx.exp2(attn_sink_log2 - mi) +) +``` + +but deliberately leaves the reported LSE untouched. All-invalid rows are +special-cased to output zero with `max_logits=-inf` and `lse=+inf`, matching the +pinned reference. + +## How can the stages overlap without racing? + +The schedule is easiest to understand as a dependency puzzle. QK must finish +before softmax consumes its logits. PV must wait until softmax has produced its +weights. Yet the gather warpgroups should keep moving whenever the in-place K or +V segment they need has become reusable. + +```{figure} ../img/flashmla_pipeline_stages.png +:width: 100% +:alt: Conceptual sparse-prefill stages and the dependencies that permit steady-state overlap + +In steady state, softmax($k-1$) may overlap QK($k$). The sole MMA issuer then +issues PV($k-1$) after QK($k$); once QK($k$) completes, softmax($k$) may overlap +that PV. Producer warpgroups gather the next safe K/V segments around this +serial issuer order. +``` + +The kernel initializes its mbarriers in warp 0, performs a cluster sync, launches +the Q prologue, allocates CTA-group TMEM, and then enters specialized loops. + +TMA completion for CTA-group gathers is routed to a named leader barrier, so +issues from the pair contribute to one expected byte count. + +The main barrier edges are easier to read as ownership transfers: + +| Barrier | Producer to consumer | Storage protected | +| --- | --- | --- | +| `bar_k_part0_ready` | WG1 to WG3 | K prefix for SS QK | +| `bar_qk_part_done` | WG3 to WG1 | permission to overwrite K prefix after SS QK completion | +| `bar_k_part1_ready` | WG1 to WG3 | K suffix for TS QK | +| `bar_qk_done` | WG3 to WG0 and WG1 | raw logits $L$ ready; K suffix reusable after QK completion | +| `bar_p_free` | WG0 to WG3 | TMEM raw-logit tile consumed before next overwrite | +| `bar_k_valid_ready/free` | warp 13 to/from WG0 | packed validity mask | +| `bar_so_ready` | WG0 to WG3 | BF16 weights $W$ ready for PV | +| `bar_v_part0_ready` / `bar_sv_part_done` | WG2 to/from WG3 | first V half | +| `bar_v_part1_ready` / `bar_sv_done` | WG2 to WG3, then WG3 to WG2 and WG0 | second V half; PV/O completion before V reuse, O rescale, or epilogue | + +For tile $k$, the sole MMA issuer first launches QK($k$). Once WG0 has turned +$L(k-1)$ into $W(k-1)$, that same issuer later launches PV($k-1$) in the serial +loop. + +QK and PV are therefore interleaved by one instruction stream, not issued as +two simultaneous tensor-core streams. Their asynchronous execution overlaps +the other warpgroups' gathers and scalar softmax work, subject to the part-level +edges above. + +The ring index is + +```python +cur_buf = k % 2 +cur_phase = (k // 2) & 1 +``` + +so a reused barrier slot can distinguish a new arrival from one made two +iterations earlier. Again, this is a two-slot *barrier/phase ring*, not two full +KV tiles resident at once. + +`bar_qk_part_done` allows the producer to replace K's prefix before its suffix +is reusable. The two `bar_sv_*` edges do the analogous job for V. + +```{figure} ../img/flashmla_pipeline.png +:width: 100% +:alt: Sparse-prefill pipeline showing QK of the current tile and PV of the previous tile + +The steady state interleaves QK($k$) and PV($k-1$) while other roles perform +part-wise K/V gathers and softmax work. Barrier phases protect in-place storage +reuse rather than selecting separate full-tile buffers. +``` + +Two kinds of fences appear around these edges. `T.ptx.tcgen05.fence.*` orders +TMEM accesses relative to thread-visible work, while +`T.ptx.fence.proxy_async("shared::cta")` establishes cross-proxy ordering between +generic and asynchronous accesses to SMEM. + +Here the proxy fence is needed both when generic stores of $W$ or the epilogue +tile precede tcgen05/TMA asynchronous reads, and after an asynchronous SMEM read +completes before generic code overwrites aliased storage. + +An mbarrier communicates completion and an ownership handoff; the proxy fence +orders memory effects across proxies. Neither is a substitute for the other. + +## How do we compile and verify the entire path? + +The pinned module targets compute capability 10 and its TMA/tcgen05 forms require +an SM100-class GPU. Use B200, CUDA 12.9 or newer, and the official Apache TVM +0.26.0 package. The pinned kernel uses that release's TIRx API rather than the +spellings on a moving development checkout. + +First install a CUDA-enabled PyTorch build that supports B200 using the +[official PyTorch selector](https://pytorch.org/get-started/locally/). The +companion repository imports PyTorch but does not declare it as a package +dependency. + +The following commands answer exactly which TVM release and kernel revision the +examples require: + +```bash +python -m pip install "apache-tvm==0.26.0" cuda-bindings +git clone https://github.com/mlc-ai/tirx-kernels.git +cd tirx-kernels +git checkout 5be39749e7dfd2c4bdae9b4d396f8ec35af07126 +pip install -e . +``` + +A one-row smoke test still exercises the full 128-head, top-k-2048 kernel while +keeping reference time modest: + +```python +from tirx_kernels.flashmla.sparse_prefill_head128_phase1 import run_test + +run_test( + label="tutorial_smoke", + s_q=1, + s_kv=8192, + topk=2048, + d_qk=576, + h_q=128, + h_kv=1, + d_v=512, + have_attn_sink=True, + have_topk_length=False, + seed=0, +) +print("compile, launch, and randomized reference check passed") +``` + +`run_test` does more than compile. It allocates randomized BF16 Q/KV, random +indices, runs the generated kernel, evaluates the FP32 PyTorch oracle one query +row at a time, and checks output, maximum logits, and LSE with explicit +tolerances. This is the right default verification path; compiling generated +PTX alone cannot find a wrong head partition or a missing validity bit. + +The repository CLI can run the full registered configuration: + +```bash +python -m tirx_kernels.test \ + --kernel sparse_flashmla_prefill_head128_phase1 \ + --config bench_regular_dqk576_hq128_s4096_kv8192_topk2048 +``` + +Useful negative tests are just as important. Set `inject_invalid_indices=True` +to cover negative and too-large row IDs, and `have_topk_length=True` to exercise +the position predicate. Test an all-invalid row and confirm the documented +zero/-infinity/+infinity convention. Finally, call the unified dispatch entry +for head-64 and small-top-k shapes so that a successful regular-head128 run is +not mistaken for full API coverage. + +## Which five invariants define this path? + +1. **The cache invariant.** One `h_kv=1` latent KV row can serve 128 query heads + because key up-projection is absorbed into each query and value up-projection + is moved after core attention. The RoPE channel stays explicit, and the QK + scale remains the model's semantic scale. + +2. **The sparse-contract invariant.** Selection happens before this kernel. + `indices` supplies the rows; duplicates remain duplicates; causal legality is + the caller's responsibility; and every `topk_length` lies in `[0, topk]`. + Sink and all-invalid conventions must remain identical in optimized and + reference paths. + +3. **The ownership invariant.** One two-CTA cluster owns one query row. The pair + partitions Q/output heads, selected K rows, and V features on different axes, + while CTA 0 warp 12 is the sole CTA-group MMA issuer. + +4. **The residency invariant.** $L$ means raw FP32 logits and $W$ means BF16 + unnormalized exponential weights. Large K, V, $L$, and $W$ workspaces are + single in-place tiles, while `NUM_BUFS=2` drives a barrier/phase ring. Among + data buffers, only the small packed-validity mask has two physical slots. + +5. **The handoff invariant.** Ready/done barriers transfer ownership of each + reusable segment, and proxy fences order generic and asynchronous SMEM + accesses. The sole issuer orders QK($k$) before PV($k-1$), while the threshold-6 + optimization preserves the reported-maximum semantics and the online LSE + recurrence. + +The first two invariants define operator semantics; the last three define this +specialization's schedule contract. Another dispatch may change tile sizes, +register budgets, ownership, or barrier topology, but it must replace those +contracts explicitly rather than silently changing the operator it computes. + +## What should you test next? + +The regular head-128 kernel is one point in a dispatch space. The pinned tree +also contains a 64-head phase-1 kernel and a 128-head `d_qk=512` small-top-k +kernel. Their different schedules are evidence that sparse attention should be +dispatched by tile economics, not forced through one universal template. + +1. **Reproduce weight absorption.** Add a causal mask to the runnable absorption + proof. Confirm that MHA and MQA modes still agree, then intentionally change + the absorbed path's scale to $1/\sqrt{D_{latent}}$ and measure the error. + +2. **Stress sparse validity.** Extend `sparse_prefill_reference` with an + all-invalid query, duplicated indices, `topk_length=0`, and sink values of + both infinities. Write down the expected `(out, max_logits, lse)` for each. + +3. **Trace ownership.** For one top-k tile, label every dimension of Q, K, $L$, $W$, + V, and O with `(CTA, local row, local column)`. Show where a logical row needs + information owned by the other CTA. + +4. **Audit residency.** Starting at the `SMEMPool` allocation, draw every alias + interval. Verify why the $d_{sq}$ Q prefix remains live while the 384-column + suffix can move to TMEM, and identify the barrier that ends each reuse hazard. + +5. **Measure the threshold.** Instrument how often `should_scale_o` is true for + random and adversarial logits. Compare threshold 6 with always-rebase and + never-rebase versions in both numerical error and TMEM O traffic. + +6. **Compare dispatches.** Use `select_kernel` on head counts 64 and 128, + `d_qk` 512 and 576, and top-k values around 1280. Predict the selected module + before running it, then inspect which constraints belong to the front door and + which are enforced by an individual specialization. + +7. **Read the generated program.** Compile the smoke shape, inspect the emitted + PTX for `tcgen05` MMA, TMA gather, mbarrier, and proxy-fence instructions, and + map each one back to a TIRx line. Then run the numerical check again: source, + generated code, and observed values are three complementary kinds of proof. + +The central lesson is broader than FlashMLA. A high-performance irregular +operator often regularizes work in stages: an indexer creates sparse addresses, +TMA gathers those addresses into dense tiles, tensor cores consume the tiles, +and explicit barriers protect aggressive storage reuse. 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tutorial figures.""" + +from __future__ import annotations + +import os +from pathlib import Path + +import matplotlib + + +matplotlib.use("Agg") + +import matplotlib.pyplot as plt +from matplotlib import font_manager +from matplotlib.patches import FancyArrowPatch, FancyBboxPatch, Rectangle + + +COLORS = { + "ink": "#1f2937", + "muted": "#4b5563", + "grid": "#d1d5db", + "line": "#64748b", + "cta0": "#bfdbfe", + "cta0_dark": "#2563eb", + "cta1": "#fbcfe8", + "cta1_dark": "#db2777", + "cross01": "#ddd6fe", + "cross10": "#ccfbf1", + "gmem": "#dbeafe", + "tma": "#bfdbfe", + "smem": "#e9d5ff", + "tmem": "#fed7aa", + "mma": "#bbf7d0", + "softmax": "#ddd6fe", + "barrier": "#fde68a", + "projection": "#fecaca", + "neutral": "#f8fafc", + "note": "#fefce8", +} + + +def configure_style(lang: str, font_path: str | None = None) -> None: + """Configure a fixed backend, font stack, and deterministic SVG IDs.""" + + plt.rcParams.update( + { + "font.family": "DejaVu Sans", + "font.sans-serif": ["DejaVu Sans"], + "font.size": 10, + "mathtext.fontset": "dejavusans", + "axes.unicode_minus": False, + "svg.fonttype": "none", + "svg.hashsalt": "flashmla-tutorial-v1", + } + ) + if lang != "zh": + return + + candidates = [ + font_path, + os.environ.get("FLASHMLA_CJK_FONT"), + "/tmp/NotoSansCJKsc-Regular.otf", + "/usr/share/fonts/opentype/noto/NotoSansCJK-Regular.ttc", + "/usr/share/fonts/opentype/noto/NotoSansCJKsc-Regular.otf", + "/usr/share/fonts/truetype/noto/NotoSansCJK-Regular.ttc", + ] + selected = next( + (Path(item) for item in candidates if item and Path(item).is_file()), None + ) + if selected is None: + raise FileNotFoundError( + "Chinese output requires a CJK font. Pass --font-path or set FLASHMLA_CJK_FONT." + ) + font_manager.fontManager.addfont(selected) + plt.rcParams["font.family"] = font_manager.FontProperties(fname=selected).get_name() + # Path Chinese glyphs so the checked-in SVG renders without a host CJK font. + plt.rcParams["svg.fonttype"] = "path" + + +def tr(lang: str, en: str, zh: str) -> str: + return zh if lang == "zh" else en + + +def rounded_box( + ax, + x: float, + y: float, + w: float, + h: float, + text: str, + color: str, + *, + fontsize: float = 9, + weight: str = "bold", + edgecolor: str | None = None, + linewidth: float = 1.2, + linestyle: str = "-", + zorder: int = 3, + text_color: str | None = None, +) -> FancyBboxPatch: + patch = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.04,rounding_size=0.06", + linewidth=linewidth, + linestyle=linestyle, + edgecolor=edgecolor or COLORS["ink"], + facecolor=color, + zorder=zorder, + ) + ax.add_patch(patch) + ax.text( + x + w / 2, + y + h / 2, + text, + ha="center", + va="center", + fontsize=fontsize, + weight=weight, + color=text_color or COLORS["ink"], + zorder=zorder + 1, + ) + return patch + + +def arrow( + ax, + start: tuple[float, float], + end: tuple[float, float], + *, + label: str | None = None, + color: str | None = None, + linewidth: float = 1.25, + linestyle: str = "-", + rad: float = 0.0, + label_offset: tuple[float, float] = (0.0, 0.12), + zorder: int = 2, +) -> FancyArrowPatch: + line_color = color or COLORS["line"] + patch = FancyArrowPatch( + start, + end, + arrowstyle="-|>", + mutation_scale=11, + linewidth=linewidth, + linestyle=linestyle, + color=line_color, + connectionstyle=f"arc3,rad={rad}", + zorder=zorder, + ) + ax.add_patch(patch) + if label: + mx = (start[0] + end[0]) / 2 + label_offset[0] + my = (start[1] + end[1]) / 2 + label_offset[1] + ax.text( + mx, + my, + label, + ha="center", + va="center", + fontsize=7.4, + color=line_color, + bbox=dict( + boxstyle="round,pad=0.12", + facecolor="white", + edgecolor="none", + alpha=0.92, + ), + zorder=zorder + 1, + ) + return patch + + +def plain_rect( + ax, + x: float, + y: float, + w: float, + h: float, + color: str, + *, + edgecolor: str | None = None, + linewidth: float = 1.1, + hatch: str | None = None, + zorder: int = 2, +) -> Rectangle: + patch = Rectangle( + (x, y), + w, + h, + facecolor=color, + edgecolor=edgecolor or COLORS["ink"], + linewidth=linewidth, + hatch=hatch, + zorder=zorder, + ) + ax.add_patch(patch) + return patch + + +def save_figure(fig, output: str | Path, *, dpi: int = 160) -> Path: + path = Path(output) + if path.suffix.lower() not in {".png", ".svg"}: + raise ValueError("--output must end in .png or .svg") + path.parent.mkdir(parents=True, exist_ok=True) + if path.suffix.lower() == ".svg": + metadata = {"Date": None, "Creator": "Modern GPU Programming for MLSys"} + else: + metadata = {"Software": "Modern GPU Programming for MLSys"} + fig.savefig( + path, + dpi=dpi, + facecolor="white", + transparent=False, + bbox_inches=None, + metadata=metadata, + ) + plt.close(fig) + if path.suffix.lower() == ".svg": + # Matplotlib emits trailing spaces in multiline SVG path data. Normalize + # generated assets so newly staged files pass Git's whitespace checks. + lines = path.read_text(encoding="utf-8").splitlines() + path.write_text( + "\n".join(line.rstrip() for line in lines) + "\n", + encoding="utf-8", + ) + return path diff --git a/img/scripts/gen_flashmla_cache_story.py b/img/scripts/gen_flashmla_cache_story.py new file mode 100644 index 00000000..5006ad66 --- /dev/null +++ b/img/scripts/gen_flashmla_cache_story.py @@ -0,0 +1,390 @@ +#!/usr/bin/env python3 +"""Generate the introductory MHA-to-MLA cache story for the FlashMLA tutorial.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + plain_rect, + rounded_box, + save_figure, + tr, +) + + +def _panel(ax, x, y, w, h, title, subtitle, color) -> None: + panel = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.06,rounding_size=0.08", + linewidth=1.35, + edgecolor=color, + facecolor="#ffffff", + linestyle="--", + zorder=0, + ) + ax.add_patch(panel) + ax.text( + x + 0.25, + y + h - 0.34, + title, + ha="left", + va="center", + fontsize=11.5, + weight="bold", + color=color, + ) + ax.text( + x + 0.25, + y + h - 0.72, + subtitle, + ha="left", + va="center", + fontsize=7.8, + color=COLORS["muted"], + ) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(18.0, 9.0)) + ax.set_xlim(0, 18) + ax.set_ylim(0, 9) + ax.axis("off") + + ax.text( + 9, + 8.68, + tr( + lang, + "How Can One MLA Cache Entry Serve 128 Query Heads?", + "一条 MLA Cache Entry 如何服务 128 个 Query Heads?", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9, + 8.28, + tr( + lang, + "cache the shared source once; preserve per-head behavior on the query and output paths", + "共享 source 只缓存一次;各 head 的差异保留在 query 与 output 路径", + ), + ha="center", + va="center", + fontsize=9.3, + color=COLORS["muted"], + ) + + _panel( + ax, + 0.35, + 1.30, + 4.45, + 6.45, + tr(lang, "1 · MHA cache", "1 · MHA cache"), + tr(lang, "materialize K and V for every head", "为每个 head 物化 K 与 V"), + COLORS["cta0_dark"], + ) + _panel( + ax, + 5.15, + 1.30, + 5.05, + 6.45, + tr(lang, "2 · MLA cache", "2 · MLA cache"), + tr( + lang, + "store one latent source per token", + "每个 token 只保存一份 latent source", + ), + "#7c3aed", + ) + _panel( + ax, + 10.55, + 1.30, + 7.10, + 6.45, + tr(lang, "3 · Absorbed execution", "3 · Absorbed execution"), + tr( + lang, + "head-specific work moves around the core", + "各 head 的特定计算移到 core 两侧", + ), + COLORS["cta1_dark"], + ) + + # MHA: a visual stack of materialized per-head cache entries. + ax.text( + 2.58, + 6.53, + tr(lang, "one cached token", "一个 cached token"), + ha="center", + fontsize=9.5, + weight="bold", + ) + row_entries = ( + ("head 0", "K_0", "V_0"), + ("head 1", "K_1", "V_1"), + ("...", "...", "..."), + ("head 127", "K_127", "V_127"), + ) + for idx, (label, k_label, v_label) in enumerate(row_entries): + y = 5.70 - idx * 0.83 + ax.text(0.72, y + 0.29, label, ha="left", va="center", fontsize=7.7) + plain_rect(ax, 1.55, y, 1.18, 0.58, COLORS["gmem"]) + plain_rect(ax, 2.73, y, 1.18, 0.58, "#bfdbfe") + ax.text( + 2.14, + y + 0.29, + k_label, + ha="center", + va="center", + fontsize=8.0, + weight="bold", + ) + ax.text( + 3.32, + y + 0.29, + v_label, + ha="center", + va="center", + fontsize=8.0, + weight="bold", + ) + rounded_box( + ax, + 0.82, + 1.72, + 3.50, + 0.88, + tr( + lang, + "cache stores a separate K/V slice\nfor every head", + "cache 为每个 head 保存\n独立的 K/V slice", + ), + COLORS["note"], + fontsize=8.5, + weight="normal", + edgecolor="#ca8a04", + ) + + # MLA: down-project content once and store it with one shared RoPE key. + rounded_box(ax, 5.55, 5.83, 1.20, 0.72, "h_s", COLORS["neutral"], fontsize=9.2) + rounded_box(ax, 7.12, 5.83, 1.35, 0.72, "W_DKV", COLORS["projection"], fontsize=8.8) + rounded_box( + ax, + 8.78, + 5.69, + 1.05, + 1.00, + "c_KV\nlatent\n512", + COLORS["smem"], + fontsize=8.0, + ) + arrow(ax, (6.75, 6.19), (7.12, 6.19)) + arrow(ax, (8.47, 6.19), (8.78, 6.19)) + rounded_box( + ax, + 5.55, + 4.47, + 2.05, + 0.78, + tr(lang, "shared RoPE key", "共享 RoPE key"), + "#bfdbfe", + fontsize=8.4, + ) + rounded_box(ax, 8.02, 4.47, 1.81, 0.78, "k_R\nRoPE 64", "#bfdbfe", fontsize=8.4) + arrow(ax, (7.60, 4.86), (8.02, 4.86)) + + ax.text( + 7.68, + 3.94, + tr(lang, "stored once per token", "每个 token 只存一次"), + ha="center", + va="center", + fontsize=9.2, + weight="bold", + color="#6d28d9", + ) + plain_rect(ax, 5.82, 2.90, 2.76, 0.76, COLORS["gmem"]) + plain_rect(ax, 8.58, 2.90, 1.20, 0.76, "#bfdbfe") + ax.text( + 7.20, 3.28, "c_KV · 512", ha="center", va="center", fontsize=9.0, weight="bold" + ) + ax.text( + 9.18, 3.28, "k_R · 64", ha="center", va="center", fontsize=8.4, weight="bold" + ) + rounded_box( + ax, + 5.82, + 1.72, + 3.96, + 0.72, + tr( + lang, + "one shared entry · not 128 expanded pairs", + "一份 shared entry · 不是 128 份展开 pair", + ), + COLORS["note"], + fontsize=8.2, + weight="normal", + edgecolor="#ca8a04", + ) + arrow(ax, (9.78, 3.28), (11.15, 4.09), color="#7c3aed", linewidth=1.6, rad=-0.05) + + # Absorbed execution: q_C alone crosses W_UK; q_R remains explicit. + rounded_box( + ax, + 10.92, + 5.89, + 1.46, + 0.70, + "q_C,i\nper head", + COLORS["neutral"], + fontsize=8.1, + ) + rounded_box( + ax, + 12.78, + 5.89, + 1.66, + 0.70, + "(W_UK,i)^T\ncontent only", + COLORS["projection"], + fontsize=7.8, + ) + rounded_box( + ax, + 10.92, + 4.93, + 1.46, + 0.70, + "q_R,i\nRoPE 64", + "#bfdbfe", + fontsize=8.1, + ) + rounded_box( + ax, + 14.88, + 5.34, + 2.28, + 1.02, + "Q_i = [q_abs,i ; q_R,i]\n512 + 64", + COLORS["tmem"], + fontsize=8.1, + ) + arrow(ax, (12.38, 6.24), (12.78, 6.24)) + arrow(ax, (14.44, 6.24), (14.88, 6.03)) + arrow( + ax, + (12.38, 5.28), + (14.88, 5.62), + label=tr(lang, "bypass W_UK", "绕过 W_UK"), + color=COLORS["cta0_dark"], + rad=-0.05, + label_offset=(0.0, -0.14), + ) + + rounded_box( + ax, + 11.15, + 3.63, + 2.56, + 0.92, + "shared K = [c_KV ; k_R]\nshared V = c_KV", + COLORS["gmem"], + fontsize=8.0, + ) + rounded_box( + ax, + 14.15, + 3.48, + 2.12, + 1.10, + tr(lang, "shared-cache\nattention core", "shared-cache\nattention core"), + COLORS["mma"], + fontsize=8.7, + ) + arrow(ax, (16.02, 5.34), (15.56, 4.58), color=COLORS["line"], rad=0.04) + arrow(ax, (13.71, 4.09), (14.15, 4.03)) + rounded_box( + ax, + 13.22, + 2.22, + 1.60, + 0.72, + "latent out_i\n512", + COLORS["tmem"], + fontsize=8.0, + ) + rounded_box( + ax, + 15.22, + 2.22, + 1.90, + 0.72, + tr( + lang, + "per-head output path\nW_UV,i / W_O", + "per-head output 路径\nW_UV,i / W_O", + ), + COLORS["projection"], + fontsize=7.6, + ) + arrow(ax, (15.05, 3.48), (14.10, 2.94), color=COLORS["line"], rad=0.04) + arrow(ax, (14.82, 2.58), (15.22, 2.58)) + ax.text( + 15.18, + 1.74, + tr( + lang, + "repeat the query/output paths for i=0…127\n→ 128 distinct head outputs", + "query/output 路径对 i=0…127 各自执行\n→ 128 份不同的 head output", + ), + ha="center", + va="center", + fontsize=8.0, + color=COLORS["muted"], + weight="bold", + ) + + rounded_box( + ax, + 1.65, + 0.30, + 14.70, + 0.66, + tr( + lang, + "Only [c_KV ; k_R] is cached. Per-head K/V need not be materialized; head-specific projections survive by reassociation around attention.", + "Cache 中只有 [c_KV ; k_R]。无需物化 per-head K/V;通过在 attention 两侧重新结合运算,仍保留各 head 的特定 projection。", + ), + COLORS["note"], + fontsize=8.4, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_cta_ownership.py b/img/scripts/gen_flashmla_cta_ownership.py new file mode 100644 index 00000000..e5f6679e --- /dev/null +++ b/img/scripts/gen_flashmla_cta_ownership.py @@ -0,0 +1,321 @@ +#!/usr/bin/env python3 +"""Generate the sparse FlashMLA head128 regular 2-CTA ownership diagram.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + plain_rect, + rounded_box, + save_figure, + tr, +) + + +def _partition_bar(ax, x, y, w, h, *, labels, colors, split="vertical"): + if split == "vertical": + cell_w = w / len(labels) + for idx, (label, color) in enumerate(zip(labels, colors, strict=True)): + plain_rect(ax, x + idx * cell_w, y, cell_w, h, color) + ax.text( + x + (idx + 0.5) * cell_w, + y + h / 2, + label, + ha="center", + va="center", + fontsize=8.6, + weight="bold", + color=COLORS["ink"], + zorder=4, + ) + else: + cell_h = h / len(labels) + for idx, (label, color) in enumerate(zip(labels, colors, strict=True)): + plain_rect(ax, x, y + (len(labels) - idx - 1) * cell_h, w, cell_h, color) + ax.text( + x + w / 2, + y + (len(labels) - idx - 0.5) * cell_h, + label, + ha="center", + va="center", + fontsize=8.6, + weight="bold", + color=COLORS["ink"], + zorder=4, + ) + + +def _logical_matrix(ax, x, y, w, h, *, title, col_axis, lang, kind): + ax.text( + x + w / 2, + y + h + 0.38, + title, + ha="center", + va="center", + fontsize=11, + weight="bold", + ) + ax.text( + x + w / 2, + y - 0.3, + col_axis, + ha="center", + va="center", + fontsize=8, + color=COLORS["muted"], + ) + ax.text( + x - 0.34, + y + h / 2, + ( + tr(lang, "Q-head rows", "Q head 行") + if kind == "k" + else tr(lang, "W rows (Q-head ownership)", "W 行(沿用 Q head 所有权)") + ), + ha="center", + va="center", + rotation=90, + fontsize=8, + color=COLORS["muted"], + ) + cell_colors = [ + [COLORS["cta0"], COLORS["cross01"]], + [COLORS["cross10"], COLORS["cta1"]], + ] + q_labels = ["Q0", "Q1"] if kind == "k" else ["W(Q0)", "W(Q1)"] + b_labels = ["K0", "K1"] if kind == "k" else ["V0", "V1"] + for row in range(2): + for col in range(2): + cx = x + col * w / 2 + cy = y + (1 - row) * h / 2 + plain_rect(ax, cx, cy, w / 2, h / 2, cell_colors[row][col]) + ax.text( + cx + w / 4, + cy + h / 4, + f"{q_labels[row]} × {b_labels[col]}", + ha="center", + va="center", + fontsize=8.5 if kind == "v" else 9, + weight="bold", + color=COLORS["ink"], + zorder=4, + ) + ax.text( + x + 0.10, + y + h - 0.11, + "heads 0:64", + ha="left", + va="top", + fontsize=6.7, + color=COLORS["muted"], + zorder=5, + ) + ax.text( + x + 0.10, + y + h / 2 - 0.11, + "heads 64:128", + ha="left", + va="top", + fontsize=6.7, + color=COLORS["muted"], + zorder=5, + ) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(16.0, 8.8)) + ax.set_xlim(0, 16) + ax.set_ylim(0, 8.8) + ax.axis("off") + + ax.text( + 8, + 8.5, + tr( + lang, + "Sparse FlashMLA Head128 Regular: 2-CTA Ownership", + "Sparse FlashMLA Head128 Regular:2-CTA 所有权", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 8, + 8.12, + tr( + lang, + "one CTA pair per query row · B_H=128 · B_TOPK=128 · D_V=512", + "每个 query row 使用一个 CTA pair · B_H=128 · B_TOPK=128 · D_V=512", + ), + ha="center", + va="center", + fontsize=9.5, + color=COLORS["muted"], + ) + + headings = [ + (0.45, tr(lang, "Q ownership", "Q 所有权")), + (5.5, tr(lang, "K selected-token ownership", "K 的选中 token 所有权")), + (10.55, tr(lang, "V feature ownership", "V feature 所有权")), + ] + for x, text in headings: + ax.text( + x, + 7.66, + text, + ha="left", + va="center", + fontsize=11, + weight="bold", + color=COLORS["ink"], + ) + + _partition_bar( + ax, + 0.65, + 6.13, + 4.15, + 1.15, + labels=("CTA 0 · Q heads 0:64", "CTA 1 · Q heads 64:128"), + colors=(COLORS["cta0"], COLORS["cta1"]), + split="horizontal", + ) + ax.text( + 2.72, + 5.88, + tr(lang, "each CTA: 64 × d_qk", "每个 CTA:64 × d_qk"), + ha="center", + fontsize=8, + color=COLORS["muted"], + ) + + _partition_bar( + ax, + 5.7, + 6.13, + 4.15, + 1.15, + labels=("CTA 0\nslots 0:64", "CTA 1\nslots 64:128"), + colors=(COLORS["cta0"], COLORS["cta1"]), + ) + ax.text( + 7.77, + 5.88, + tr(lang, "within the current sparse B_TOPK tile", "当前 sparse B_TOPK tile 内"), + ha="center", + fontsize=8, + color=COLORS["muted"], + ) + + _partition_bar( + ax, + 10.75, + 6.13, + 4.15, + 1.15, + labels=("CTA 0\nfeatures 0:256", "CTA 1\nfeatures 256:512"), + colors=(COLORS["cta0"], COLORS["cta1"]), + ) + ax.text( + 12.82, + 5.88, + tr( + lang, + "each half covers all 128 selected-token rows", + "每个 feature half 覆盖全部 128 个选中 token 行", + ), + ha="center", + fontsize=8, + color=COLORS["muted"], + ) + + _logical_matrix( + ax, + 0.85, + 1.75, + 5.3, + 2.7, + title=tr( + lang, + "QK · cta_group::2 → logits L [128 heads × 128 slots]", + "QK · cta_group::2 → logits L [128 heads × 128 slots]", + ), + col_axis=tr(lang, "selected-token columns", "选中 token 列"), + lang=lang, + kind="k", + ) + _logical_matrix( + ax, + 9.85, + 1.75, + 5.3, + 2.7, + title=tr( + lang, + "PV · cta_group::2 → output O [128 heads × 512 features]", + "PV · cta_group::2 → output O [128 heads × 512 features]", + ), + col_axis=tr(lang, "output-feature columns", "输出 feature 列"), + lang=lang, + kind="v", + ) + + rounded_box( + ax, + 6.70, + 2.48, + 2.6, + 1.25, + tr( + lang, + "L → WG0 softmax → W\nsame head × slot shape", + "L → WG0 softmax → W\n保持相同的 head × slot 形状", + ), + COLORS["softmax"], + fontsize=8.7, + ) + arrow(ax, (6.15, 3.1), (6.70, 3.1), label="L") + arrow(ax, (9.30, 3.1), (9.85, 3.1), label="W") + # Ownership-to-logical-tile guide arrows. + arrow(ax, (2.72, 5.76), (2.72, 4.68), color=COLORS["cta0_dark"], linewidth=1.0) + arrow( + ax, (7.77, 5.76), (5.4, 4.7), color=COLORS["cta1_dark"], linewidth=1.0, rad=0.08 + ) + arrow(ax, (12.82, 5.76), (12.82, 4.68), color=COLORS["cta1_dark"], linewidth=1.0) + + rounded_box( + ax, + 1.0, + 0.52, + 14.0, + 0.62, + tr( + lang, + "Every colored quadrant is a required block product. Cross-colored quadrants are not cross-CTA reductions; cta_group::2 combines operand halves without an explicit DSMEM copy.", + "每个彩色象限都是必需的 block product。交叉配色象限不是跨 CTA reduction;cta_group::2 在没有显式 DSMEM copy 的情况下组合 operand halves。", + ), + COLORS["note"], + fontsize=8.7, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_dataflow.py b/img/scripts/gen_flashmla_dataflow.py new file mode 100644 index 00000000..2650a6db --- /dev/null +++ b/img/scripts/gen_flashmla_dataflow.py @@ -0,0 +1,484 @@ +#!/usr/bin/env python3 +"""Generate the sparse FlashMLA head128 regular SMEM/TMEM data-flow diagram.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + plain_rect, + rounded_box, + save_figure, + tr, +) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(19.0, 9.4)) + ax.set_xlim(0, 19) + ax.set_ylim(0, 9.4) + ax.axis("off") + + ax.text( + 9.5, + 9.08, + tr( + lang, + "Sparse FlashMLA Head128 Regular: Data Residency", + "Sparse FlashMLA Head128 Regular:数据驻留", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9.5, + 8.68, + tr( + lang, + "one CTA's view; cta_group::2 combines the pair's operand halves", + "单个 CTA 的视图;cta_group::2 会组合 CTA pair 的 operand halves", + ), + ha="center", + va="center", + fontsize=9.5, + color=COLORS["muted"], + ) + + # Q path: one prefix remains in SMEM while the fixed 384-column suffix moves to TMEM. + rounded_box(ax, 0.35, 6.63, 1.65, 0.86, "Q\nGMEM", COLORS["gmem"], fontsize=9.5) + rounded_box( + ax, + 2.55, + 6.43, + 2.35, + 1.25, + tr( + lang, + "q_full · SMEM\n64 × d_qk per CTA", + "q_full · SMEM\n每个 CTA 为 64 × d_qk", + ), + COLORS["smem"], + fontsize=9, + ) + rounded_box( + ax, + 5.63, + 7.02, + 2.18, + 0.78, + tr( + lang, + "Q prefix · SMEM\nd_sq = d_qk − 384", + "Q prefix · SMEM\nd_sq = d_qk − 384", + ), + COLORS["smem"], + fontsize=8.5, + ) + rounded_box( + ax, + 5.63, + 5.94, + 2.18, + 0.78, + tr(lang, "q_tmem · TMEM\nfixed suffix 384", "q_tmem · TMEM\n固定 suffix 384"), + COLORS["tmem"], + fontsize=8.5, + ) + rounded_box( + ax, + 8.48, + 6.34, + 1.92, + 1.18, + tr(lang, "QK MMA\nSS prefix + TS suffix", "QK MMA\nSS prefix + TS suffix"), + COLORS["mma"], + fontsize=9, + ) + arrow(ax, (2.0, 7.06), (2.55, 7.06), label="TMA") + arrow(ax, (4.9, 7.2), (5.63, 7.4), label=tr(lang, "stays", "保留"), rad=-0.05) + arrow(ax, (4.9, 6.86), (5.63, 6.33), label="SMEM→TMEM", rad=0.08) + arrow(ax, (7.81, 7.4), (8.48, 7.18)) + arrow(ax, (7.81, 6.33), (8.48, 6.68)) + + # Sparse gather path and validity mask. + rounded_box(ax, 0.35, 4.66, 1.65, 0.82, "indices\nGMEM", COLORS["gmem"], fontsize=9) + rounded_box( + ax, + 0.35, + 3.34, + 1.65, + 0.92, + "KV cache\nGMEM\n[s_kv, 1, d_qk]", + COLORS["gmem"], + fontsize=8.5, + ) + rounded_box( + ax, + 2.65, + 4.56, + 2.5, + 0.92, + tr( + lang, + "WG1 gathered K · SMEM\n64 slots × d_qk per CTA", + "WG1 gather K · SMEM\n每个 CTA:64 slots × d_qk", + ), + COLORS["smem"], + fontsize=8.3, + ) + rounded_box( + ax, + 2.65, + 3.10, + 2.5, + 0.98, + tr( + lang, + "WG2 gathered V · SMEM\n128 slots × 256 features per CTA", + "WG2 gather V · SMEM\n每个 CTA:128 slots × 256 features", + ), + COLORS["smem"], + fontsize=8.1, + ) + rounded_box( + ax, + 5.72, + 4.45, + 1.82, + 0.93, + tr( + lang, + "is_k_valid · SMEM\n2 slots × 16 bytes", + "is_k_valid · SMEM\n2 个 slot × 16 bytes", + ), + COLORS["barrier"], + fontsize=8.1, + ) + arrow(ax, (2.0, 5.08), (2.65, 5.08), label=tr(lang, "selected slots", "选中 slots")) + arrow( + ax, + (2.0, 4.76), + (2.65, 3.83), + color=COLORS["line"], + rad=-0.05, + ) + # Route mask metadata above the K box so the dependency does not cut through its label. + ax.plot( + [2.0, 2.25, 5.28], [5.32, 5.76, 5.76], color=COLORS["line"], lw=1.25, zorder=2 + ) + arrow(ax, (5.28, 5.76), (6.22, 5.38), color=COLORS["line"], rad=0.05) + ax.text( + 3.82, + 5.86, + tr(lang, "bounds + topk_length", "边界 + topk_length"), + ha="center", + va="center", + fontsize=7.3, + color=COLORS["line"], + ) + arrow(ax, (2.0, 3.72), (2.65, 4.83), label="gather4", rad=-0.12) + arrow(ax, (2.0, 3.72), (2.65, 3.59), label="gather4", rad=0.05) + # K takes a low elbow under q_tmem, then enters QK from below. + ax.plot( + [5.15, 5.5, 7.82], [5.32, 5.61, 5.61], color=COLORS["line"], lw=1.25, zorder=2 + ) + arrow(ax, (7.82, 5.61), (8.82, 6.34), label="K", color=COLORS["line"], rad=-0.05) + + # Logits, online softmax, weights, and public statistics. + rounded_box( + ax, + 10.92, + 6.36, + 1.86, + 1.15, + "tmem_p · TMEM\nL logits\n64 × 128 view", + COLORS["tmem"], + fontsize=8.5, + ) + rounded_box( + ax, + 13.25, + 6.10, + 1.94, + 1.48, + tr( + lang, + "WG0 online softmax\nmask · max · exp · sum", + "WG0 online softmax\nmask · max · exp · sum", + ), + COLORS["softmax"], + fontsize=8.7, + ) + rounded_box( + ax, + 13.18, + 4.42, + 2.08, + 0.95, + "s_smem_gemm · SMEM\nW weights · 64 × 128", + COLORS["smem"], + fontsize=8.3, + ) + rounded_box( + ax, + 16.0, + 6.29, + 2.05, + 1.08, + tr( + lang, + "max_logits / lse\nGMEM · sink excluded", + "max_logits / lse\nGMEM · 不含 sink", + ), + COLORS["gmem"], + fontsize=8.2, + ) + rounded_box( + ax, + 15.62, + 5.12, + 2.35, + 0.75, + tr( + lang, + "mi · real_mi · li\nWG0 registers", + "mi · real_mi · li\nWG0 registers", + ), + COLORS["neutral"], + fontsize=8.0, + ) + rounded_box( + ax, + 16.10, + 4.22, + 1.87, + 0.64, + tr(lang, "optional attn_sink\nGMEM", "可选 attn_sink\nGMEM"), + COLORS["gmem"], + fontsize=7.7, + ) + arrow(ax, (10.4, 6.93), (10.92, 6.93)) + arrow(ax, (12.78, 6.93), (13.25, 6.93)) + arrow( + ax, + (7.54, 4.92), + (13.25, 6.42), + label=tr(lang, "mask ready", "mask 就绪"), + rad=-0.10, + ) + arrow( + ax, (14.22, 6.10), (14.22, 5.37), label=tr(lang, "cast/store W", "转换/写入 W") + ) + arrow(ax, (15.19, 6.93), (16.0, 6.93)) + arrow(ax, (15.10, 6.36), (15.78, 5.76), color=COLORS["line"], rad=0.05) + + # PV path and epilogue. + rounded_box( + ax, + 8.52, + 2.96, + 1.78, + 1.08, + tr(lang, "PV MMA\nW × V", "PV MMA\nW × V"), + COLORS["mma"], + fontsize=9.2, + ) + rounded_box( + ax, + 10.92, + 2.92, + 1.86, + 1.14, + "o_tmem · TMEM\nO accumulator\n64 × 512 view", + COLORS["tmem"], + fontsize=8.4, + ) + rounded_box( + ax, + 13.25, + 2.92, + 1.94, + 1.14, + tr( + lang, + "WG0 epilogue\nO~ / (li + sink term)\n→ bf16", + "WG0 epilogue\nO~ /(li + sink 项)\n→ bf16", + ), + COLORS["softmax"], + fontsize=7.7, + ) + rounded_box( + ax, + 15.65, + 2.92, + 1.55, + 1.14, + "o_smem\nSMEM\n64 × 512", + COLORS["smem"], + fontsize=8.3, + ) + rounded_box(ax, 17.64, 3.04, 1.05, 0.9, "out\nGMEM", COLORS["gmem"], fontsize=8.7) + arrow(ax, (5.15, 3.59), (8.52, 3.50), label="V") + arrow(ax, (13.18, 4.86), (10.0, 4.04), label="W", rad=0.10) + arrow(ax, (10.3, 3.5), (10.92, 3.5)) + arrow(ax, (12.78, 3.5), (13.25, 3.5), label="O~") + arrow( + ax, + (16.05, 5.12), + (14.84, 4.06), + label="li", + color=COLORS["line"], + rad=0.05, + ) + arrow( + ax, + (16.10, 4.54), + (15.19, 3.75), + label=tr(lang, "denominator only", "仅进入分母"), + color=COLORS["line"], + rad=0.03, + label_offset=(0.30, -0.04), + ) + arrow(ax, (15.19, 3.5), (15.65, 3.5), label="TMEM→SMEM") + arrow(ax, (17.2, 3.5), (17.64, 3.5), label="TMA") + + # Exact lifetime aliasing from the pinned SharedMemoryPlan. + outer = FancyBboxPatch( + (0.42, 0.22), + 18.16, + 1.82, + boxstyle="round,pad=0.05,rounding_size=0.06", + linewidth=1.2, + linestyle="--", + edgecolor="#7c3aed", + facecolor="#faf5ff", + zorder=1, + ) + ax.add_patch(outer) + ax.text( + 0.72, + 1.80, + tr( + lang, + "Per-CTA SMEM union: the same address range is reused by lifetime", + "每个 CTA 的 SMEM union:同一地址范围按生命周期复用", + ), + ha="left", + va="center", + fontsize=10, + weight="bold", + color="#6d28d9", + zorder=3, + ) + rounded_box( + ax, + 0.72, + 0.52, + 3.0, + 0.88, + tr( + lang, + "prologue\nq_full = prefix | suffix384", + "prologue\nq_full = prefix | suffix384", + ), + COLORS["smem"], + fontsize=8.3, + ) + arrow( + ax, (3.72, 0.96), (4.36, 0.96), label=tr(lang, "reuse", "复用"), color="#7c3aed" + ) + plain_rect(ax, 4.42, 0.52, 1.65, 0.88, COLORS["smem"], edgecolor=COLORS["ink"]) + plain_rect(ax, 6.07, 0.52, 2.0, 0.88, "#ddd6fe", edgecolor=COLORS["ink"]) + plain_rect(ax, 8.07, 0.52, 2.0, 0.88, "#c4b5fd", edgecolor=COLORS["ink"]) + ax.text( + 5.24, + 0.96, + tr(lang, "Q prefix\nlive", "Q prefix\n存活"), + ha="center", + va="center", + fontsize=8, + weight="bold", + zorder=4, + ) + ax.text( + 7.07, + 0.96, + tr(lang, "one V\nworkspace", "单份 V\nworkspace"), + ha="center", + va="center", + fontsize=8, + weight="bold", + zorder=4, + ) + ax.text( + 9.07, + 0.96, + tr(lang, "one K\nworkspace", "单份 K\nworkspace"), + ha="center", + va="center", + fontsize=8, + weight="bold", + zorder=4, + ) + ax.text( + 7.24, + 0.32, + tr( + lang, + "steady-state views are adjacent, not duplicate stages", + "稳态 views 相邻,并非复制的 stages", + ), + ha="center", + fontsize=7.3, + color=COLORS["muted"], + ) + arrow( + ax, + (10.07, 0.96), + (10.75, 0.96), + label=tr(lang, "reuse", "复用"), + color="#7c3aed", + ) + rounded_box( + ax, + 10.82, + 0.52, + 2.72, + 0.88, + tr(lang, "epilogue\no_smem · 64 × 512", "epilogue\no_smem · 64 × 512"), + COLORS["smem"], + fontsize=8.3, + ) + ax.text( + 14.0, + 0.96, + tr( + lang, + "K and V are adjacent in the steady-state region.\nThat region reuses Q's tail; later o_smem reuses the union base for the O epilogue.", + "K 与 V 位于相邻的稳态区域。\n该区域复用 Q tail;随后 o_smem 再复用 union base 完成 O epilogue。", + ), + ha="left", + va="center", + fontsize=8.1, + color=COLORS["muted"], + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_mla_modes.py b/img/scripts/gen_flashmla_mla_modes.py new file mode 100644 index 00000000..538a8b41 --- /dev/null +++ b/img/scripts/gen_flashmla_mla_modes.py @@ -0,0 +1,384 @@ +#!/usr/bin/env python3 +"""Generate the two equivalent MLA attention-core views used by the tutorial.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + plain_rect, + rounded_box, + save_figure, + tr, +) + + +def _panel( + ax, x: float, y: float, w: float, h: float, title: str, subtitle: str, color: str +) -> None: + panel = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.06,rounding_size=0.08", + linewidth=1.35, + edgecolor=color, + facecolor="#ffffff", + linestyle="--", + zorder=0, + ) + ax.add_patch(panel) + ax.text( + x + 0.28, + y + h - 0.34, + title, + ha="left", + va="center", + fontsize=12, + weight="bold", + color=color, + ) + ax.text( + x + 0.28, + y + h - 0.72, + subtitle, + ha="left", + va="center", + fontsize=7.8, + color=COLORS["muted"], + ) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(18.0, 9.4)) + ax.set_xlim(0, 18) + ax.set_ylim(0, 9.4) + ax.axis("off") + + ax.text( + 9, + 9.08, + tr( + lang, + "MLA: Two Equivalent Attention-Core Views of One Cache", + "MLA:同一份 Cache 的两种等价 Attention Core 视图", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9, + 8.70, + tr( + lang, + "move the up-projections across the attention core without changing the cached latent state", + "在 attention core 两侧移动 up-projection,而不改变缓存的 latent state", + ), + ha="center", + va="center", + fontsize=9.3, + color=COLORS["muted"], + ) + + # One common compressed cache is the source for both views. + ax.text( + 9, + 8.26, + tr(lang, "one MLA KV cache entry", "同一条 MLA KV cache entry"), + ha="center", + va="center", + fontsize=10, + weight="bold", + ) + plain_rect(ax, 6.15, 7.35, 4.25, 0.72, COLORS["gmem"], edgecolor=COLORS["ink"]) + plain_rect(ax, 10.40, 7.35, 1.45, 0.72, "#bfdbfe", edgecolor=COLORS["ink"]) + ax.text( + 8.27, + 7.71, + "c_KV [latent 512]", + ha="center", + va="center", + fontsize=9.3, + weight="bold", + zorder=4, + ) + ax.text( + 11.12, + 7.71, + "k_R [RoPE 64]", + ha="center", + va="center", + fontsize=8.8, + weight="bold", + zorder=4, + ) + ax.text( + 9, + 7.15, + tr( + lang, + "stored once; the diagrams below differ only in where W_UK and W_UV run", + "只缓存一份;下方两种视图只改变 W_UK 与 W_UV 的执行位置", + ), + ha="center", + va="center", + fontsize=7.8, + color=COLORS["muted"], + ) + + _panel( + ax, + 0.35, + 1.42, + 8.32, + 5.30, + tr(lang, "MHA mode", "MHA mode"), + tr( + lang, + "expand per-head K and V before the core", + "在 core 之前展开每个 head 的 K 与 V", + ), + COLORS["cta0_dark"], + ) + _panel( + ax, + 9.33, + 1.42, + 8.32, + 5.30, + tr(lang, "Absorbed MQA mode", "Absorbed MQA mode"), + tr( + lang, + "absorb W_UK into q_C; q_R bypasses; move W_UV after the core", + "将 W_UK 吸收到 q_C;q_R 绕过;把 W_UV 移到 core 之后", + ), + COLORS["cta1_dark"], + ) + arrow(ax, (7.52, 7.35), (4.58, 6.43), color=COLORS["cta0_dark"], rad=0.08) + arrow(ax, (10.47, 7.35), (13.55, 6.43), color=COLORS["cta1_dark"], rad=-0.08) + + # Left: explicit per-head K/V expansion before a conventional MHA-shaped core. + rounded_box( + ax, + 0.82, + 4.82, + 2.05, + 0.82, + "per-head Q\n[q_C 128 ; q_R 64]", + COLORS["neutral"], + fontsize=8.3, + ) + rounded_box( + ax, 0.82, 3.78, 1.72, 0.75, "c_KV\nlatent 512", COLORS["gmem"], fontsize=8.4 + ) + rounded_box( + ax, 0.82, 2.76, 1.72, 0.70, "k_R\nRoPE 64", COLORS["gmem"], fontsize=8.3 + ) + rounded_box(ax, 3.05, 4.02, 1.28, 0.70, "W_UK", COLORS["projection"], fontsize=9) + rounded_box(ax, 3.05, 3.00, 1.28, 0.70, "W_UV", COLORS["projection"], fontsize=9) + rounded_box( + ax, + 4.86, + 3.97, + 2.20, + 0.82, + "per-head K\n[k_C 128 ; k_R 64]", + COLORS["smem"], + fontsize=8.2, + ) + rounded_box( + ax, 4.86, 2.92, 2.20, 0.76, "per-head V\nv_C 128", COLORS["smem"], fontsize=8.4 + ) + rounded_box( + ax, + 3.08, + 1.72, + 2.70, + 0.84, + tr( + lang, + "MHA attention core\nper-head K / V", + "MHA attention core\nper-head K / V", + ), + COLORS["mma"], + fontsize=8.7, + ) + rounded_box( + ax, 6.34, 1.76, 1.75, 0.76, "per-head out\n128", COLORS["neutral"], fontsize=8.5 + ) + arrow(ax, (2.54, 4.15), (3.05, 4.37)) + arrow(ax, (2.54, 4.00), (3.05, 3.35)) + arrow(ax, (4.33, 4.37), (4.86, 4.37)) + # k_R bypasses W_UK and joins K below that projection box. + ax.plot( + [2.54, 2.76, 4.55], [3.11, 3.88, 3.88], color=COLORS["line"], lw=1.25, zorder=2 + ) + arrow( + ax, + (4.55, 3.88), + (5.15, 3.97), + label=tr(lang, "concat", "拼接"), + color=COLORS["line"], + rad=-0.03, + ) + arrow(ax, (4.33, 3.35), (4.86, 3.30)) + # Route Q around the left edge so it does not cut through c_KV/W_UV. + ax.plot( + [1.84, 0.62, 0.62, 2.72], + [4.82, 4.82, 2.14, 2.14], + color=COLORS["line"], + lw=1.25, + zorder=2, + ) + arrow(ax, (2.72, 2.14), (3.08, 2.14), color=COLORS["line"]) + arrow(ax, (5.70, 3.97), (4.82, 2.56), color=COLORS["line"], rad=0.04) + arrow(ax, (5.70, 2.92), (5.18, 2.56), color=COLORS["line"], rad=-0.02) + arrow(ax, (5.78, 2.14), (6.34, 2.14)) + + # Right: only the content query absorbs W_UK. The per-head RoPE query + # bypasses that projection and is concatenated immediately before QK. + rounded_box( + ax, + 9.78, + 5.18, + 1.48, + 0.66, + "q_C · per head\ncontent 128", + COLORS["neutral"], + fontsize=8.0, + ) + rounded_box( + ax, + 9.78, + 4.37, + 1.48, + 0.62, + "q_R · per head\nRoPE 64", + "#bfdbfe", + fontsize=8.0, + ) + rounded_box( + ax, + 11.72, + 5.14, + 1.45, + 0.74, + tr(lang, "(W_UK)^T q_C\ncontent only", "(W_UK)^T q_C\n仅 content"), + COLORS["projection"], + fontsize=7.9, + ) + rounded_box( + ax, + 13.62, + 4.64, + 2.78, + 1.02, + "absorbed Q\n[q_abs 512 ; q_R 64] = 576", + COLORS["tmem"], + fontsize=8.2, + ) + rounded_box( + ax, + 9.83, + 3.30, + 2.30, + 0.94, + "shared KV · h_kv=1\n[c_KV 512 ; k_R 64]\nV uses c_KV 512", + COLORS["gmem"], + fontsize=8.0, + ) + rounded_box( + ax, + 12.35, + 2.44, + 2.42, + 0.94, + tr(lang, "absorbed MQA\nattention core", "absorbed MQA\nattention core"), + COLORS["mma"], + fontsize=8.8, + ) + rounded_box( + ax, 15.18, 2.51, 1.55, 0.80, "latent out\n512", COLORS["tmem"], fontsize=8.5 + ) + rounded_box( + ax, + 14.30, + 1.58, + 1.45, + 0.70, + tr(lang, "W_UV\nafter core", "W_UV\n移到 core 后"), + COLORS["projection"], + fontsize=8.0, + ) + rounded_box( + ax, 16.18, 1.58, 1.05, 0.70, "out\n128", COLORS["neutral"], fontsize=8.3 + ) + arrow(ax, (11.26, 5.51), (11.72, 5.51)) + arrow(ax, (13.17, 5.51), (13.62, 5.30)) + # The explicit positional channel never passes through W_UK. + arrow( + ax, + (11.26, 4.68), + (13.62, 4.91), + label=tr(lang, "bypass W_UK", "绕过 W_UK"), + color=COLORS["cta0_dark"], + rad=-0.06, + label_offset=(0.0, -0.15), + ) + arrow(ax, (15.05, 4.64), (13.83, 3.38), color=COLORS["line"], rad=-0.05) + arrow(ax, (10.98, 3.30), (12.64, 3.08), color=COLORS["line"], rad=0.03) + arrow(ax, (14.77, 2.91), (15.18, 2.91)) + arrow(ax, (15.95, 2.51), (15.02, 2.28), color=COLORS["line"], rad=0.06) + arrow(ax, (15.75, 1.93), (16.18, 1.93)) + + # Explicit equivalence and chapter scope. + ax.text( + 9, + 1.23, + tr( + lang, + "Equivalent after projection reassociation: both produce the same per-head output 128", + "重新结合 projection 后等价:两种视图都产生相同的 per-head output 128", + ), + ha="center", + va="center", + fontsize=8.0, + color="#7c3aed", + weight="bold", + ) + rounded_box( + ax, + 2.1, + 0.24, + 13.8, + 0.76, + tr( + lang, + "The d_qk=576 sparse-prefill case studied here uses the absorbed MQA view:\nshared KV [512+64], absorbed Q 576, latent output 512. These dimensions do not describe every FlashMLA kernel.", + "本章重点分析的 d_qk=576 sparse-prefill case 采用 absorbed MQA 视图:\nshared KV [512+64]、absorbed Q 576、latent output 512。这些维度并不代表所有 FlashMLA kernel。", + ), + COLORS["note"], + fontsize=8.2, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_pipeline.py b/img/scripts/gen_flashmla_pipeline.py new file mode 100644 index 00000000..64eebcb9 --- /dev/null +++ b/img/scripts/gen_flashmla_pipeline.py @@ -0,0 +1,448 @@ +#!/usr/bin/env python3 +"""Generate the sparse FlashMLA head128 regular steady-state pipeline diagram.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + rounded_box, + save_figure, + tr, +) + + +def _row(ax, y: float, title: str, role: str) -> None: + rounded_box( + ax, 0.12, y, 2.05, 0.82, f"{title}\n{role}", COLORS["neutral"], fontsize=8.4 + ) + ax.plot([2.42, 18.7], [y + 0.41, y + 0.41], color="#e5e7eb", lw=1.0, zorder=0) + + +def _barrier_note(ax, x: float, y: float, text: str, *, fontsize: float = 7.0) -> None: + ax.text( + x, + y, + text, + ha="center", + va="center", + fontsize=fontsize, + color="#92400e", + bbox=dict( + boxstyle="round,pad=0.14", facecolor=COLORS["barrier"], edgecolor="#d97706" + ), + zorder=7, + ) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(19.0, 10.5)) + ax.set_xlim(0, 19) + ax.set_ylim(0, 10.5) + ax.axis("off") + + ax.text( + 9.5, + 10.16, + tr( + lang, + "Sparse FlashMLA Head128 Regular: Steady-State Pipeline", + "Sparse FlashMLA Head128 Regular:稳态 Pipeline", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9.5, + 9.76, + tr( + lang, + "softmax(k−1) may overlap QK(k); after QK(k) is issued, softmax(k) may overlap asynchronous PV(k−1); widths are not cycle measurements", + "softmax(k−1) 可与 QK(k) 重叠;QK(k) 发出后,softmax(k) 可与异步 PV(k−1) 重叠;方框宽度不表示 cycle 数", + ), + ha="center", + va="center", + fontsize=9.4, + color=COLORS["muted"], + ) + arrow(ax, (2.42, 9.24), (18.62, 9.24), color="#9ca3af", linewidth=1.0) + ax.text( + 10.5, + 9.31, + tr(lang, "time", "时间"), + ha="center", + va="bottom", + fontsize=8, + color=COLORS["muted"], + style="italic", + ) + + y_k = 7.83 + y_v = 6.23 + y_mma = 4.63 + y_mask = 3.17 + y_soft = 1.57 + _row(ax, y_k, "WG1", tr(lang, "K gather producer", "K gather producer")) + _row(ax, y_v, "WG2", tr(lang, "V gather producer", "V gather producer")) + _row(ax, y_mma, "WG3 · CTA0 warp 12", tr(lang, "QK / PV issue", "发起 QK / PV")) + _row(ax, y_mask, "WG3 · warp 13", tr(lang, "validity mask", "有效性 mask")) + _row(ax, y_soft, "WG0", tr(lang, "softmax + O rescale", "softmax + O 重缩放")) + + # Current K was gathered earlier into the one in-place K workspace. + rounded_box( + ax, + 2.54, + y_k + 0.06, + 1.18, + 0.70, + "K(k) part0\nready", + "#dbeafe", + fontsize=7.5, + edgecolor="#60a5fa", + ) + rounded_box( + ax, + 3.92, + y_k + 0.06, + 1.18, + 0.70, + "K(k) part1\nready", + "#dbeafe", + fontsize=7.5, + edgecolor="#60a5fa", + ) + + # The leader issues two QK segments, then two PV segments for the prior tile. + rounded_box( + ax, + 5.40, + y_mma + 0.03, + 1.26, + 0.76, + "QK(k)\nSS prefix", + COLORS["mma"], + fontsize=8.0, + ) + rounded_box( + ax, + 7.35, + y_mma + 0.03, + 1.26, + 0.76, + "QK(k)\nTS suffix384", + COLORS["mma"], + fontsize=8.0, + ) + rounded_box( + ax, + 10.28, + y_mma + 0.03, + 1.35, + 0.76, + "PV(k−1)\npart0", + COLORS["mma"], + fontsize=8.0, + ) + rounded_box( + ax, + 12.36, + y_mma + 0.03, + 1.35, + 0.76, + "PV(k−1)\npart1", + COLORS["mma"], + fontsize=8.0, + ) + arrow(ax, (6.66, y_mma + 0.41), (7.35, y_mma + 0.41), color=COLORS["line"]) + arrow(ax, (8.61, y_mma + 0.41), (10.28, y_mma + 0.41), color=COLORS["line"]) + arrow(ax, (11.63, y_mma + 0.41), (12.36, y_mma + 0.41), color=COLORS["line"]) + ax.text( + 9.42, + y_mma + 0.18, + tr(lang, "same issue warp · source order", "同一个 issue warp · 源码顺序"), + ha="center", + va="center", + fontsize=6.9, + color=COLORS["muted"], + style="italic", + ) + + # Current K readiness gates each QK segment; score-TMEM reuse has its own gate. + arrow(ax, (3.72, y_k + 0.39), (5.73, y_mma + 0.79), color="#2563eb", rad=-0.06) + _barrier_note(ax, 4.55, 6.74, "k_part0_ready[k]") + arrow(ax, (5.10, y_k + 0.39), (7.68, y_mma + 0.79), color="#2563eb", rad=-0.08) + _barrier_note(ax, 6.42, 6.98, "k_part1_ready[k]") + rounded_box( + ax, + 4.92, + 4.06, + 2.10, + 0.43, + tr( + lang, + "incoming from prior WG0(k−1) · p_free[k−1]", + "来自前一轮 WG0(k−1) · p_free[k−1]", + ), + "#f3e8ff", + fontsize=6.5, + weight="normal", + edgecolor="#7c3aed", + linestyle="--", + ) + arrow( + ax, + (5.97, 4.49), + (5.97, y_mma + 0.03), + color="#7c3aed", + linestyle="--", + linewidth=1.1, + ) + + # QK segment completion releases the same K workspace for k+1, part by part. + rounded_box( + ax, + 6.70, + y_k + 0.06, + 1.42, + 0.70, + "gather K(k+1)\npart0", + COLORS["tma"], + fontsize=7.6, + ) + rounded_box( + ax, + 8.68, + y_k + 0.06, + 1.42, + 0.70, + "gather K(k+1)\npart1", + COLORS["tma"], + fontsize=7.6, + ) + arrow(ax, (6.03, y_mma + 0.79), (7.12, y_k + 0.06), color="#059669", rad=0.04) + _barrier_note(ax, 6.72, 7.25, "qk_part_done[k]") + arrow(ax, (7.98, y_mma + 0.79), (9.10, y_k + 0.06), color="#059669", rad=0.04) + _barrier_note(ax, 8.64, 7.32, "qk_done[k]") + + # The prior V parts are already ready for PV(k-1). + rounded_box( + ax, + 8.18, + y_v + 0.06, + 1.15, + 0.70, + "V(k−1)\npart0 ready", + "#dbeafe", + fontsize=7.2, + edgecolor="#60a5fa", + ) + rounded_box( + ax, + 9.48, + y_v + 0.06, + 1.15, + 0.70, + "V(k−1)\npart1 ready", + "#dbeafe", + fontsize=7.2, + edgecolor="#60a5fa", + ) + arrow(ax, (9.33, y_v + 0.38), (10.62, y_mma + 0.79), color="#2563eb", rad=-0.04) + arrow(ax, (10.63, y_v + 0.28), (12.70, y_mma + 0.79), color="#2563eb", rad=-0.08) + rounded_box( + ax, + 9.88, + 4.06, + 2.14, + 0.43, + tr( + lang, + "incoming from prior WG0(k−1) · so_ready[k−1]", + "来自前一轮 WG0(k−1) · so_ready[k−1]", + ), + "#f3e8ff", + fontsize=6.4, + weight="normal", + edgecolor="#7c3aed", + linestyle="--", + ) + arrow( + ax, + (10.95, 4.49), + (10.95, y_mma + 0.03), + color="#7c3aed", + linestyle="--", + linewidth=1.1, + ) + + # Each completed PV half releases the one V workspace for the matching k half. + rounded_box( + ax, + 11.72, + y_v + 0.06, + 1.38, + 0.70, + "gather V(k)\npart0", + COLORS["tma"], + fontsize=7.6, + ) + rounded_box( + ax, + 13.80, + y_v + 0.06, + 1.38, + 0.70, + "gather V(k)\npart1", + COLORS["tma"], + fontsize=7.6, + ) + arrow(ax, (10.95, y_mma + 0.79), (12.12, y_v + 0.06), color="#059669", rad=0.04) + _barrier_note(ax, 11.78, 5.94, "sv_part_done[k−1]") + arrow(ax, (13.03, y_mma + 0.79), (14.20, y_v + 0.06), color="#059669", rad=0.04) + _barrier_note(ax, 13.87, 5.94, "sv_done[k−1]") + + # Mask production runs on a separate warp and feeds WG0. + rounded_box( + ax, + 5.72, + y_mask + 0.06, + 1.92, + 0.70, + tr( + lang, + "pack mask(k)\n8 indices / lane", + "pack mask(k)\n每个 lane 处理 8 indices", + ), + COLORS["barrier"], + fontsize=7.6, + ) + + # WG0 consumes L(k), computes W in registers while PV(k-1) is active, then safely reuses W/O. + rounded_box( + ax, + 8.72, + y_soft + 0.03, + 1.55, + 0.76, + tr(lang, "load L(k)\nfrom TMEM", "从 TMEM\n读取 L(k)"), + COLORS["tmem"], + fontsize=7.8, + ) + rounded_box( + ax, + 10.55, + y_soft + 0.03, + 2.22, + 0.76, + tr( + lang, + "mask L(k)\nmax / exp / row sum", + "mask L(k)\nmax / exp / row sum", + ), + COLORS["softmax"], + fontsize=7.8, + ) + rounded_box( + ax, + 13.78, + y_soft + 0.03, + 3.05, + 0.76, + tr( + lang, + "after sv_done(k−1): write W(k)\noptional O rescale · so_ready[k]", + "等待 sv_done(k−1) 后:写入 W(k)\n按需重缩放 O · so_ready[k]", + ), + COLORS["softmax"], + fontsize=7.7, + ) + arrow(ax, (8.0, y_mma + 0.03), (9.32, y_soft + 0.79), color="#7c3aed", rad=0.05) + _barrier_note(ax, 8.50, 3.76, "qk_done[k]") + arrow(ax, (7.64, y_mask + 0.41), (10.90, y_soft + 0.79), color="#d97706", rad=0.07) + _barrier_note(ax, 8.35, 2.86, "k_valid_ready[k]") + arrow(ax, (12.77, y_soft + 0.41), (13.78, y_soft + 0.41), color="#7c3aed") + _barrier_note(ax, 13.25, y_soft + 0.72, "wait sv_done[k−1]") + arrow(ax, (13.03, y_mma + 0.03), (14.30, y_soft + 0.79), color="#059669", rad=-0.05) + arrow( + ax, + (9.49, y_soft + 0.03), + (9.49, 0.94), + label=tr( + lang, + "TMEM L load complete → p_free[k] → future QK(k+1)", + "TMEM L 读取完成 → p_free[k] → 后续 QK(k+1)", + ), + color="#7c3aed", + linestyle="--", + label_offset=(1.45, 0.0), + ) + arrow( + ax, + (16.35, y_soft + 0.03), + (17.52, 0.94), + label=tr(lang, "so_ready[k] → future PV(k)", "so_ready[k] → 后续 PV(k)"), + color="#7c3aed", + linestyle="--", + label_offset=(0.10, 0.0), + rad=0.05, + ) + rounded_box( + ax, + 15.42, + y_mask + 0.06, + 2.08, + 0.70, + tr( + lang, + "pack mask(k+2)\nreuse slot k%2", + "pack mask(k+2)\n复用 slot k%2", + ), + COLORS["barrier"], + fontsize=7.4, + ) + arrow( + ax, + (11.35, y_soft + 0.79), + (15.80, y_mask + 0.06), + color="#d97706", + linestyle="--", + rad=-0.08, + ) + _barrier_note(ax, 13.55, 2.88, "k_valid_free[k]", fontsize=6.6) + + # Exact scope of the two-slot ring in the pinned regular kernel. + rounded_box( + ax, + 0.62, + 0.18, + 17.76, + 0.62, + tr( + lang, + "NUM_BUFS=2 is a barrier/phase ring: slot=k%2, phase=(k//2)&1. K, V, and s_smem_gemm are single in-place workspaces (plus two small mask slots), not two complete K/V stages.", + "NUM_BUFS=2 是 barrier/phase ring:slot=k%2,phase=(k//2)&1。K、V 与 s_smem_gemm 都是单份原位 workspace(另有两个小型 mask slots),并非两份完整 K/V stages。", + ), + COLORS["note"], + fontsize=8.3, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_pipeline_stages.py b/img/scripts/gen_flashmla_pipeline_stages.py new file mode 100644 index 00000000..8b5ea583 --- /dev/null +++ b/img/scripts/gen_flashmla_pipeline_stages.py @@ -0,0 +1,478 @@ +#!/usr/bin/env python3 +"""Generate the fill, steady-state, and drain story for sparse FlashMLA.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + rounded_box, + save_figure, + tr, +) + + +def _panel(ax, x, y, w, h, title, subtitle, color) -> None: + panel = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.06,rounding_size=0.08", + linewidth=1.35, + edgecolor=color, + facecolor="#ffffff", + linestyle="--", + zorder=0, + ) + ax.add_patch(panel) + ax.text( + x + 0.24, + y + h - 0.32, + title, + ha="left", + va="center", + fontsize=11.2, + weight="bold", + color=color, + ) + ax.text( + x + 0.24, + y + h - 0.70, + subtitle, + ha="left", + va="center", + fontsize=7.6, + color=COLORS["muted"], + ) + + +def _lane(ax, x0, x1, y, label, lang) -> None: + ax.text( + x0, + y, + label, + ha="left", + va="center", + fontsize=7.1, + color=COLORS["muted"], + weight="bold", + ) + ax.plot([x0 + 0.76, x1], [y, y], color="#e5e7eb", lw=1.0, zorder=0) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(18.0, 9.6)) + ax.set_xlim(0, 18) + ax.set_ylim(0, 9.6) + ax.axis("off") + + ax.text( + 9, + 9.27, + tr( + lang, + "How Does the One-Step-Lag Pipeline Fill and Drain?", + "相差一个 Tile 的 Pipeline 如何填充与排空?", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9, + 8.88, + tr( + lang, + "N = num_k_blocks; one WG3 issuer loop executes k=0…N and serially issues QK before PV", + "N = num_k_blocks;一个 WG3 issuer loop 执行 k=0…N,并按顺序先发 QK、再发 PV", + ), + ha="center", + va="center", + fontsize=9.2, + color=COLORS["muted"], + ) + + # The mathematical dependency is simple; scheduling staggers adjacent tiles. + rounded_box( + ax, + 2.02, + 7.83, + 2.02, + 0.62, + "QK(t) → L(t)", + COLORS["mma"], + fontsize=8.6, + ) + rounded_box( + ax, + 5.35, + 7.83, + 2.60, + 0.62, + "softmax(t) → W(t)", + COLORS["softmax"], + fontsize=8.6, + ) + rounded_box( + ax, + 9.24, + 7.83, + 2.30, + 0.62, + "PV(t) → O~(t)", + COLORS["mma"], + fontsize=8.6, + ) + arrow(ax, (4.04, 8.14), (5.35, 8.14), label="L(t)") + arrow(ax, (7.95, 8.14), (9.24, 8.14), label="W(t)") + ax.text( + 13.95, + 8.14, + tr( + lang, + "logical dependency for one tile\nexecution overlaps neighboring tiles", + "单个 tile 的逻辑依赖\n执行时与相邻 tiles 重叠", + ), + ha="center", + va="center", + fontsize=8.1, + color=COLORS["muted"], + style="italic", + ) + + y0 = 1.42 + h = 5.94 + _panel( + ax, + 0.35, + y0, + 4.40, + h, + tr(lang, "Fill · k=0", "填充 · k=0"), + tr( + lang, + "the issuer has no previous tile to multiply", + "issuer 尚无上一 tile 可执行 PV", + ), + COLORS["cta0_dark"], + ) + _panel( + ax, + 5.02, + y0, + 8.33, + h, + tr(lang, "Steady state · 1 ≤ k < N", "稳态 · 1 ≤ k < N"), + tr( + lang, + "adjacent softmax work overlaps asynchronous MMAs", + "相邻 tile 的 softmax 与异步 MMA 重叠", + ), + "#7c3aed", + ) + _panel( + ax, + 13.62, + y0, + 4.03, + h, + tr(lang, "Drain · k=N", "排空 · k=N"), + tr(lang, "the issuer has no new QK tile", "issuer 不再有新的 QK tile"), + COLORS["cta1_dark"], + ) + + # Fill: Q prologue, QK(0), and the first softmax; no PV is issued at k=0. + rounded_box( + ax, + 0.72, + 5.82, + 3.66, + 0.58, + tr( + lang, + "prologue: Q TMA · TMEM alloc · initial K/V gather", + "prologue:Q TMA · TMEM alloc · 首轮 K/V gather", + ), + COLORS["gmem"], + fontsize=7.6, + weight="normal", + ) + _lane(ax, 0.68, 4.38, 5.25, "WG3", lang) + _lane(ax, 0.68, 4.38, 4.08, "WG0", lang) + _lane(ax, 0.68, 4.38, 2.87, "WG1/2", lang) + rounded_box(ax, 1.65, 4.88, 1.56, 0.72, "QK(0)", COLORS["mma"], fontsize=8.8) + rounded_box( + ax, + 3.47, + 4.91, + 0.66, + 0.66, + "PV\n—", + COLORS["neutral"], + fontsize=7.7, + weight="normal", + edgecolor="#9ca3af", + linestyle="--", + ) + rounded_box( + ax, + 2.10, + 3.71, + 1.82, + 0.74, + "softmax(0)", + COLORS["softmax"], + fontsize=8.4, + ) + arrow(ax, (2.84, 4.88), (2.72, 4.45), label="L(0)", rad=0.03) + rounded_box( + ax, + 1.37, + 2.50, + 2.65, + 0.72, + tr(lang, "prepare safe next segments", "准备下一批可安全复用的 segments"), + COLORS["tma"], + fontsize=7.8, + weight="normal", + ) + ax.text( + 2.55, + 1.91, + tr(lang, "issuer branch: QK(0) only", "issuer 分支:仅 QK(0)"), + ha="center", + va="center", + fontsize=8.1, + color=COLORS["muted"], + weight="bold", + ) + + # Steady state: make the two legal overlaps explicit without depicting two issuers. + _lane(ax, 5.34, 13.00, 5.65, "WG3", lang) + _lane(ax, 5.34, 13.00, 4.20, "WG0", lang) + _lane(ax, 5.34, 13.00, 2.72, "WG1/2", lang) + arrow(ax, (6.15, 6.37), (12.78, 6.37), color="#9ca3af", linewidth=1.0) + ax.text( + 9.46, + 6.44, + tr(lang, "issuer program order / time", "issuer 程序顺序 / 时间"), + ha="center", + va="bottom", + fontsize=7.2, + color=COLORS["muted"], + style="italic", + ) + + # Light overlap bands sit behind the actual operation boxes. + ax.axvspan(6.14, 8.58, ymin=0.41, ymax=0.66, color="#eff6ff", alpha=0.75, zorder=-1) + ax.axvspan( + 9.62, 12.47, ymin=0.41, ymax=0.66, color="#fdf2f8", alpha=0.75, zorder=-1 + ) + rounded_box(ax, 6.38, 5.27, 1.86, 0.76, "QK(k)", COLORS["mma"], fontsize=9.0) + rounded_box( + ax, + 9.72, + 5.27, + 2.16, + 0.76, + "PV(k−1)", + COLORS["mma"], + fontsize=9.0, + ) + arrow( + ax, + (8.24, 5.65), + (9.72, 5.65), + label=tr(lang, "same issuer · serial issue", "同一 issuer · 串行发出"), + color=COLORS["ink"], + linewidth=1.5, + label_offset=(0.0, 0.18), + ) + rounded_box( + ax, + 6.05, + 3.82, + 2.58, + 0.76, + "softmax(k−1) → W(k−1)", + COLORS["softmax"], + fontsize=8.0, + ) + rounded_box( + ax, + 9.88, + 3.82, + 2.52, + 0.76, + "softmax(k) → W(k)", + COLORS["softmax"], + fontsize=8.0, + ) + arrow( + ax, + (8.63, 4.20), + (10.03, 5.27), + label="W(k−1) ready", + color="#7c3aed", + rad=-0.06, + label_offset=(0.35, 0.25), + ) + arrow( + ax, + (7.93, 5.27), + (10.12, 4.58), + label="L(k) ready", + color="#7c3aed", + rad=0.05, + label_offset=(0.40, -0.34), + ) + ax.text( + 7.34, + 3.43, + tr(lang, "legal overlap A", "合法重叠 A"), + ha="center", + va="center", + fontsize=7.4, + color=COLORS["cta0_dark"], + weight="bold", + ) + ax.text( + 11.11, + 3.43, + tr(lang, "legal overlap B", "合法重叠 B"), + ha="center", + va="center", + fontsize=7.4, + color=COLORS["cta1_dark"], + weight="bold", + ) + rounded_box( + ax, + 6.02, + 2.35, + 2.82, + 0.72, + tr(lang, "gather safe K(k+1) parts", "gather 可复用的 K(k+1) parts"), + COLORS["tma"], + fontsize=7.7, + weight="normal", + ) + rounded_box( + ax, + 9.55, + 2.35, + 2.82, + 0.72, + tr(lang, "gather safe V(k) parts", "gather 可复用的 V(k) parts"), + COLORS["tma"], + fontsize=7.7, + weight="normal", + ) + ax.text( + 9.18, + 1.87, + tr( + lang, + "QK(k) and PV(k−1) are not concurrently issued", + "QK(k) 与 PV(k−1) 并非同时发出", + ), + ha="center", + va="center", + fontsize=8.2, + color="#6d28d9", + weight="bold", + ) + + # Drain: the extra loop iteration performs only the final PV, then WG0 normalizes. + _lane(ax, 13.92, 17.30, 5.65, "WG3", lang) + _lane(ax, 13.92, 17.30, 4.20, "WG0", lang) + _lane(ax, 13.92, 17.30, 2.72, "WG1/2", lang) + rounded_box( + ax, + 14.64, + 5.30, + 0.86, + 0.70, + "QK\n—", + COLORS["neutral"], + fontsize=7.6, + weight="normal", + edgecolor="#9ca3af", + linestyle="--", + ) + rounded_box(ax, 15.78, 5.27, 1.34, 0.76, "PV(N−1)", COLORS["mma"], fontsize=8.1) + arrow(ax, (15.50, 5.65), (15.78, 5.65), color=COLORS["ink"]) + rounded_box( + ax, + 14.53, + 3.77, + 2.58, + 0.86, + tr( + lang, + "wait sv_done(N−1)\nnormalize + epilogue", + "等待 sv_done(N−1)\n归一化 + epilogue", + ), + COLORS["softmax"], + fontsize=7.8, + ) + arrow(ax, (16.48, 5.27), (16.20, 4.63), color="#7c3aed", rad=0.03) + rounded_box( + ax, + 14.62, + 2.37, + 2.42, + 0.70, + tr(lang, "no more gathers", "不再发起 gather"), + COLORS["neutral"], + fontsize=8.0, + weight="normal", + edgecolor="#9ca3af", + linestyle="--", + ) + ax.text( + 15.64, + 1.87, + tr(lang, "issuer branch: PV(N−1) only", "issuer 分支:仅 PV(N−1)"), + ha="center", + va="center", + fontsize=8.0, + color=COLORS["muted"], + weight="bold", + ) + + rounded_box( + ax, + 1.25, + 0.30, + 15.50, + 0.72, + tr( + lang, + "Source-order loop: for k in [0, N]: if k < N issue QK(k); if k > 0 issue PV(k−1). MMAs execute asynchronously, but one warp issues them in that order.", + "源码顺序:for k in [0, N]:若 k < N 则发 QK(k);若 k > 0 则发 PV(k−1)。MMA 异步执行,但由同一个 warp 按此顺序发出。", + ), + COLORS["note"], + fontsize=8.15, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/img/scripts/gen_flashmla_sparse_story.py b/img/scripts/gen_flashmla_sparse_story.py new file mode 100644 index 00000000..a7b6b6bf --- /dev/null +++ b/img/scripts/gen_flashmla_sparse_story.py @@ -0,0 +1,467 @@ +#!/usr/bin/env python3 +"""Generate the selection-versus-attention story for sparse FlashMLA prefill.""" + +from __future__ import annotations + +import argparse + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch + +from flashmla_diagram_common import ( + COLORS, + arrow, + configure_style, + plain_rect, + rounded_box, + save_figure, + tr, +) + + +def _panel(ax, x, y, w, h, title, subtitle, color) -> None: + panel = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.06,rounding_size=0.08", + linewidth=1.35, + edgecolor=color, + facecolor="#ffffff", + linestyle="--", + zorder=0, + ) + ax.add_patch(panel) + ax.text( + x + 0.25, + y + h - 0.34, + title, + ha="left", + va="center", + fontsize=11.3, + weight="bold", + color=color, + ) + ax.text( + x + 0.25, + y + h - 0.72, + subtitle, + ha="left", + va="center", + fontsize=7.8, + color=COLORS["muted"], + ) + + +def draw(lang: str, output: str, font_path: str | None = None) -> None: + configure_style(lang, font_path) + fig, ax = plt.subplots(figsize=(18.0, 9.2)) + ax.set_xlim(0, 18) + ax.set_ylim(0, 9.2) + ax.axis("off") + + ax.text( + 9, + 8.86, + tr( + lang, + "Who Chooses the Tokens in Sparse FlashMLA?", + "Sparse FlashMLA 中由谁选择 Tokens?", + ), + ha="center", + va="center", + fontsize=18, + weight="bold", + ) + ax.text( + 9, + 8.46, + tr( + lang, + "the indexer ranks candidates; sparse prefill receives row addresses and only performs attention", + "indexer 对 candidates 排序;sparse prefill 接收 row addresses,只负责 attention", + ), + ha="center", + va="center", + fontsize=9.3, + color=COLORS["muted"], + ) + + _panel( + ax, + 0.35, + 1.34, + 4.55, + 6.65, + tr(lang, "1 · Select outside the kernel", "1 · 在 kernel 外完成选择"), + tr( + lang, + "lightning indexer scores candidate rows", + "lightning indexer 为 candidate rows 打分", + ), + COLORS["cta0_dark"], + ) + _panel( + ax, + 5.18, + 1.34, + 5.80, + 6.65, + tr(lang, "2 · Pass an address list", "2 · 传入 address list"), + tr( + lang, + "one list is shared by all 128 query heads", + "同一份 list 由全部 128 个 query heads 共享", + ), + "#7c3aed", + ) + _panel( + ax, + 11.26, + 1.34, + 6.39, + 6.65, + tr(lang, "3 · Attend over selected rows", "3 · 对选中 rows 执行 attention"), + tr( + lang, + "gather first; then run the dense tile chain", + "先 gather,再执行规则的 tile 计算链", + ), + COLORS["cta1_dark"], + ) + + # Selection is an upstream operator, not part of this sparse-prefill kernel. + rounded_box( + ax, + 0.75, + 6.10, + 1.26, + 0.74, + "query q", + COLORS["neutral"], + fontsize=8.7, + ) + rounded_box( + ax, + 0.75, + 4.65, + 1.26, + 0.90, + tr(lang, "candidate\nKV rows", "candidate\nKV rows"), + COLORS["gmem"], + fontsize=8.4, + ) + rounded_box( + ax, + 2.40, + 5.12, + 1.87, + 1.30, + tr( + lang, + "lightning indexer\nscore + top-k", + "lightning indexer\nscore + top-k", + ), + "#fef3c7", + fontsize=9.0, + edgecolor="#d97706", + ) + arrow(ax, (2.01, 6.47), (2.40, 6.05)) + arrow(ax, (2.01, 5.10), (2.40, 5.55)) + rounded_box( + ax, + 1.03, + 3.32, + 3.18, + 0.90, + tr( + lang, + "output: selected row addresses\nnot gathered K/V values", + "输出:选中 rows 的 addresses\n不是已 gather 的 K/V values", + ), + COLORS["barrier"], + fontsize=8.4, + weight="normal", + ) + arrow(ax, (3.34, 5.12), (2.91, 4.22)) + rounded_box( + ax, + 0.78, + 1.78, + 3.68, + 0.78, + tr( + lang, + "different operator · its own cost", + "独立 operator · 有自己的计算成本", + ), + COLORS["note"], + fontsize=8.4, + weight="normal", + edgecolor="#ca8a04", + ) + + # Concrete semantics for one query row. + ax.text( + 8.08, + 6.67, + "indices[q, 0, :]", + ha="center", + va="center", + fontsize=10, + weight="bold", + ) + values = ("42", "7", "42", "−1", "91", "13") + states = ( + tr(lang, "valid", "有效"), + tr(lang, "valid", "有效"), + tr(lang, "duplicate", "重复"), + "OOB", + tr(lang, "valid", "有效"), + tr(lang, "length tail", "长度 tail"), + ) + fills = ( + COLORS["cta0"], + COLORS["cta0"], + COLORS["cross01"], + "#fecaca", + COLORS["cta0"], + "#e5e7eb", + ) + x0 = 5.60 + cell_w = 0.82 + for idx, (value, state, fill) in enumerate(zip(values, states, fills, strict=True)): + x = x0 + idx * cell_w + plain_rect(ax, x, 5.82, cell_w, 0.64, fill) + ax.text( + x + cell_w / 2, + 6.14, + value, + ha="center", + va="center", + fontsize=9, + weight="bold", + ) + ax.text( + x + cell_w / 2, + 5.56, + state, + ha="center", + va="center", + fontsize=6.5, + color=COLORS["muted"], + ) + ax.plot([x0, x0 + 5 * cell_w], [5.30, 5.30], color="#7c3aed", lw=1.3) + ax.plot([x0, x0], [5.24, 5.36], color="#7c3aed", lw=1.3) + ax.plot([x0 + 5 * cell_w, x0 + 5 * cell_w], [5.24, 5.36], color="#7c3aed", lw=1.3) + ax.text( + x0 + 2.5 * cell_w, + 5.10, + "topk_length[q] = 5", + ha="center", + va="center", + fontsize=7.8, + color="#6d28d9", + weight="bold", + ) + + rounded_box( + ax, + 5.70, + 4.05, + 4.82, + 0.76, + tr( + lang, + "valid = 0 ≤ idx < s_kv AND slot < topk_length", + "valid = 0 ≤ idx < s_kv 且 slot < topk_length", + ), + COLORS["barrier"], + fontsize=8.3, + weight="normal", + ) + rounded_box( + ax, + 5.82, + 2.93, + 2.18, + 0.70, + "h_kv = 1", + COLORS["gmem"], + fontsize=8.8, + ) + rounded_box( + ax, + 8.32, + 2.93, + 2.06, + 0.70, + "Q heads 0…127", + COLORS["neutral"], + fontsize=8.3, + ) + arrow( + ax, + (8.00, 3.28), + (8.32, 3.28), + label=tr(lang, "same list", "同一份 list"), + color="#7c3aed", + label_offset=(0.0, 0.17), + ) + ax.text( + 8.08, + 2.20, + tr( + lang, + "duplicates participate twice; invalid slots are masked", + "重复 row 会参与两次;invalid slots 被 mask", + ), + ha="center", + va="center", + fontsize=8.1, + color=COLORS["muted"], + weight="bold", + ) + + # The kernel turns irregular addresses into regular QK/softmax/PV tiles. + rounded_box( + ax, + 11.66, + 6.11, + 1.46, + 0.74, + "Q\n[128, d_qk]", + COLORS["neutral"], + fontsize=8.0, + ) + rounded_box( + ax, + 11.66, + 4.72, + 1.46, + 0.92, + "KV cache\n[s_kv, 1, d_qk]", + COLORS["gmem"], + fontsize=7.7, + ) + rounded_box( + ax, + 13.51, + 4.94, + 1.32, + 1.46, + tr( + lang, + "gather\nselected rows\n+ validity", + "gather\n选中 rows\n+ validity", + ), + COLORS["smem"], + fontsize=7.8, + ) + arrow(ax, (13.12, 5.18), (13.51, 5.40), label="rows", rad=-0.05) + arrow( + ax, + (10.98, 5.86), + (13.51, 6.07), + label="indices", + color="#7c3aed", + rad=-0.06, + ) + + rounded_box(ax, 15.25, 5.95, 1.04, 0.72, "QK", COLORS["mma"], fontsize=9.0) + rounded_box( + ax, + 16.55, + 5.95, + 0.78, + 0.72, + "L", + COLORS["tmem"], + fontsize=9.0, + ) + arrow(ax, (13.12, 6.48), (15.25, 6.31), label="Q") + arrow(ax, (14.83, 5.84), (15.25, 6.13), label="K", rad=-0.05) + arrow(ax, (16.29, 6.31), (16.55, 6.31)) + + rounded_box( + ax, + 15.02, + 4.48, + 2.10, + 0.92, + tr( + lang, + "mask L → softmax\n→ BF16 weights W", + "mask L → softmax\n→ BF16 weights W", + ), + COLORS["softmax"], + fontsize=8.0, + ) + arrow(ax, (16.94, 5.95), (16.25, 5.40), label="L", rad=0.05) + rounded_box(ax, 14.15, 3.02, 1.16, 0.76, "PV\nW × V", COLORS["mma"], fontsize=8.5) + arrow(ax, (15.65, 4.48), (14.98, 3.78), label="W", rad=0.04) + arrow( + ax, + (14.18, 4.94), + (14.47, 3.78), + label=tr(lang, "V = first 512 cols", "V = 前 512 cols"), + color=COLORS["line"], + rad=-0.12, + label_offset=(-0.60, -0.02), + ) + rounded_box( + ax, + 15.72, + 2.82, + 1.52, + 1.16, + "out [128,512]\nmax_logits\nlse", + COLORS["gmem"], + fontsize=7.8, + ) + arrow(ax, (15.31, 3.40), (15.72, 3.40)) + + rounded_box( + ax, + 11.80, + 1.76, + 5.32, + 0.66, + tr( + lang, + "the kernel performs no ranking; it consumes addresses and computes attention", + "kernel 不执行排序;它消费 addresses 并计算 attention", + ), + COLORS["note"], + fontsize=8.2, + weight="normal", + edgecolor="#ca8a04", + ) + + rounded_box( + ax, + 1.55, + 0.30, + 14.90, + 0.66, + tr( + lang, + "No causal flag exists in this interface: the caller's list determines allowed keys; the kernel only applies bounds and optional length masking.", + "该接口没有 causal flag:允许访问哪些 keys 由 caller 的 list 决定;kernel 只应用边界检查与可选的 length mask。", + ), + COLORS["note"], + fontsize=8.3, + weight="normal", + edgecolor="#ca8a04", + ) + + save_figure(fig, output, dpi=160) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--lang", choices=("en", "zh"), default="en") + parser.add_argument("--output", required=True) + parser.add_argument("--font-path") + args = parser.parse_args() + draw(args.lang, args.output, args.font_path) diff --git a/index.md b/index.md index 6975f80b..45ca9fac 100644 --- a/index.md +++ b/index.md @@ -14,9 +14,9 @@ high-performance implementation. This book develops both. The book proceeds from hardware to programming model to complete kernels. It first introduces GPU organization and execution, then presents the programming model used throughout the book, and finally builds high-performance kernels step by step. The main target is NVIDIA Blackwell, and the -running examples are General Matrix-Matrix Multiplication (GEMM) and FlashAttention. Along the way, -the book develops the key ideas behind GPU optimization: data layout, asynchronous data movement, -and asynchronous coordination. +running examples are General Matrix-Matrix Multiplication (GEMM), FlashAttention, and FlashMLA. +Along the way, the book develops the key ideas behind GPU optimization: data layout, asynchronous +data movement, and asynchronous coordination. The material grows out of the [Machine Learning Systems](https://mlsyscourse.org/) course series at Carnegie Mellon University. The examples use the **TIRx** Python DSL so that the ideas can be @@ -37,8 +37,9 @@ This book is open source. Contributions, corrections, and examples are welcome t foundation for the code examples throughout the book. - **Part III, GEMM: Tiled to SOTA.** A complete guide to optimizing a tiled GEMM, built up through TMA pipelining, persistent scheduling, warp specialization, and 2-CTA clusters. -- **Part IV, Flash Attention 4.** A complete attention kernel built from the Part III techniques: - two MMAs with softmax between them, online-softmax rescaling, causal masking, and GQA. +- **Part IV, Attention Kernels.** This part first builds Flash Attention 4 from the Part III + techniques, then introduces Multi-head Latent Attention and maps a sparse FlashMLA prefill + operator to a two-CTA Blackwell kernel. - **Appendices.** TIRx language reference, a reproducible GPU benchmarking and profiling workflow, compiler internals, and a guide to debugging asynchronous kernels. @@ -75,10 +76,11 @@ chapter_gemm_advanced/index ``` ```{toctree} -:caption: Part IV, Flash Attention 4 +:caption: Part IV, Attention Kernels :maxdepth: 2 chapter_flash_attention/index +chapter_flashmla/index ``` ```{toctree} diff --git a/zh/chapter_flashmla/index.md b/zh/chapter_flashmla/index.md new file mode 100644 index 00000000..22eecfab --- /dev/null +++ b/zh/chapter_flashmla/index.md @@ -0,0 +1,1000 @@ +(chap_flashmla)= +# FlashMLA + +先看一个表面上的矛盾。普通 MHA 会为每个 token 保存 $n_h$ 份互不相同的 +head 切片;K 或 V 的总宽度各为 $n_h d_h$。本章研究的 Blackwell kernel +接受 128 个 query heads,但它的 KV tensor 却只有一个 head。一条 cached KV +entry 必须同时服务这 128 个 heads,保留各 head 不同的 attention 行为,并 +产生 128 份各含 512 个 coordinates 的 output。 + +这个问题分为三层。MLA 解释 cache 为何可以共享;weight absorption 解释各 head +的 projection 去了哪里;FlashMLA kernel 则解释如何把共享 cache rows 的稀疏 +列表变成 2-CTA 协作的 dense tensor-core computation。 + +```{figure} ../../img/flashmla_cache_story_zh.svg +:width: 100% +:alt: 一条 latent KV cache entry 通过吸收投影服务 128 个 query heads + +缓存为每个 token 保存一份 latent content vector 和一份共享 RoPE key。各 +head 的行为保留在 query 与 output 路径中,而不是展开成 128 份 K/V cache +entries。 +``` + +:::{admonition} 概览 +:class: overview + +- 理解 MLA 如何共享 latent KV cache、MHA/MQA 两种执行模式,以及 weight absorption。 +- 从 sparse contract 追踪到 Blackwell 上由 2 个 CTA 协作完成的数据流程序。 +- 运行可执行 reference,并在 B200 上编译、验证固定版本的 TIRx 实现。 +::: + +*FlashMLA* 这个名字包含两个容易混淆的概念。MLA 是一种 attention 架构, +它将 key-value 状态压缩成 latent vector;FlashMLA 则是 DeepSeek 提供的 +高性能 attention kernel library,其中既包含 dense 和 sparse operator,也 +覆盖 prefill 与 decode。 + +本章会先推导 MLA 架构,再让 sparse contract 真正运行起来,最后沿用 FA4 +从算法深入 schedule 的分析方式,研究一条具体的 library 路径:Blackwell 上 +regular 128-query-head sparse-prefill forward kernel。 + +本章实现固定使用 +[`mlc-ai/tirx-kernels@5be39749`](https://github.com/mlc-ai/tirx-kernels/tree/5be39749e7dfd2c4bdae9b4d396f8ec35af07126)。 +下文所有 TIRx API 写法和代码摘录都来自这个 revision。这一点很重要: +compiler API 仍在演进,而教材示例必须能够复现。 + +## 为什么 MHA 要为每个 head 分别缓存 K/V 状态? + +设 $h_t\in\mathbb{R}^{d_{model}}$ 是 token $t$ 的 hidden state。普通 +multi-head attention(MHA)会为每个 head $i$ 分别做 projection: + +$$ +q_{t,i}=W_i^Q h_t,\qquad +k_{t,i}=W_i^K h_t,\qquad +v_{t,i}=W_i^V h_t. +$$ + +对于位置 $t$ 上的 query,head $i$ 计算: + +$$ +p_{t,s,i}=\operatorname{softmax}_s +\left(\frac{q_{t,i}^{\mathsf T}k_{s,i}}{\sqrt{d_h}}\right), +\qquad +o_{t,i}=\sum_s p_{t,s,i}v_{s,i}. +$$ + +Output projection 会混合各个 head 的结果。但在 autoregressive generation +期间,所有更早位置的 $k_{s,i}$ 和 $v_{s,i}$ 都必须继续可用。因此,每层的 +cache 需要为每个 token 保存 $2n_h d_h$ 个元素,也就是为每个 head 分别保存 +一份 K slice 和一份 V slice。 + +若固定 $d_{model}=n_h d_h$,仅改变 head 数并不一定改变这项总宽度。结构上的 +代价在于 cache 仍需 materialize 各 head 的独立状态。 + +在长序列 decode 中,读取这些随 token history 增长的 slices 会主导整个 step。 + +Multi-query attention(MQA)让所有 query heads 共享一个 K/V head,以此 +减小 cache;grouped-query attention 则在组内共享。它们都是有用的模型架构, +但 MLA 采用了另一条路径:保留具有表达能力的 per-head projection,同时只 +cache 一个共享的低维数据源,需要时可以从中恢复各 head 的表示。 + +### MLA 如何只缓存一次,却恢复 per-head 行为? + +最初的 [DeepSeek-V2 MLA 推导](https://arxiv.org/abs/2405.04434)先定义一个 +joint latent KV vector: + +$$ +c_t^{KV}=W^{DKV}h_t, +$$ + +再分别做 up-projection: + +$$ +k_{t,i}^{C}=W_i^{UK}c_t^{KV},\qquad +v_{t,i}^{C}=W_i^{UV}c_t^{KV}. +$$ + +上标 $C$ 表示不含位置信息的 *content* channel。关键在于,cache 不需要为 +每个 head 保存展开后的 $k^C$ 和 $v^C$,只需为每个 token 保存一份 +$c^{KV}$。 + +MLA 还可以引入一个独立的低秩 latent,对 query projection 做分解: + +$$ +c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +$$ + +Query 侧的这项分解会降低训练时的 activation memory,但不会进一步缩小 KV +cache。 + +它也发生在 core-attention API 之前:传给 FlashMLA 的 `q` tensor 已经是 +projection 后的 query。因此,下文把 $q^C$ 视为输入,重点讨论决定 cache 与 +kernel operands 的 KV 侧 compression。 + +RoPE 让这幅简单图景变得复杂。如果在 $W^{UK}$ 与 dot product 之间加入 +position-dependent rotation,矩阵就无法再重新结合。为此,MLA 使用 +decoupled positional channel:每个 query head 有自己的 $q_{t,i}^{R}$, +而所有 heads 共享一个 cached $k_t^R$。真正以 MHA 形式计算的 score 使用: + +$$ +q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad +k_{s,i}=[k_{s,i}^{C};k_s^R]. +$$ + +此时 cache 保存的是 $[c_s^{KV};k_s^R]$,仍然由所有 heads 共享。 +Positional channel 保持显式,weight absorption 只作用于 content channel。 + +### 各 head 的 up-projection 去了哪里? + +MLA 的 core attention 可以用两种代数上相关的模式执行。不能因为其中一种 +叫 MQA mode,就把所有 MLA 模型都理解成普通 MQA 模型。 + +| MLA 执行模式 | 提交给 kernel 的 core-attention K/V | Up-projection 发生的位置 | +| --- | --- | --- | +| MHA mode | 每个 head 的 $[W_i^{UK}c^{KV};k^R]$ 和 $W_i^{UV}c^{KV}$ | Core attention 之前 | +| MQA mode | 共享的 $[c^{KV};k^R]$ 和共享 latent value $c^{KV}$ | 吸收到 query 与 output 路径 | + +```{figure} ../../img/flashmla_mla_modes_zh.svg +:width: 100% +:alt: MLA 的 MHA 与 MQA 执行模式,以及两条 weight-absorption 路径 + +MLA 的 MHA mode 在 core attention 之前展开 latent KV;MQA mode 则把 key +up-projection 移到 query 路径,把 value up-projection 移到 output 路径。 +两种模式都显式保留共享的 RoPE key。 +``` + +图中已经给出答案,下面两个恒等式会证明它。Key 一侧先重新结合矩阵乘法: + +$$ +(q_{t,i}^{C})^{\mathsf T}W_i^{UK}c_s^{KV} +=\left((W_i^{UK})^{\mathsf T}q_{t,i}^{C}\right)^{\mathsf T}c_s^{KV}. +$$ + +定义吸收权重后的 query +$q_{t,i}^{A}=(W_i^{UK})^{\mathsf T}q_{t,i}^{C}$,content score 就可以直接 +与 cached latent 做 dot product。Value 一侧则利用线性关系: + +$$ +\sum_s p_{t,s,i}W_i^{UV}c_s^{KV} +=W_i^{UV}\left(\sum_s p_{t,s,i}c_s^{KV}\right). +$$ + +因此,$W_i^{UV}$ 可以与模型的 output projection 合并。Attention +kernel 不必真正 materialize 展开的 per-head K 或 per-head V。 + +这个区别体现在实际执行上,而不只是记号不同。 +[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) +Appendix A 说明,DeepSeek-V3.1-Terminus 在 training 和 prefill 时使用 MHA +mode,在 decode 时使用 MQA mode。相比之下,DeepSeek Sparse Attention +(DSA)即使在 sparse prefill 中也采用 MLA 的 MQA mode,因为每个被选中的 +latent KV entry 会由所有 query heads 共享。因此,这条 sparse-prefill 路径 +中常见的 $d_{qk}=576$、$d_v=512$ contract 表示吸收权重后的 MQA +representation:576 这一变体由 512 个 latent content coordinates 和 64 个 +RoPE coordinates 组成。它不是所有 MLA 或 FlashMLA operator 的通用 shape; +实现还支持 $d_{qk}=512$ 变体。 + +### 一个小程序能否证明两种模式一致? + +下面的 CPU 程序同时构造两种执行方式。MHA 路径显式展开 K/V,MQA 路径吸收 +相同的矩阵,并且两边都加入共享的 RoPE score term。使用 Float64 可以 +让等价性检查足够敏感,从而发现 index 转置或 contraction 写错之类的问题。 + +```python +import math +import torch + +torch.manual_seed(0) +Q, K, H = 3, 5, 4 +D_CONTENT, D_LATENT, D_VALUE, D_ROPE, D_MODEL = 7, 6, 8, 3, 11 + +# 每个 head 的 query、每个 key token 一份共享 latent KV,以及共享 RoPE key。 +q_content = torch.randn(Q, H, D_CONTENT, dtype=torch.float64) +q_rope = torch.randn(Q, H, D_ROPE, dtype=torch.float64) +c_kv = torch.randn(K, D_LATENT, dtype=torch.float64) +k_rope = torch.randn(K, D_ROPE, dtype=torch.float64) + +W_UK = torch.randn(H, D_CONTENT, D_LATENT, dtype=torch.float64) +W_UV = torch.randn(H, D_VALUE, D_LATENT, dtype=torch.float64) +W_O = torch.randn(D_MODEL, H, D_VALUE, dtype=torch.float64) + +# MHA mode:为每个 head 显式展开 key 和 value。 +k_content = torch.einsum("hdc,kc->khd", W_UK, c_kv) +v_content = torch.einsum("hvc,kc->khv", W_UV, c_kv) +scale = 1.0 / math.sqrt(D_CONTENT + D_ROPE) +scores_mha = ( + torch.einsum("qhd,khd->qhk", q_content, k_content) + + torch.einsum("qhr,kr->qhk", q_rope, k_rope) +) * scale +prob = torch.softmax(scores_mha, dim=-1) +head_out_mha = torch.einsum("qhk,khv->qhv", prob, v_content) +model_out_mha = torch.einsum("mhv,qhv->qm", W_O, head_out_mha) + +# MQA mode:把 W_UK 移到 Q,attention 直接读取 c_kv,再把 W_UV 移到 output。 +q_absorbed = torch.einsum("qhd,hdc->qhc", q_content, W_UK) +scores_mqa = ( + torch.einsum("qhc,kc->qhk", q_absorbed, c_kv) + + torch.einsum("qhr,kr->qhk", q_rope, k_rope) +) * scale +latent_out = torch.einsum("qhk,kc->qhc", torch.softmax(scores_mqa, -1), c_kv) +W_O_absorbed = torch.einsum("mhv,hvc->mhc", W_O, W_UV) +model_out_mqa = torch.einsum("mhc,qhc->qm", W_O_absorbed, latent_out) + +torch.testing.assert_close(scores_mha, scores_mqa, rtol=1e-12, atol=1e-12) +torch.testing.assert_close(model_out_mha, model_out_mqa, rtol=1e-12, atol=1e-12) +print("weight absorption: exact up to float64 roundoff") +``` + +注意,这里的 scale 仍然由模型语义中的 QK head dimension 决定。不能仅仅因为 +吸收权重后的 dot product 恰好有 $D_{latent}$ 个 coordinates,就把它改成 +$1/\sqrt{D_{latent}}$。 + +## Sparse kernel 会自己选择 token 吗? + +Dense attention 会访问每个合法的 KV token。DSA 先用轻量的 *lightning +indexer* 为候选 tokens 打分,并为每个 query 选出一个 top-$k$ 集合;sparse +core attention 随后只读取这些 latent KV entries。若原始 context length 为 +$L$,prefill 的 core-attention 计算量会从 $O(L^2)$ 变成 $O(Lk)$,不过 +indexer 自身也有开销。 + +```{figure} ../../img/flashmla_sparse_story_zh.svg +:width: 100% +:alt: Lightning indexer 先选择 token,sparse-prefill kernel 再执行 attention + +Token selection 与 sparse core attention 是两个相互独立的算子。Indexer +产生 row addresses;sparse-prefill kernel gather 这些 rows,再完成 +QK--softmax--PV 计算。 +``` + +本章研究的 sparse-prefill operator 不计算 index scores,也不执行 top-k +selection,而是直接接收 `indices` tensor。因此它的语义 contract 是: + +1. gather 指定的 KV rows; +2. 将越界位置和被 length mask 的位置标为 invalid; +3. 对剩余 rows 计算 attention;如果 caller 给出了重复 indices,重复项也会参与计算; +4. 返回 output、maximum logit 和 log-sum-exp。 + +这个 interface 没有 causal flag。若 caller 需要 causal attention,就必须生成 +一个只含允许访问的 keys 的 index list。稀疏性本身并不等同于 causal mask。 + +如果提供 `topk_length`,每个 query 的值都必须满足 +`0 <= topk_length[q] <= topk`。这是 caller 应保证的前置条件,而不是 +kernel 会自动 clip 的输入;大于 `topk` 会让固定版本的 kernel 走到 +`indices` storage 之外。 + +这个 prefill interface 也没有 batch dimension。在下文研究的 port 中, +`h_kv=1`,所以 `indices` 的 shape 是 `[s_q, 1, topk]`:每个 query token +提供一份 selected-token list,它的 128 个 query heads 共用这份 list。Serving +system 必须在调用前 flatten batch,或用其他方式完成 batch mapping。 + +### FlashMLA 是一个 kernel,还是一族算子? + +*Prefill* 并行处理 prompt 中的 query tokens;*decode* 则在复用 KV cache 的 +同时,每一步加入一个新 query(或一小组 speculative queries)。 +[FlashMLA 官方仓库](https://github.com/deepseek-ai/FlashMLA)将 kernel 组织成 +四类: + +| Selection | Sequence stage | 代表性用途 | +| --- | --- | --- | +| dense | prefill | MHA forward 与 backward | +| dense | decode | 为新生成的 queries 读取 MLA KV cache | +| token-sparse | prefill | 对 selected-token list 执行 DSA core attention | +| token-sparse | decode | 对 selected FP8 KV cache 执行 DSA inference | + +所以,FlashMLA 既不等同于 sparse attention,也不等同于本章这个 kernel。 + +本章选择 sparse prefill operator,是因为它把一个系统问题展示得很清楚: +irregular TMA gather 如何为规则的 tensor-core tiles 供数?Sparse decode 有 +不同的 paged-cache、scheduling 和 reduction contract,不在本章范围内。 + +Upstream sparse-prefill public call 在概念上是: + +```text +out, max_logits, lse = flash_mla_sparse_fwd( + q, kv, indices, sm_scale, + d_v=512, + attn_sink=attn_sink, # optional [h_q], float32 + topk_length=topk_length, # optional [s_q], int32 +) +``` + +固定版本的 TIRx repository 在统一的 `flash_mla_sparse_fwd` registry entry 中 +沿用了这个 public name,再根据 shape dispatch 到三个 SM100 phase-1 modules +之一。 + +:::{admonition} Port 范围:`sm_scale` 已固定 +:class: warning + +上面的 upstream call 会在 runtime 接收 `sm_scale`。固定版本的 TIRx entry +保留了 registry name 和 shape dispatch,却**没有**保留完整的 call +signature:三个 prefill modules 都将 scale specialize 为 +`1 / sqrt(d_qk)`,launch ABI 中没有 scale argument。在这个 revision 中, +通过 `**kwargs` wrappers 传入 `sm_scale=...` 会被静默忽略。因此,下文 +的 B200 示例验证的是固定 scale 的教学 port,而不是 upstream +`flash_mla_sparse_fwd` 的 drop-in replacement。若模型语义中的 QK scale +不同,就必须将正确数值暴露为参数,或在编译时将其 specialize。 + +Weight absorption 并不构成改变该 scale 的理由。 +::: + +## 能否先把 sparse contract 写成可执行 reference? + +阅读 kernel 之前,先写一个明确处理各种边界情况的 reference。在吸收权重后的 +MQA contract 中,`kv[:, 0, :]` 同时提供 K 和 V:全部 `d_qk` coordinates +参与 QK,前 `d_v` 个 coordinates 则作为 latent value。PyTorch gather 之前 +必须先 clamp invalid indices,再将其 mask 掉;如果直接用 `-1` 做 index,就会 +错误地选择最后一行。 + +越界地址对应的 V row 还要在 PV 前清零,因为按照 IEEE arithmetic,softmax +weight 为 0 并不能消除 NaN。对于只因 `topk_length` 而被 mask、地址本身仍合法的 +row,这里有意不做净化,以匹配后文说明的固定版本 kernel 行为。 + +下面的完整 CPU block 回答这些规则、attention sink 和全 invalid 约定能否共存 +于一个可执行 oracle 中: + +```python +import math +import torch + +def sparse_prefill_reference( + q, kv, indices, sm_scale, d_v, *, attn_sink=None, topk_length=None +): + """Reference for q[SQ,H,D], kv[SKV,1,D], indices[SQ,1,TOPK].""" + s_q, h_q, d_qk = q.shape + s_kv, h_kv, kv_width = kv.shape + assert h_kv == 1 and kv_width == d_qk and d_v <= d_qk + assert indices.shape[:2] == (s_q, 1) + + idx = indices[:, 0].to(torch.long) # [SQ, TOPK] + topk = idx.shape[1] + assert topk > 0 + in_range = (idx >= 0) & (idx < s_kv) + safe_idx = idx.clamp(0, s_kv - 1) + focused_kv = kv[:, 0].float()[safe_idx] # [SQ, TOPK, D] + + # OOB index 只把 clamp 后的边界 row 当作安全的 gather 地址。PV 前清零这些 + # V rows,避免 sentinel row 的 NaN 经 0 * NaN 泄漏。刻意保留 topk_length + # 之后、但地址合法的 rows,以匹配 kernel 已说明的异常 NaN 行为。 + focused_v = torch.where( + in_range[:, :, None], + focused_kv[:, :, :d_v], + torch.zeros_like(focused_kv[:, :, :d_v]), + ) + + position = torch.arange(topk, device=q.device)[None, :] + if topk_length is not None: + assert topk_length.shape == (s_q,) + assert bool(((0 <= topk_length) & (topk_length <= topk)).all()) + length = ( + topk_length.to(torch.long)[:, None] + if topk_length is not None + else torch.full((s_q, 1), topk, device=q.device) + ) + valid = in_range & (position < length) + + logits = torch.einsum("qhd,qkd->qhk", q.float(), focused_kv) * sm_scale + logits = logits.masked_fill(~valid[:, None, :], -torch.inf) + max_logits = logits.amax(dim=-1) + have_valid = valid.any(dim=-1)[:, None] + + # 避免所有 selected indices 都 invalid 时出现 (-inf)-(-inf)。 + softmax_origin = torch.where(have_valid, max_logits, torch.zeros_like(max_logits)) + weight = torch.exp(logits - softmax_origin[:, :, None]) + weight = torch.where(valid[:, None, :], weight, torch.zeros_like(weight)) + denominator = weight.sum(dim=-1) + numerator = torch.einsum("qhk,qkv->qhv", weight, focused_v) + + if attn_sink is None: + sink_term = torch.zeros_like(denominator) + else: + sink_term = torch.exp(attn_sink.float()[None, :] - softmax_origin) + out = numerator / (denominator + sink_term).clamp_min(torch.finfo(torch.float32).tiny)[ + :, :, None + ] + out = torch.where(have_valid[:, :, None], out, torch.zeros_like(out)) + + # FlashMLA 报告的 LSE 不包含 attention sink。全 invalid 时约定为 + # max_logits=-inf、lse=+inf、output=0。 + lse = torch.where( + have_valid, + max_logits + torch.log(denominator), + torch.full_like(max_logits, torch.inf), + ) + return out, max_logits, lse + + +torch.manual_seed(1) +q = torch.randn(2, 3, 6) +kv = torch.randn(9, 1, 6) +indices = torch.tensor([[[0, 3, -1, 12]], [[8, 1, 4, 2]]], dtype=torch.int32) +topk_length = torch.tensor([3, 2], dtype=torch.int32) +attn_sink = torch.randn(3) +out, max_logits, lse = sparse_prefill_reference( + q, kv, indices, 1 / math.sqrt(6), 4, + attn_sink=attn_sink, + topk_length=topk_length, +) +assert out.shape == (2, 3, 4) +assert max_logits.shape == lse.shape == (2, 3) +assert torch.isfinite(out).all() + +# OOB sentinel 不能继承其安全地址所指 row 中的 NaN。 +nan_q = torch.ones(1, 1, 2) +nan_kv = torch.tensor([[[torch.nan, torch.nan]], [[2.0, 3.0]]]) +nan_indices = torch.tensor([[[-1, 1]]], dtype=torch.int32) +nan_out, _, _ = sparse_prefill_reference(nan_q, nan_kv, nan_indices, 1.0, 2) +torch.testing.assert_close(nan_out, torch.tensor([[[2.0, 3.0]]])) +print(out.shape, max_logits.shape, lse.shape) +``` + +Attention sink 等价于额外加入一个 logit,并令与它关联的 value vector 为 0。 +它只改变 output denominator: + +$$ +O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} +{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. +$$ + +其中 $a_i$ 是 per-head sink logit。它不影响 `max_logits` 或返回的 `lse`; +编写独立 oracle 时很容易漏掉这个细节。 + +## 本章具体研究哪一个 Blackwell 案例? + +下面聚焦 +[`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py)。 +虽然内部的 `phase1` 名称继承自 upstream FlashMLA,但这条 prefill 路径会在 +一个 kernel 中生成完整的 `(out, max_logits, lse)`;它不是等待 combine +kernel 的 partial split-KV output。 + +Regular head-128 案例可以自然衔接前面的 FlashAttention 章节:它保留熟悉的 +QK--softmax--PV 主链,再加入 irregular gather、吸收权重后的 latent KV 和 +2-CTA cooperative ownership,让读者不必同时面对所有新概念。 + +先明确一组命名,避免后文混淆。在数学推导中,$p$ 表示归一化后的 softmax +probability;而在固定版本的源码里,`tmem_p` 和 register 变量 `p` 保存的是 +**原始 QK logits**,下文将它们记作 $L$。源码中的 `s_frag` 和 +`s_smem_gemm` 保存 BF16 **未归一化指数权重**,下文记作 $W$。只有在 +epilogue 中用 `li`(以及可选的 sink term)除 accumulated output 后, +最终 output 才完成归一化。 + +下面较短的 TIRx 代码块都是固定版本 kernel 的上下文摘录,不是 standalone +program。最后一节会编译并做数值验证;可以独立执行的 blocks 会显式说明。 + +### 哪些 shape 会进入 regular head-128 路径? + +Regular head-128 module 固定使用以下 tile constants: + +```python +B_H = 128 +B_TOPK = 128 +D_V = 512 +NUM_BUFS = 2 +NUM_THREADS = 512 +D_TQ = 384 +``` + +它的输入输出 contract 是: + +| Tensor | Shape | Type | 含义 | +| --- | --- | --- | --- | +| `q` | `[s_q, 128, d_qk]` | BF16 | 吸收权重后的 queries | +| `kv` | `[s_kv, 1, d_qk]` | BF16 | 共享 latent/positional KV rows | +| `indices` | `[s_q, 1, topk]` | int32 | 直接 KV row indices | +| `attn_sink` | `[128]` | FP32 | 可选的 per-head sink logits | +| `topk_length` | `[s_q]` | int32 | 可选的有效 prefix length;每项位于 `[0, topk]` | +| `out` | `[s_q, 128, 512]` | BF16 | sparse-attention 结果 | +| `max_logits` | `[s_q, 128]` | FP32 | 最大 scaled logit | +| `lse` | `[s_q, 128]` | FP32 | 不含 sink 的 natural-log sum-exp | + +这个 module 接受 512 或 576 的 `d_qk`,要求 `h_kv=1`、`d_v=512`,并要求 +regular path 的 `topk` 是 128 的正整数倍。对于 128 heads,统一 front door 还会 +多做一次选择:`d_qk=512` 且 `topk<=1280` 时进入 small-top-k 实现;其他 +支持的 head-128 shapes 进入本章的 regular 实现。Head-64 shapes 使用另一个 +kernel。 + +`topk > 0` 是调用者必须满足的前置条件。统一 front door 会拒绝 +`topk<=0`,但固定版本各 specialization 的 `_cfg().validate()` 只检查整除性, +没有检查正数条件。因此,直接 import 某个 specialization 时仍须拒绝或避开 +非正的 `topk`;local validator 接受它并不意味着这种 launch 有效。 + +无需 launch GPU kernel 就能检查 dispatch: + +```python +from tirx_kernels.flashmla.flash_mla_sparse_fwd import ( + dispatch_reason, + select_kernel, +) + +shape = dict(h_q=128, h_kv=1, d_qk=576, d_v=512, topk=2048) +assert select_kernel(**shape) == "sparse_flashmla_prefill_head128_phase1" +print(dispatch_reason(**shape)) +# sm100 h_q=128 dispatches to regular head128 phase1 +``` + +Dispatch 本身记录在固定版本的 +[`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120) +中。把 dispatch 与 device schedule 分开,可以避免把一个 specialization 错当成 +整个 operator。 + +### 为什么一个 query row 需要两个 CTA? + +Launch grid 包含 `2 * s_q` 个 CTA,并将相邻 CTA 两两组成 cluster: + +```python +block_idx = T.cta_id([2 * s_q]) +T.cta_id_in_cluster([2]) +cta_idx: T.let = block_idx % 2 +s_q_idx: T.let = block_idx // 2 +thread_idx = T.thread_id([512]) +T.warpgroup_id([4]) +``` + +因此,一个 cluster 负责一个 query row。每个 CTA 含 4 个 warpgroups。先看 +ownership 图。这里最不寻常的是,QK 与 PV 之间的切分轴会发生变化。 + +```{figure} ../../img/flashmla_cta_ownership_zh.svg +:width: 100% +:alt: 两个 CTA 对 query heads、selected K rows 和 V feature columns 的 ownership + +对于每个 query row,CTA pair 会在 QK 与 PV 之间改变 logical partition。 +每个 CTA 最终写出 64 个完整的 output heads,每个 head 含 512 个 +coordinates。 +``` + +这个 CTA pair 会用三种不同方式切分三个轴: + +| 一个 128-token top-k tile 中的资源 | CTA 0 | CTA 1 | +| --- | --- | --- | +| Query/output head ownership | heads 0--63 | heads 64--127 | +| K-row gather ownership | selected tokens 0--63 | selected tokens 64--127 | +| V-feature gather ownership | value columns 0--255 | value columns 256--511 | + +所以,2-CTA tensor-core operation 不只是“两个 CTA 各做同一个循环的一半”。 +QK 需要形成 128 heads 与 128 selected tokens 的 cross-product,PV 再沿 token +维度做 contraction,得到 512 个 value coordinates。这两次 GEMM 之间的 partition +会发生旋转;collective `cta_group=2` MMA、配对的 SMEM/TMEM layouts 和 +cross-CTA barriers 共同组成一个 logical tile。 + +这个划分可以直接从固定版本源码看出:Q 按 `cta_idx` chunk,K producer 选择 +每个 top-k block 的 `cta_idx` 半块,V producer 则从 `cta_idx * 256` 开始。 + +## 各个 tile 放在哪里? + +Blackwell tensor memory(TMEM)让 `tcgen05` 可以把大型 accumulator 放在 +tensor cores 附近,但它不会取代 shared memory(SMEM)。TMA gather 的数据先 +到达 SMEM,softmax warpgroup 也必须在 SMEM 中 materialize BF16 未归一化 +权重,供 PV GEMM 使用。 + +```{figure} ../../img/flashmla_dataflow_zh.svg +:width: 100% +:alt: Global memory、shared memory、tensor memory 与 registers 之间的数据移动 + +Q 被拆成 SMEM prefix 和 TMEM suffix。Gather 后的 K/V 进入 SMEM;原始 QK +logits 与 output 在 TMEM 中累积;未归一化 softmax weights 再经过 SMEM 交给 +PV。 +``` + +对一个 CTA 而言,重要的 logical views 如下: + +| Storage | Logical tile | Lifetime 与用途 | +| --- | --- | --- | +| SMEM `q_full` | `64 x d_qk` BF16 | Q prologue;其 prefix 留给 SS QK | +| TMEM `q_tmem` | `64 x 384` BF16 | Q 的 suffix,供 TS QK 使用 | +| SMEM `k_smem` | `64 x d_qk` BF16 | 128-row K tile 中由本 CTA gather 的一半 | +| TMEM `tmem_p` | `64 x 128` FP32 logical view | 交给 softmax 的原始 QK logits $L$ | +| SMEM `s_smem_gemm` | `64 x 128` BF16 | 交给 PV 的未归一化指数权重 $W$ | +| SMEM `v_smem_gemm` | `128 x 256` BF16 logical view | `v_smem` 的 rearranged view:所有 tile rows、本 CTA 的 V columns | +| TMEM `o_tmem` | `64 x 512` FP32 logical view | running unnormalized output | +| SMEM `o_smem` | `64 x 512` BF16 | TMA store 前的 epilogue staging | + +这些都是 logical views;CTA-group TMEM layout 和 rearrangement 决定 MMA 与 +load/store instructions 的实际 lane mapping。源码分配一个 512-column +CTA-group TMEM pool,再从中切出 O、raw-logit 和 Q views。 + +SMEM 采用激进的 alias 与复用策略。只要 lifetime 允许,`q_full`、gather 后的 +K/V region 和 output epilogue 就会复用类似 union 的 base。最后 384 个 Q columns 移到 +TMEM 后,只有 $d_{sq}=d_{qk}-384$ 的 prefix 仍需保持 live,供 QK 第一部分 +使用。`d_qk=512` 时 $d_{sq}=128$;`d_qk=576` 时则为 192。具体 allocation +plan 见 +[`sparse_prefill_head128_phase1.py` lines 302--365](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L302-L365)。 + +这里要特别澄清一个容易误解的点:`NUM_BUFS = 2` **没有**分配两份完整的 K、V、 +$L$ 或 $W$ tile,这些 arrays 都没有 stage axis。`NUM_BUFS` 用于两槽 +barrier/phase ring,也为小型 packed-validity mask 提供两个 slots;completion +barrier 则保证可以安全地分段覆盖同一个大型 tile 的 physical storage。把这种 +layout 称作“double-buffered K/V”,就会让人误以为存在两份实际上并不存在的 +storage。 + +## 每次数据交接由哪个 warpgroup 负责? + +四个 warpgroups 各做不同工作,而不是 lockstep 前进: + +| Warpgroup | Warps | 职责 | +| --- | --- | --- | +| WG0 | 0--3 | 从 TMEM 加载原始 logits $L$,mask、online softmax、写权重 $W$、rescale O、执行 epilogue | +| WG1 | 4--7 | 加载 index fragments,并为 K 发起 gather4 TMA | +| WG2 | 8--11 | 加载 index fragments,并为 V 发起 gather4 TMA | +| WG3 | 12--15 | CTA 0 的 warp 12 发起 CTA-group QK/PV MMA;每个 CTA 的 warp 13 构造 validity mask | + +WG3 中剩下的 warps 并没有承担另一个隐藏 stage。这种不对称 role assignment +是有意设计的:一个 elected lane 就能为 CTA pair 发起 asynchronous MMA, +而 exponentiation、row reduction、packing 和 epilogue conversion 则适合使用 +较多 lanes。 + +Register budget 也与 role 对应。WG0 将上限提高到 144 registers,WG3 提高到 +168;producer groups 则降到 96。固定版本 API 用 +`T.ptx.setmaxnreg(True, ...)` 表示提高,用 +`T.ptx.setmaxnreg(False, ...)` 表示降低。 + +### 不规则的 rows 如何变成规则的 tiles? + +稀疏的 row addresses 破坏了 dense attention 所用的 contiguous 2-D copy pattern。 +WG1 和 WG2 使用显式 TMA `gather4`:一次 issue 提供恰好 4 个 row coordinates, +让一个 warp 可以把不连续的 KV rows 搬进规则的 SMEM tile。共享 helper 固定了 +CTA-pair policy。 + +下面的上下文摘录回答两个具体问题:一次 `gather4` issue 读取哪些 addresses, +它的 completion 又交给哪个 barrier。Index names 和 slices 与固定 revision +完全相同: + +```python +_kv_gather_tma = partial( + tma_config, + dispatch="tma_explicit", + cta_group=2, + cta_mask=T.uint16(1), + cache_hint=T.uint64(0x14F0000000000000), +) + +for row_group in T.unroll(WG1_ROWS_PER_WARP): + for col_atom in T.unroll(col_count): + col = T.meta_var((col_start + col_atom) * 64) + Tx.copy_async( + k_gather_tile[ + row_group * 4 : row_group * 4 + 4, + col_atom * 64 : col_atom * 64 + 64, + ], + kv_tma[0:1, col : col + 64], + **_kv_gather_tma( + mbar=leader_mbar(bar.ptr_to([cur_buf])), + gather4=[indices_int4[row_group, lane] for lane in range(4)], + ), + ) +``` + +Gather 与 validity 相关,但两者是分开的。Warp 13 的每个 active lane 加载 8 个 +indices,并调用 `pack_valid_mask8`。当且仅当下面两个条件同时满足时,bit $i$ +才为 1: + +$$ +0\leq\text{index}_i 0: + sq_smem = q_full.sub[:, :d_sq] + Tx.gemm_async( + tmem_p[:, :], + sq_smem[:, :d_sq], + k_smem[:, :d_sq], + **_mma_config(accum=mma_p_accumulate, smem_desc=mma_smem_desc), + ) + mma_p_accumulate = T.uint32(1) + +Tx.gemm_async( + tmem_p[:, :], + q_tmem[:, :D_TQ], + k_smem[:, d_sq : d_sq + D_TQ], + **_mma_config(accum=mma_p_accumulate, smem_desc=mma_smem_desc), +) +``` + +第一步是 SS:Q 和 K operands 都由 SMEM 描述。第二步是 TS:Q 的 384-column +suffix 来自 TMEM,K 仍在 SMEM。两步写入同一个 FP32 raw-logit accumulator +(源码中的 `tmem_p`);第一步清零,第二步累加。这样拆分 Q 后,SMEM 中只需 +保留较小的 Q prefix,使 union allocation 成为可能,同时不必放弃较大 suffix +所使用的 TS path。 + +Softmax 之后,PV 是 SS GEMM:BF16 $W$ 和 V 都在 SMEM,FP32 O accumulator +则留在 TMEM。Kernel 将 V rows 和 output columns 各分成两半,四种组合共同 +更新全部 512 个 value coordinates。 + +## Online softmax 如何避免不必要的 O 重缩放? + +对于连续到来的 score tiles,普通 online-softmax recurrence 会保存 row origin +$m$、denominator $\ell$ 和未归一化 output $\widetilde O$。使用 base 2 时, +若下一块 tile 含有 scaled scores $r$,则: + +$$ +m'=\max(m,\max r),\qquad +\alpha=2^{m-m'}, +$$ + +$$ +\ell'=\alpha\ell+\sum_j2^{r_j-m'},\qquad +\widetilde O'=\alpha\widetilde O+\sum_j2^{r_j-m'}v_j. +$$ + +概念上,实现会将 natural-unit logits 乘以模型语义中的 QK scale 与 +`log2(e)`,再使用 `exp2`。在本章的固定 scale port 中,编译期 +`sm_scale_div_log2` 就是 `(1 / sqrt(d_qk)) * log2(e)`。这与原来的 +softmax 相同,只是改写成直接映射到快速 base-2 exponential instructions +的形式。 + +每次 row maximum 增加时都重缩放完整的 512-coordinate O tile,代价会很高。 +Head-128 kernel 因此使用 lazy threshold: + +```python +should_scale_o: T.bool = ( + T.ptx.any_sync(T.uint32(0xFFFFFFFF), cur_pi_max - mi > 6.0) != 0 +) + +if not should_scale_o: + scale_for_old = 1.0 + new_max = mi +else: + new_max = T.max(cur_pi_max, mi) + scale_for_old = T.ptx.exp2(mi - new_max) +``` + +如果新 tile maximum 比保存的 origin 至多高 6 个 base-2 units,kernel 会继续 +保留旧 origin。新的 exponential 此时最大可能达到 $2^6=64$,但 accumulated +O 无需 rescale。一旦差值超过 6,kernel 就执行 rebase,同时 rescale $\ell$ +和已经存在的 O。Warp-wide `any_sync` 让参与计算的 rows 使用一致的决策。 + +`real_mi` 单独维护截至当前看到的精确 maximum,所以这项优化不会改变 +`max_logits`:`mi` 是 recurrence 使用的 numerical origin,`real_mi` 则是 +最终报告的统计量。结束时,两个 64-token half 对每个 logical row 的贡献会被 +合并,kernel 输出: + +$$ +\mathrm{lse}=m\ln 2+\ln\ell. +$$ + +可选的 attention sink 将最终 output scale 改成: + +```python +output_scale: T.float32 = T.cuda.fdividef( + T.float32(1.0), li + T.ptx.exp2(attn_sink_log2 - mi) +) +``` + +但它有意不改变报告的 LSE。对于全 invalid row,特殊分支会输出 0,同时令 +`max_logits=-inf`、`lse=+inf`,与固定版本 reference 一致。 + +## 各个阶段如何安全重叠? + +把这个 schedule 看成一个依赖关系问题最容易理解。QK 必须先完成,softmax +才能消费它的 logits;softmax 必须先产生 weights,PV 才能开始。但是,只要 +原位复用的 K 或 V segment 已经安全释放,负责 gather 的 warpgroups 就应该 +继续向前推进。 + +```{figure} ../../img/flashmla_pipeline_stages_zh.svg +:width: 100% +:alt: QK、softmax 与 PV 在相邻 tile 之间的稳态重叠 + +Softmax($k-1$) 可与 QK($k$) 重叠;唯一的 MMA issuer 串行发出 QK($k$) 与 +PV($k-1$);随后 softmax($k$) 可与异步执行的 PV($k-1$) 重叠。这不是两条 +同时发射 QK 与 PV 的 tensor-core streams。 +``` + +Kernel 先由 warp 0 初始化 mbarriers,执行 cluster sync,launch Q prologue, +分配 CTA-group TMEM,再进入 specialized loops。 + +CTA-group gather 的 TMA completion 会被路由到指定的 leader barrier,使 +CTA pair 发出的操作共同满足同一 expected byte count。 + +把主要 barrier edges 写成 ownership transfer 会更容易理解: + +| Barrier | Producer 到 consumer | 保护的 storage | +| --- | --- | --- | +| `bar_k_part0_ready` | WG1 到 WG3 | SS QK 使用的 K prefix | +| `bar_qk_part_done` | WG3 到 WG1 | SS QK 完成后允许覆盖 K prefix | +| `bar_k_part1_ready` | WG1 到 WG3 | TS QK 使用的 K suffix | +| `bar_qk_done` | WG3 到 WG0 和 WG1 | 原始 logits $L$ ready;QK 完成后 K suffix 可复用 | +| `bar_p_free` | WG0 到 WG3 | 下一次覆盖前,TMEM raw-logit tile 已被消费 | +| `bar_k_valid_ready/free` | warp 13 到/从 WG0 | packed validity mask | +| `bar_so_ready` | WG0 到 WG3 | PV 所需的 BF16 权重 $W$ ready | +| `bar_v_part0_ready` / `bar_sv_part_done` | WG2 到/从 WG3 | 第一半 V | +| `bar_v_part1_ready` / `bar_sv_done` | WG2 到 WG3,再由 WG3 到 WG2 和 WG0 | 第二半 V;复用 V、rescale O 或执行 epilogue 前,PV/O 已完成 | + +对于 tile $k$,唯一的 MMA issuer 先 launch QK($k$)。WG0 把 $L(k-1)$ 转成 +$W(k-1)$ 后,同一个 issuer 才在 serial loop 后部 launch PV($k-1$)。因此, +QK 与 PV 由同一 instruction stream 交错发起,而不是两条同时发射的 +tensor-core streams。 + +在 steady state 中,softmax($k-1$) 可以与 QK($k$) 重叠。唯一 issuer 在 +QK($k$) 之后发出 PV($k-1$);QK($k$) 完成后,softmax($k$) 又可以与仍在异步 +执行的 PV($k-1$) 重叠。所有这些重叠仍受上述 part-level edges 约束。 + +Ring index 是: + +```python +cur_buf = k % 2 +cur_phase = (k // 2) & 1 +``` + +这样,复用的 barrier slot 可以区分本轮的新 arrival 与两轮之前的旧 arrival。 + +再次强调,这是一条 two-slot *barrier/phase ring*,并不是让两个完整 KV tiles +同时 resident。 + +`bar_qk_part_done` 允许 producer 在 K suffix 可以复用之前先替换 K prefix。 +两条 `bar_sv_*` edge 对 V 做同样的事。 + +```{figure} ../../img/flashmla_pipeline_zh.svg +:width: 100% +:alt: Sparse-prefill pipeline,其中当前 tile 执行 QK,前一个 tile 执行 PV + +在稳态中,QK($k$) 与 PV($k-1$) 交错发起,其他 roles 同时执行分段 K/V +gather 和 softmax。Barrier phase 保护 in-place storage reuse,而不是选择两份 +完整 tile buffer。 +``` + +这些 edges 周围会出现两类 fence。`T.ptx.tcgen05.fence.*` 对 TMEM access 与 +thread-visible work 做 ordering;`T.ptx.fence.proxy_async("shared::cta")` 则在 +SMEM 的 generic access 与 asynchronous access 之间建立 cross-proxy ordering。 + +这里既包括 generic store 写入 $W$ 或 epilogue tile 后,tcgen05/TMA 执行 +asynchronous read,也包括 asynchronous SMEM read 完成后,generic code 覆写 +alias storage。 + +Mbarrier 传达 completion 与 ownership handoff;proxy fence 则对不同 proxy 的 +memory effects 做 ordering,两者不能互相替代。 + +## 如何编译并验证整条路径? + +固定版本 module 面向 compute capability 10,其 TMA/tcgen05 形式要求 SM100 +class GPU。环境应使用 B200、CUDA 12.9 或更高版本,以及官方 Apache TVM +0.26.0 package。 + +Kernel 使用的是这个 release 的 TIRx API,而不是持续变化的 development +checkout 写法。 + +首先通过 [PyTorch 官方选择器](https://pytorch.org/get-started/locally/)安装 +支持 B200 的 CUDA-enabled PyTorch build。Companion repository 会 import +PyTorch,但没有把它声明为 package dependency。 + +随后安装 TVM、固定 kernel repository,再运行示例: + +```bash +python -m pip install "apache-tvm==0.26.0" cuda-bindings +git clone https://github.com/mlc-ai/tirx-kernels.git +cd tirx-kernels +git checkout 5be39749e7dfd2c4bdae9b4d396f8ec35af07126 +pip install -e . +``` + +只用一个 query row 的 smoke test 仍会覆盖完整的 128-head、top-k-2048 +kernel,同时保持 reference 时间较短: + +```python +from tirx_kernels.flashmla.sparse_prefill_head128_phase1 import run_test + +run_test( + label="tutorial_smoke", + s_q=1, + s_kv=8192, + topk=2048, + d_qk=576, + h_q=128, + h_kv=1, + d_v=512, + have_attn_sink=True, + have_topk_length=False, + seed=0, +) +print("compile, launch, and randomized reference check passed") +``` + +`run_test` 不只是 compile。它会分配随机 BF16 Q/KV 和随机 indices,运行生成的 +kernel,逐个 query row 求 FP32 PyTorch oracle,再用明确的 tolerance 检查 +output、maximum logits 和 LSE。这才是默认应使用的验证路径;仅仅编译出 PTX +无法发现 head partition 错误或遗漏 validity bit。 + +Repository CLI 可以运行完整的 registered configuration: + +```bash +python -m tirx_kernels.test \ + --kernel sparse_flashmla_prefill_head128_phase1 \ + --config bench_regular_dqk576_hq128_s4096_kv8192_topk2048 +``` + +Negative tests 同样重要。设置 `inject_invalid_indices=True` 可以覆盖负数和过大的 +row ID,设置 `have_topk_length=True` 可以覆盖 position predicate。还应测试全 +invalid row,并确认约定的 0/-infinity/+infinity 行为。最后,对 head-64 和 +small-top-k shapes 调用统一 dispatch entry,避免把一次成功的 regular-head128 +运行误认为完整 API coverage。 + +## 哪五条不变量定义了这条路径? + +1. **缓存不变量(cache invariant)。** 一条 `h_kv=1` 的 latent KV row 可以 + 服务 128 个 query heads,是因为 key up-projection 已吸收到各 head 的 query + 路径,而 value up-projection 被移到 core attention 之后。RoPE channel 仍 + 保持显式,QK scale 仍是模型语义规定的 scale。 + +2. **稀疏契约不变量(sparse-contract invariant)。** Token selection 发生在 + 这个 kernel 之前;`indices` 提供 rows,重复项仍按重复项计算,因果合法性由 + caller 保证,并且每个 `topk_length` 都必须位于 `[0, topk]`。优化路径与 + reference path 必须保持相同的 attention sink 和全 invalid 约定。 + +3. **所有权不变量(ownership invariant)。** 一个 2-CTA cluster 负责一个 + query row。这对 CTA 沿不同的轴切分 Q/output heads、selected K rows 和 V + features;CTA 0 的 warp 12 是 CTA-group MMA 的唯一 issuer。 + +4. **驻留不变量(residency invariant)。** $L$ 表示 FP32 原始 logits,$W$ + 表示 BF16 未归一化指数权重。K、V、$L$ 和 $W$ 的大型 workspace 都是原位 + 复用的单份 tile,而 `NUM_BUFS=2` 驱动的是 barrier/phase ring。在数据缓冲区 + (data buffers)中,只有小型 packed-validity mask 才有两个 physical slots。 + +5. **交接不变量(handoff invariant)。** Ready/done barriers 转移每个可复用 + segment 的 ownership,proxy fences 则对 generic 与 asynchronous SMEM + access 排序。唯一 issuer 保证 QK($k$) 先于 PV($k-1$) 发射,而 threshold + 为 6 的优化保证上报 maximum 的语义不变,并保持 online LSE 的递推关系。 + +前两条不变量定义 operator semantics,后三条定义这个 specialization 的 +schedule contract。其他 dispatch 可以修改 tile sizes、register budgets、 +ownership 或 barrier topology,但必须显式给出替代 contract,而不能悄悄改变 +operator 所计算的结果。 + +## 接下来应该测试什么? + +Regular head-128 kernel 只是 dispatch space 中的一个点。固定版本源码树还包含 +64-head phase-1 kernel,以及 128-head `d_qk=512` small-top-k kernel。它们使用 +不同 schedule,这说明 sparse attention 应根据 tile economics 做 dispatch, +而不应被强行塞进一个 universal template。 + +1. **复现 weight absorption。** 给可执行的 absorption proof 加入 causal mask。 + 确认 MHA mode 与 MQA mode 仍然一致,再故意把 absorbed path 的 scale 改为 + $1/\sqrt{D_{latent}}$,测量产生的误差。 + +2. **压力测试 sparse validity。** 在 `sparse_prefill_reference` 中加入全 invalid + query、重复 indices、`topk_length=0`,以及正负无穷的 sink values。分别写出 + 预期的 `(out, max_logits, lse)`。 + +3. **追踪 ownership。** 对一个 top-k tile,给 Q、K、$L$、$W$、V 和 O 的每个 + dimension 标注 `(CTA, local row, local column)`,找出一个 logical row 在哪些 + 位置需要另一个 CTA 拥有的信息。 + +4. **审计 residency。** 从 `SMEMPool` allocation 开始画出每个 alias interval。 + 验证为什么 $d_{sq}$ Q prefix 必须保持 live,而 384-column suffix 可以移到 + TMEM,并找出结束每个 reuse hazard 的 barrier。 + +5. **测量 threshold。** 对 random 和 adversarial logits 加入 instrumentation, + 统计 `should_scale_o` 取 true 的频率。比较 threshold 6、always-rebase 和 + never-rebase 三个版本的 numerical error 与 TMEM O traffic。 + +6. **比较 dispatch。** 对 head count 64/128、`d_qk` 512/576,以及 1280 附近的 + top-k values 调用 `select_kernel`。运行前先预测选择的 module,再检查哪些 + constraint 属于 front door,哪些由单个 specialization 强制执行。 + +7. **阅读 generated program。** 编译 smoke shape,在生成的 PTX 中找到 + `tcgen05` MMA、TMA gather、mbarrier 和 proxy-fence instructions,再把它们 + 映射回对应 TIRx line。最后重新运行 numerical check:source、generated + code 和实际观察值是三类互补的证据。 + +本章的核心结论并不局限于 FlashMLA。高性能 irregular operator 往往会分阶段 +把工作规则化:indexer 生成 sparse addresses,TMA 把这些 addresses gather 成 +dense tiles,tensor cores 消费 tiles,显式 barrier 则保护激进的 storage +reuse。只有同时理解 algorithm、dispatch contract、ownership map 和 memory +protocol,才能把高速 kernel 从难以理解的产物变成可以解释的程序。 diff --git a/zh/index.md b/zh/index.md index 63337fd0..1c8e6553 100644 --- a/zh/index.md +++ b/zh/index.md @@ -4,7 +4,7 @@ 要让这些 kernel 真正跑得快,不能只罗列优化技巧。近年来的 GPU 架构引入了更丰富的内存空间、新的数据搬运机制和越来越专用化的执行单元。要充分利用这些硬件能力,既要理解 GPU 如何执行程序,也要掌握一个基础 kernel 如何逐步演变成高性能实现。本书将围绕这两个方面展开。 -本书按照从硬件、编程模型到完整 kernel 的顺序展开。我们会先介绍 GPU 的组织方式和执行模型,再学习本书使用的编程模型,最后逐步构建高性能 kernel。本书主要面向 NVIDIA Blackwell,并以 General Matrix-Matrix Multiplication(GEMM)和 FlashAttention 为贯穿全书的示例。在构建这些 kernel 的过程中,还会系统介绍数据布局、异步数据搬运和异步协作等关键主题。 +本书按照从硬件、编程模型到完整 kernel 的顺序展开。我们会先介绍 GPU 的组织方式和执行模型,再学习本书使用的编程模型,最后逐步构建高性能 kernel。本书主要面向 NVIDIA Blackwell,并以 General Matrix-Matrix Multiplication(GEMM)、FlashAttention 和 FlashMLA 为贯穿全书的示例。在构建这些 kernel 的过程中,还会系统介绍数据布局、异步数据搬运和异步协作等关键主题。 本书内容源自卡内基梅隆大学的 [Machine Learning Systems](https://mlsyscourse.org/) 课程系列。书中的示例使用 TIRx Python DSL,让读者能够在真实 kernel 中学习、运行和验证这些概念。TIRx 会明确表示与硬件执行有关的选择,因此可以结合可运行的代码分析控制流、内存访问和同步逻辑。 @@ -16,7 +16,7 @@ - **第一部分:理解 GPU。** 这一部分介绍 GPU 的整体架构组织、编写高性能 kernel 的通用方法,以及数据布局、异步内存操作和协作等关键概念,并建立后续章节所依赖的硬件理解。 - **第二部分:TIRx 概览。** 这一部分介绍 TIRx 的核心组成部分,为理解后续章节中的代码示例做准备。 - **第三部分:GEMM:从 Tiled 到 SOTA。** 这一部分完整讲解如何优化一个 tiled GEMM,并逐步加入 TMA pipelining、persistent scheduling、warp specialization 和 2-CTA cluster。 -- **第四部分:Flash Attention 4。** 这一部分基于第三部分的技术构建完整的 attention kernel:两个 MMA,中间插入 softmax,并包含 online-softmax rescaling、causal mask 和 GQA。 +- **第四部分:注意力内核。** 这一部分首先基于第三部分的技术构建 Flash Attention 4,随后介绍 Multi-head Latent Attention,并将一个稀疏 FlashMLA prefill 算子映射为 Blackwell 上的 2-CTA kernel。 - **附录。** TIRx 语言参考、可复现的 GPU 性能测量与分析流程、编译器内部机制,以及异步 kernel 调试指南。 ```{toctree} @@ -52,10 +52,11 @@ chapter_gemm_advanced/index ``` ```{toctree} -:caption: 第四部分:Flash Attention 4 +:caption: 第四部分:注意力内核 :maxdepth: 2 chapter_flash_attention/index +chapter_flashmla/index ``` ```{toctree} From dab8e07591ba4cedaf0f6cfffd87e981a6ef6031 Mon Sep 17 00:00:00 2001 From: tlopex <820958424@qq.com> Date: Wed, 12 Aug 2026 01:08:30 -0400 Subject: [PATCH 2/5] Refine FlashMLA tutorial flow and diagrams --- chapter_flashmla/index.md | 727 +- img/flashmla_cache_story.png | Bin 251236 -> 306129 bytes img/flashmla_cache_story_zh.svg | 6088 +++++++++------- img/flashmla_cta_ownership.png | Bin 199760 -> 198280 bytes img/flashmla_cta_ownership_zh.svg | 48 +- img/flashmla_dataflow.png | Bin 331547 -> 343397 bytes img/flashmla_dataflow_zh.svg | 7636 +++++++++------------ img/flashmla_pipeline.png | Bin 315386 -> 350726 bytes img/flashmla_pipeline_zh.svg | 7346 ++++++++++---------- img/flashmla_sparse_story_zh.svg | 62 +- img/scripts/gen_flashmla_cache_story.py | 173 +- img/scripts/gen_flashmla_cta_ownership.py | 28 +- img/scripts/gen_flashmla_dataflow.py | 672 +- img/scripts/gen_flashmla_pipeline.py | 635 +- img/scripts/gen_flashmla_sparse_story.py | 2 +- zh/chapter_flashmla/index.md | 690 +- 16 files changed, 11795 insertions(+), 12312 deletions(-) diff --git a/chapter_flashmla/index.md b/chapter_flashmla/index.md index b691f24b..22d1cd15 100644 --- a/chapter_flashmla/index.md +++ b/chapter_flashmla/index.md @@ -1,51 +1,91 @@ (chap_flashmla)= # FlashMLA -Start with an apparent contradiction. The Blackwell kernel studied in this -chapter accepts 128 query heads, but its KV tensor has only one head. One cached -KV entry must somehow serve all 128 heads, preserve head-specific attention, and -produce 128 different 512-coordinate outputs. - -That puzzle has three layers. MLA explains why the cache can be shared. -Weight absorption explains where the per-head projections went. The FlashMLA -kernel explains how a sparse list of shared cache rows becomes a dense, -two-CTA tensor-core computation. - -```{figure} ../img/flashmla_cache_story.png -:width: 100% -:alt: One latent KV cache entry serving 128 query heads through absorbed projections - -The cache stores one latent content vector and one shared RoPE key per token. -Per-head behavior survives on the query and output sides rather than as 128 -materialized K/V cache entries. -``` - :::{admonition} Overview :class: overview -- Derive MLA's shared latent cache, MHA/MQA execution modes, and weight absorption. -- Turn the sparse-attention contract into a 2-CTA Blackwell dataflow program. -- Run executable references, then compile and verify the pinned kernel on B200. +- Start from an ordinary MHA KV cache and derive why MLA stores one shared + compressed state per token, including where the head-specific K/V + transformations move. +- Define the FlashMLA sparse-prefill operator: an external indexer selects KV + rows, then FlashMLA attends over those rows. An executable reference fixes its + numerical behavior and edge cases. +- Use the TIRx `flash_mla_sparse_fwd` entry to understand shape dispatch and how + it specializes the QK scale, then follow the regular head-128 + specialization through two-CTA ownership, data residency, specialized roles, + and the pipeline before compiling and verifying it on B200. ::: -The name *FlashMLA* combines two ideas that are easy to conflate. MLA is an -attention architecture that compresses key-value state into a latent vector. -FlashMLA is DeepSeek's library of optimized attention kernels, spanning dense -and sparse operators across prefill and decoding. +Before introducing MLA, recall why ordinary attention needs a **KV cache**. To +compute a new query, attention must read the keys and values of earlier tokens. +Recomputing them every time would repeat a large amount of work, so the system +caches the K/V states and lets later queries read them directly. + +In ordinary multi-head attention (MHA), every attention head has its own K and +V. The KV cache must therefore store every head's K/V for every processed token. +As the context grows, the amount of state that must be stored and read grows +with it. MLA's first goal is to reduce this cache. + +**Multi-head Latent Attention (MLA)** uses a different cache representation. +Instead of storing expanded K/V for every head, it stores one compressed state +per token and shares that state across all heads. This does not merge all heads +into one. Each head still has its own transformations; the cache simply no +longer stores the K/V produced by those transformations as long-lived state. We +will derive how one shared state can preserve head-specific behavior. + +MLA specifies what the cache stores and how attention is computed; FlashMLA +addresses how to perform those computations efficiently on a GPU. **FlashMLA** +is DeepSeek's library of optimized GPU kernels for MLA, with operators for +different attention stages and cache formats. + +This chapter begins with sparse prefill. *Prefill* means processing the prompt's +query tokens in parallel; *sparse* means that an external indexer first selects +the relevant KV rows and attention visits only those rows. + +The sparse-prefill operator does not map to one immutable kernel. This chapter +keeps three layers distinct. The FlashMLA `flash_mla_sparse_fwd` interface is +the semantic thread: it defines the inputs, outputs, and computation of sparse +prefill. The TIRx registry entry with the same name is a dispatch bridge with a +narrower call signature: its specializations bind `sm_scale` to +`1 / sqrt(d_qk)` and it selects a head-64, regular head-128, or small-top-k +head-128 specialization by shape. The regular head-128 specialization is the +implementation thread: it shows how Blackwell schedules that computation. +Other implementations appear only when comparing operator families, dispatch, +and design tradeoffs. + +In the regular head-128 specialization, MLA's sharing is especially visible. +One query token corresponds to a query row containing 128 query heads, while +each cached token contributes one shared KV row. How can 128 heads read the same +KV row and still produce different results? The next figure gives the first +clue. What is shared is the source state used to form K/V, not the final +representation consumed by every head. Head-specific transformations remain on +the two sides of the dot-product, softmax, and weighted-sum core. We will list +the exact tensor shapes after deriving MLA. -We will derive the architecture, make the sparse contract executable, and then -read one specific library path with the same algorithm-to-schedule depth used -for FA4: the regular 128-query-head sparse-prefill forward kernel on Blackwell. +```{figure} ../img/flashmla_cache_story.png +:width: 100% +:alt: Ordinary MHA caches separate key and value data for every head; MLA stores one shared compressed state and keeps head-specific work around attention + +Ordinary MHA stores a separate key/value slice per head. MLA stores one shared +compressed content state plus shared position information per token; +head-specific query and output transformations happen before and after +attention. +``` -Our implementation reference is pinned to -[`mlc-ai/tirx-kernels@5be39749`](https://github.com/mlc-ai/tirx-kernels/tree/5be39749e7dfd2c4bdae9b4d396f8ec35af07126). -All TIRx API spellings and excerpts below come from that revision. This matters: -the compiler APIs are evolving, while a textbook example must be reproducible. +The figure gives intuition, but it does not yet explain how a shared state +preserves head-specific behavior or prove why moving these transformations +leaves the computation unchanged. We will first quantify the ordinary MHA +cache, derive what MLA stores, and prove why the transformations can move. Only +then will we turn to the sparse operator and the regular head-128 +specialization's Blackwell schedule. -## Why does MHA cache separate K/V for every head? +## Start with the ordinary MHA KV cache -Let $h_t\in\mathbb{R}^{d_{model}}$ be the hidden state of token $t$. Ordinary -multi-head attention (MHA) projects it independently for every head $i$: +The intuition above does not yet tell us how large the cache is. Let +$h_t\in\mathbb{R}^{d_{model}}$ be the hidden state of token $t$. Write $n_h$ +for the number of heads and $d_h$ for the width of one head; $i$ selects a head, +while $s$ will select a cached key-token position. Ordinary MHA produces a +separate query, key, and value for every head $i$: $$ q_{t,i}=W_i^Q h_t,\qquad @@ -100,22 +140,11 @@ The superscript $C$ denotes the non-positional, or *content*, channel. The key observation is that the cache need not store the expanded $k^C$ and $v^C$ for every head. It stores one $c^{KV}$ per token instead. -MLA may also factor the query projection through a separate low-rank latent, - -$$ -c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. -$$ - -This query-side factorization reduces activation memory during training, but it -does not reduce the KV cache. - -It also happens before the core-attention API: the `q` tensor passed to FlashMLA -already contains the projected query. We therefore treat $q^C$ as an input and -focus on the KV-side compression that determines the cache and kernel operands. - -RoPE complicates this simple picture. A position-dependent rotation between -$W^{UK}$ and a dot product would prevent the matrices from being reassociated. -MLA therefore uses a decoupled positional channel: each query head has +Rotary positional embedding (RoPE) rotates a position-carrying subspace of Q +and K. This complicates the simple picture above: inserting that +position-dependent rotation between $W^{UK}$ and a dot product would prevent +the matrices from being reassociated. MLA therefore uses a decoupled positional +channel: each query head has $q_{t,i}^{R}$, while all heads share a cached $k_t^R$. The actual MHA-form score uses @@ -127,12 +156,31 @@ $$ The cache is now $[c_s^{KV};k_s^R]$, still shared across heads. The positional channel remains explicit; weight absorption applies to the content channel. +:::{admonition} The query side can also be compressed +:class: note + +MLA may factor the query projection through a separate low-rank latent, + +$$ +c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +$$ + +This factorization mainly reduces activation memory during training; it does +not shrink the KV cache further. It also happens before FlashMLA's core +attention: the `q` tensor presented to the sparse-prefill operator is already +projected. We therefore treat $q^C$ as an input and continue along the KV-cache +path. +::: + ### Where do the per-head up-projections go? -MLA admits two algebraically related core-attention modes. This should not be -taken to mean that every MLA model is an ordinary MQA model. +We now know what the cache stores, but one question remains: must every head's +$W_i^{UK}$ and $W_i^{UV}$ still run explicitly before attention? MLA admits two +algebraically equivalent core-attention modes. Here “MQA mode” names an +execution strategy; it does not mean that every MLA model is an ordinary MQA +model. -| MLA execution mode | Core-attention K/V presented to the kernel | Where up-projection occurs | +| MLA execution mode | K/V used by core attention | Where up-projection occurs | | --- | --- | --- | | MHA mode | Per-head $[W_i^{UK}c^{KV};k^R]$ and $W_i^{UV}c^{KV}$ | Before core attention | | MQA mode | Shared $[c^{KV};k^R]$ and shared latent values $c^{KV}$ | Absorbed into the query and output paths | @@ -165,21 +213,12 @@ $$ Consequently, $W_i^{UV}$ can be composed with the model's output projection. Neither expanded per-head K nor expanded per-head V needs to be materialized by -the attention kernel. +the core-attention computation. -The distinction is operational, not merely notational. Appendix A of the -[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) -states that DeepSeek-V3.1-Terminus used MHA mode for training and prefill and MQA -mode for decoding. - -DeepSeek Sparse Attention (DSA), by contrast, instantiates MLA in MQA mode even -for sparse prefill because each selected latent KV entry is shared by all query -heads. - -Thus the $d_{qk}=576$, $d_v=512$ contract commonly seen in this sparse-prefill -path is an absorbed MQA representation: 512 latent content coordinates plus a -64-coordinate RoPE channel. It is not a universal shape for MLA or every -FlashMLA operator. The implementation also supports a $d_{qk}=512$ variant. +The DeepSeek Sparse Attention (DSA) sparse-prefill operator studied here uses +this MQA mode: every selected latent KV entry is shared by all query heads. +Before discussing model-specific choices or implementation shapes such as 512 +and 576, we can verify the algebraic equivalence with a small program. ### Can a small program prove the two modes agree? @@ -237,7 +276,11 @@ Notice that the scale remains the scale of the model's semantic QK head, not $1/\sqrt{D_{latent}}$ merely because the absorbed dot product happens to have $D_{latent}$ coordinates. -## Does the sparse kernel choose the tokens? +Weight absorption has answered how one shared KV row can serve many query +heads. The next, independent question is who selects the list of KV rows that +the sparse-prefill operator receives. + +## Does the sparse-prefill operator choose the tokens? Dense attention visits every eligible KV token. DSA first uses a lightweight *lightning indexer* to score candidate tokens and chooses a top-$k$ set for each @@ -247,10 +290,10 @@ $O(L^2)$ to $O(Lk)$ for prefill, although the indexer has its own cost. ```{figure} ../img/flashmla_sparse_story.png :width: 100% -:alt: A lightning indexer selecting token rows before the sparse FlashMLA attention kernel +:alt: A lightning indexer selecting token rows before the sparse-prefill attention operator Selection and attention are separate operators. The indexer produces row -addresses; the sparse-prefill kernel gathers those rows and performs the +addresses; the sparse-prefill operator gathers those rows and performs the QK--softmax--PV computation. ``` @@ -270,73 +313,27 @@ not itself a causal mask. When `topk_length` is present, every query must satisfy `0 <= topk_length[q] <= topk`. This is a caller precondition, not a value that -the kernel clips automatically: a value above `topk` makes the pinned kernel -walk beyond the logical `indices` storage. - -This prefill interface also has no batch dimension. In the port studied below, -`h_kv=1`, so `indices` has shape `[s_q, 1, topk]`: each query token supplies one -selected-token list, and all 128 of its query heads share that list. A serving -system must flatten or otherwise map batches before making this call. - -### Is FlashMLA one kernel or an operator family? - -*Prefill* processes the prompt's query tokens in parallel; *decoding* adds a new -query (or a small speculative group) step by step while reusing the KV cache. -The [official FlashMLA repository](https://github.com/deepseek-ai/FlashMLA) -organizes its kernels into four broad families: - -| Selection | Sequence stage | Representative purpose | -| --- | --- | --- | -| dense | prefill | MHA forward and backward | -| dense | decoding | read an MLA KV cache for newly generated queries | -| token-sparse | prefill | DSA core attention over a selected token list | -| token-sparse | decoding | DSA inference over a selected FP8 KV cache | - -FlashMLA is therefore neither synonymous with sparse attention nor with the -kernel in this chapter. - -We use its sparse prefill operator because it makes one systems question -especially visible: how can irregular TMA gathers feed regular tensor-core -tiles? Sparse decode has a different paged-cache, scheduling, and reduction -contract and is outside this chapter's boundary. +the TIRx prefill specializations clip automatically. They use it to +determine how many selected-row tiles to visit, so a value above `topk` can make +a specialization step beyond the logical `indices` storage. -The public upstream sparse-prefill call is conceptually +This prefill interface also has no batch dimension. Each query token supplies +one selected-token list, and all `h_q` query heads share that list. A serving +system must flatten or otherwise map batches before making this call. We will +define the exact tensor shape and the symbols `s_q`, `h_q`, `h_kv`, and `topk` +when we enter the regular head-128 specialization. -```text -out, max_logits, lse = flash_mla_sparse_fwd( - q, kv, indices, sm_scale, - d_v=512, - attn_sink=attn_sink, # optional [h_q], float32 - topk_length=topk_length, # optional [s_q], int32 -) -``` - -The pinned TIRx repository reuses the public name in its unified -`flash_mla_sparse_fwd` registry entry, then dispatches to one of three SM100 -phase-1 modules by shape. - -:::{admonition} Port scope: `sm_scale` is fixed -:class: warning - -The upstream call above accepts `sm_scale` at runtime. The pinned TIRx entry -preserves the registry name and shape dispatch, **not** the complete call -signature. All three prefill modules specialize the scale to `1 / sqrt(d_qk)`, -and the launch ABI has no scale argument. - -In this revision, passing `sm_scale=...` through the `**kwargs` wrappers is -silently ignored. The B200 examples below therefore validate a fixed-scale -teaching port, not a drop-in replacement for upstream `flash_mla_sparse_fwd`. - -A model whose semantic QK scale differs must expose or specialize the correct -value. Weight absorption does not justify changing that scale. -::: +These rules now say what the operator accepts and rejects. Next we turn them +into an executable CPU reference, so that the semantics stand on their own +before we discuss the FlashMLA implementation. ## Can we make the sparse contract executable first? -Before reading the kernel, we need a reference that makes edge cases explicit. -For the absorbed MQA contract, `kv[:, 0, :]` supplies both K and V: all `d_qk` -coordinates participate in QK, while the first `d_v` coordinates are the latent -value. +Before examining any GPU specialization, we need a reference that makes edge +cases explicit. For the absorbed MQA contract, `kv[:, 0, :]` supplies both K and +V: all `d_qk` coordinates participate in QK, while the first `d_v` coordinates +are the latent value. Here `d_qk` is the Q/K width, `sm_scale` is the model's +semantic QK scale, and `d_v` is the requested value/output width. Invalid indices must be clamped *before* a PyTorch gather and then masked out. Directly indexing with `-1` would incorrectly select the last row. @@ -344,10 +341,32 @@ Directly indexing with `-1` would incorrectly select the last row. The gathered V row for an out-of-range address is also cleared before PV, because a zero softmax weight does not neutralize a NaN under IEEE arithmetic. We deliberately leave an in-range row masked only by `topk_length` unsanitized -to match the pinned kernel behavior discussed below. +because neither the FlashMLA interface nor the three TIRx prefill +specializations promise to sanitize that exceptional input. -The complete CPU block answers whether those rules, the attention sink, and the -all-invalid convention can coexist in one executable oracle: +An attention sink is equivalent to adding a logit whose value vector is zero. +It changes only the output denominator: + +$$ +O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} +{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. +$$ + +Here $a_i$ is the per-head sink logit. It has no effect on `max_logits` or the +returned log-sum-exp (`lse`). If every selected position is invalid, the +operator instead uses the explicit convention `out=0`, `max_logits=-inf`, and +`lse=+inf`. + +The executable oracle follows four stages: + +1. validate and safely gather the requested rows; +2. construct the validity predicate and clear only out-of-range V sentinels; +3. compute scaled logits, unnormalized weights, numerator, denominator, and the + optional sink term; and +4. normalize the output and return the two statistics, including the all-invalid + convention. + +The complete CPU block puts those stages in one place: ```python import math @@ -445,61 +464,121 @@ torch.testing.assert_close(nan_out, torch.tensor([[[2.0, 3.0]]])) print(out.shape, max_logits.shape, lse.shape) ``` -An attention sink is equivalent to adding a logit whose value vector is zero. -It changes only the output denominator: +The reference makes the sparse-prefill operator's numerical contract executable +for defined inputs and return conventions. Its treatment of the exceptional +NaN case identified above mirrors the TIRx specializations; it does not add a +sanitization guarantee to the interface. Every dispatched TIRx specialization +must reproduce the defined results when the operator scale equals its +specialized `1 / sqrt(d_qk)` value. Tile partitioning, storage reuse, and +pipeline overlap belong to an implementation, not to the operator contract. -$$ -O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} -{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. -$$ +## Where does sparse prefill sit in the FlashMLA family? -Here $a_i$ is the per-head sink logit. It has no effect on `max_logits` or the -returned `lse`, a detail that is easy to miss when writing an independent -oracle. +FlashMLA is a library that spans both the sequence stage and the selection +pattern. Unlike prefill, *decoding* adds a new query (or a small speculative +group) step by step while reusing the KV cache. The +[official FlashMLA repository](https://github.com/deepseek-ai/FlashMLA) +organizes its operators and their implementations into four broad families: + +| Selection | Sequence stage | Representative purpose | +| --- | --- | --- | +| dense | prefill | MHA forward and backward | +| dense | decoding | read an MLA KV cache for newly generated queries | +| token-sparse | prefill | DSA core attention over a selected token list | +| token-sparse | decoding | DSA inference over a selected FP8 KV cache | + +This chapter follows the token-sparse prefill cell. At the operator level, its +distinctive feature is an externally selected list of irregular KV row +addresses. We choose the regular head-128 specialization as the implementation +thread because it makes the corresponding Blackwell question concrete: how can +the Tensor Memory Accelerator (TMA) gather those addresses into regular +tensor-core tiles? Sparse decode has a different paged-cache, scheduling, and +reduction contract and is outside this chapter's boundary. In TIRx it is a +separately registered implementation that launches a split-KV main kernel +followed by a separate combine kernel; it is not a fourth target of the +`flash_mla_sparse_fwd` dispatch bridge. + +The FlashMLA sparse-prefill interface is conceptually + +```text +out, max_logits, lse = flash_mla_sparse_fwd( + q, kv, indices, sm_scale, + d_v=512, + attn_sink=attn_sink, # optional [h_q], float32 + topk_length=topk_length, # optional [s_q], int32 +) +``` + +The tensor dimensions and explicit arguments have the semantics exercised by +the oracle: `h_q` is the query-head count, `s_q` is the query-row count, +`sm_scale` scales QK scores, `d_v` selects the value/output width, `attn_sink` +optionally adds one zero-valued logit per query head, and `topk_length` limits +each query's valid index prefix. The call returns the normalized output, maximum +scaled logit, and log-sum-exp without the sink. + +The TIRx tree connects this interface to device code through a registry entry +that deliberately reuses the name `flash_mla_sparse_fwd`. TIRx +extends TVM 0.26's TIR Python DSL: `T` denotes the TIR script namespace, while +`Tx` contains GPU-kernel helpers. The registry entry is a dispatch bridge: by +shape, it selects one of three SM100 phase-1 specializations of the same +sparse-prefill computation. + +:::{admonition} The TIRx entry specializes `sm_scale` +:class: warning + +The FlashMLA interface above accepts `sm_scale` at runtime. The TIRx dispatch +entry exposes a narrower call signature: all three prefill specializations bind +the scale to `1 / sqrt(d_qk)`, and the launch application binary interface +(ABI) has no scale argument. + +Passing `sm_scale=...` through the `**kwargs` wrappers is silently ignored. The +B200 examples below therefore validate the computation only at +`sm_scale = 1 / sqrt(d_qk)`; they do not demonstrate runtime-scale parity with +the complete FlashMLA interface. + +A model whose semantic QK scale differs must expose or specialize the correct +value. Weight absorption does not justify changing that scale. +::: ## Which Blackwell case are we studying? We now focus on [`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py). -Despite the internal `phase1` name inherited from upstream FlashMLA, this +Despite the internal `phase1` name, this prefill path produces the complete `(out, max_logits, lse)` result in one kernel; it is not a partial split-KV output awaiting a combine kernel. This regular head-128 case is a useful bridge from the preceding FlashAttention chapter. It retains the familiar QK--softmax--PV chain, then adds irregular -gather, absorbed latent KV, and cooperative 2-CTA ownership. +gather, absorbed latent KV, and cooperative thread-block ownership. + +In the source, a cooperative thread array (CTA) is one CUDA thread block; a +thread-block cluster is a hardware group of CTAs that can participate in +collective operations. A warpgroup is four warps, or 128 threads, assigned one +specialized role. This kernel pairs two CTAs in one cluster. One naming warning prevents confusion later. In the mathematical introduction, -$p$ denotes a normalized softmax probability. In the pinned source, however, +$p$ denotes a normalized softmax probability. In the implementation, however, `tmem_p` and the register variable `p` hold **raw QK logits**. In the schedule discussion we will call those logits $L$. The source's `s_frag` and `s_smem_gemm` hold BF16 **unnormalized exponential weights**, which we will call $W$. -The weights are not normalized in place. The final output becomes normalized -only when the accumulated output is divided by `li` plus the optional sink term -in the epilogue. +The weights are not normalized in place. Here `li` names the running softmax +denominator. The final output becomes normalized only when the accumulated +output is divided by `li` plus the optional sink term in the epilogue. -All shorter TIRx code blocks below are contextual excerpts from the pinned -kernel, not standalone programs. The complete module is compiled and +All shorter TIRx code blocks below are contextual excerpts from the linked +implementation, not standalone programs. The complete module is compiled and numerically verified in the final section. Blocks intended to run independently are called out explicitly. ### Which shapes reach the regular head-128 path? -The regular head-128 module fixes the following tile constants: - -```python -B_H = 128 -B_TOPK = 128 -D_V = 512 -NUM_BUFS = 2 -NUM_THREADS = 512 -D_TQ = 384 -``` - -Its input and output contract is: +The algorithmic discussion only needed “one shared latent KV.” Now that we are +entering a concrete implementation, we can state every tensor shape. The +regular head-128 module has this shape-specialized signature: | Tensor | Shape | Type | Meaning | | --- | --- | --- | --- | @@ -512,19 +591,52 @@ Its input and output contract is: | `max_logits` | `[s_q, 128]` | FP32 | maximum scaled logit | | `lse` | `[s_q, 128]` | FP32 | natural-log sum-exp, without sink | -The module accepts `d_qk` 512 or 576, requires `h_kv=1`, `d_v=512`, and requires -the regular path's `topk` to be a positive multiple of 128. The unified front -door makes one additional choice for 128 heads: `d_qk=512` with `topk<=1280` goes to the -small-top-k implementation; other supported head-128 shapes go to this regular -implementation. Head-64 shapes use a separate kernel. +The 128 is the query-head count from the opening question, while the 1 in `kv` +means that every head shares the same KV row. A common $d_{qk}=576$ case combines +512 latent-content coordinates with 64 RoPE coordinates; `d_v=512` is the +latent-value width. These are shapes of this absorbed MQA representation, not a +universal MLA contract. + +The choice can also differ by model and stage. Appendix A of the +[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) +states that DeepSeek-V3.1-Terminus used MHA mode for training and prefill and MQA +mode for decoding, whereas DSA sparse prefill uses MQA mode. + +With the specialization's tensor shapes fixed, the following constants +determine one tile's execution: + +```python +B_H = 128 +B_TOPK = 128 +D_V = 512 +NUM_BUFS = 2 +NUM_THREADS = 512 +D_TQ = 384 +``` -The positive-`topk` condition is a required caller precondition. The unified front -door rejects `topk<=0`, but the pinned per-implementation `_cfg().validate()` +The names map directly to the work we will trace: `B_H` is the 128-head logical +tile, `B_TOPK` is the 128 selected rows processed per streaming tile, `D_V` is +the value/output width, and `D_TQ` is the 384-coordinate Q suffix placed in +Blackwell tensor memory. `NUM_THREADS=512` gives each CTA four warpgroups. +`NUM_BUFS=2` names two synchronization slots (and two small validity-mask +slots), not two full K/V data stages; the residency and pipeline sections will +make that distinction concrete. + +The regular head-128 specialization accepts `d_qk` 512 or 576, requires +`h_kv=1`, `d_v=512`, and requires `topk` to be a positive multiple of 128. The +TIRx dispatch entry makes one additional choice for 128 heads: `d_qk=512` +with `topk<=1280` selects the small-top-k head-128 specialization; other +supported head-128 shapes select this regular head-128 specialization. Head-64 +shapes select the head-64 specialization. + +The positive-`topk` condition is a required caller precondition. The TIRx +dispatch entry rejects `topk<=0`, but the per-specialization `_cfg().validate()` methods check divisibility without checking positivity. A direct import of one -specialization must therefore still reject or avoid nonpositive `topk`; acceptance -by that local validator does not make such a launch valid. +specialization must therefore still reject or avoid nonpositive `topk`; +acceptance by that local validator does not make such a launch valid. -This dispatch can be inspected without launching a GPU kernel: +After completing the repository setup in the final section, this dispatch can +be inspected without launching a GPU kernel: ```python from tirx_kernels.flashmla.flash_mla_sparse_fwd import ( @@ -538,27 +650,35 @@ print(dispatch_reason(**shape)) # sm100 h_q=128 dispatches to regular head128 phase1 ``` -The dispatch itself is documented in the pinned +The dispatch itself is documented in [`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120). Keeping dispatch separate from the device schedule prevents a tutorial from mistaking one specialization for the entire operator. -### Why does one query row need two CTAs? - -The launch grid contains `2 * s_q` CTAs and clusters adjacent CTAs in pairs: +Before assigning hardware roles, reduce one selected tile to six semantic +steps. This is the bridge between the CPU oracle and the schedule: -```python -block_idx = T.cta_id([2 * s_q]) -T.cta_id_in_cluster([2]) -cta_idx: T.let = block_idx % 2 -s_q_idx: T.let = block_idx // 2 -thread_idx = T.thread_id([512]) -T.warpgroup_id([4]) +```text +for each selected 128-row tile: + 1. gather the tile's K rows + 2. gather its V rows and build the validity mask + 3. compute raw logits L = Q @ K.T + 4. update masked online softmax, producing W, origin mi, and denominator li + 5. rescale the running state when needed, then accumulate O~ += W @ V +after all selected tiles: + 6. normalize O~ by li + sink; store out, max_logits, and lse ``` -One cluster therefore owns one query row, and each CTA has four warpgroups. -Start with the ownership map: the unusual point is that the partition axis -changes between QK and PV. +The arithmetic is now familiar. The next question is how two thread blocks can +cooperate on these six steps without duplicating the whole tile. + +### Why does one query row need two CTAs? + +The difficulty lies in steps 3 and 5 of the tile skeleton. QK must form every +pair of 128 query heads and 128 selected tokens; PV then contracts the token +axis to produce 512 value coordinates. The implementation therefore lets two +CTAs form one logical tile and changes their partition axis between QK and PV. +Start with that ownership map before reading the launch code. ```{figure} ../img/flashmla_cta_ownership.png :width: 100% @@ -580,23 +700,48 @@ The pair divides three different axes in three different ways: This is why a 2-CTA tensor-core operation is more than “two CTAs doing half the same loop.” QK needs the cross-product of 128 heads and 128 selected tokens; PV then contracts those tokens into 512 value coordinates. The partition rotates -between the two GEMMs. Collective `cta_group=2` MMA, paired SMEM/TMEM layouts, -and cross-CTA barriers together form the logical tile. +between the two GEMMs. Collective `cta_group=2` MMA, paired on-chip layouts, and +cross-CTA synchronization together form the logical tile. + +Now return to the source to verify the launch topology. The grid contains +`2 * s_q` CTAs and clusters adjacent CTAs in pairs: + +```python +block_idx = T.cta_id([2 * s_q]) +T.cta_id_in_cluster([2]) +cta_idx: T.let = block_idx % 2 +s_q_idx: T.let = block_idx // 2 +thread_idx = T.thread_id([512]) +T.warpgroup_id([4]) +``` -The division follows directly from the pinned source: Q is chunked by -`cta_idx`, the K producer selects the `cta_idx` half of every top-k block, and -the V producer starts at `cta_idx * 256`. +One cluster therefore owns one query row, and each CTA has four warpgroups. The +same division appears in the data indexing: Q is chunked by `cta_idx`, the K +producer selects the `cta_idx` half of every top-k block, and the V producer +starts at `cta_idx * 256`. ## Where do the tiles live? -Blackwell's tensor memory (TMEM) lets `tcgen05` keep large accumulators close to -the tensor cores. It does not replace shared memory (SMEM). TMA gathers arrive in -SMEM, and the softmax warpgroup must materialize BF16 unnormalized weights in -SMEM for the PV GEMM. +The ownership map says *who* computes each piece; residency explains where a +piece waits between producers and consumers. Four hardware terms are enough to +read the next figure: + +- global memory (GMEM) holds the input and output tensors; +- shared memory (SMEM) is the ordinary on-chip scratchpad visible to a CTA; +- the Tensor Memory Accelerator (TMA) moves data asynchronously between GMEM + and SMEM and provides the sparse `gather4` path used here; +- Blackwell tensor memory (TMEM) is a separate on-chip space used by the + `tcgen05` tensor-core instruction family for operands and accumulators. + +TMEM does not replace SMEM. TMA gathers arrive in SMEM, and the softmax +warpgroup must materialize BF16 unnormalized weights in SMEM for the PV GEMM. +In the source's MMA shorthand, **SS** means that both matrix operands come from +SMEM; **TS** means that the first comes from TMEM and the second from SMEM. The +Q prefix follows the SS path and its suffix follows the TS path. ```{figure} ../img/flashmla_dataflow.png :width: 100% -:alt: Data movement between global memory, shared memory, tensor memory, and registers +:alt: Data residency and lifetime reuse across global memory, shared memory, tensor memory, and WG0 registers during QK, softmax, PV, and the epilogue Q is split between an SMEM prefix and a TMEM suffix. Gathered K/V enter SMEM, raw QK logits and the output accumulate in TMEM, and unnormalized softmax @@ -620,8 +765,9 @@ These are logical views; CTA-group TMEM layouts and rearrangements give the MMA and load/store instructions their physical lane mapping. The source allocates one 512-column CTA-group TMEM pool, then carves out O, raw-logit, and Q views. -SMEM is aggressively aliased. `q_full`, the gathered K/V region, and the output -epilogue reuse a union-like base when their lifetimes permit. +The source object named `SMEMPool` describes the corresponding shared-memory +allocation. SMEM is aggressively aliased: `q_full`, the gathered K/V region, +and the output epilogue reuse a union-like base when their lifetimes permit. After the final 384 Q columns have moved to TMEM, only the $d_{sq}=d_{qk}-384$ prefix must stay live for the first QK part. For @@ -653,10 +799,14 @@ role assignment is deliberate: one elected lane can issue asynchronous MMA for the CTA pair, while many lanes are useful for exponentiation, row reductions, packing, and epilogue conversion. +:::{admonition} Why the register limits differ +:class: note + The register budgets match the roles. WG0 raises its limit to 144 registers and -WG3 to 168; producer groups lower theirs to 96. The pinned API spells these calls +WG3 to 168; producer groups lower theirs to 96. The TIRx API spells these calls as `T.ptx.setmaxnreg(True, ...)` for an increase and `T.ptx.setmaxnreg(False, ...)` for a decrease. +::: ### How do irregular rows become regular tiles? @@ -667,7 +817,16 @@ SMEM tile. The next contextual excerpt answers which addresses one `gather4` issue reads and which barrier receives its completion. Its index names and slices are kept -exactly as they appear at the pinned revision: +exactly as they appear in the linked implementation: + +- `gather4=[...]` supplies the four KV source-row coordinates for this issue; +- `cur_buf = k % NUM_BUFS` selects the current slot in the two-slot barrier ring; + and +- `bar` is the ready-barrier array passed to this copy helper. `leader_mbar` + selects the CTA-pair leader's slot, where TMA reports asynchronous completion. + +The remaining names describe the surrounding layouts; they are not additional +stages hidden from the diagram. ```python _kv_gather_tma = partial( @@ -709,19 +868,21 @@ not an assumed zero value from the gather, decides whether a finite KV row participates in attention. Masking must happen before online-softmax state is updated. -As in the upstream API, callers should still avoid NaNs in in-range KV rows -referenced beyond `topk_length`. The optimized data path does not promise to -sanitize that exceptional case. +Callers should avoid NaNs in in-range KV rows referenced beyond `topk_length`. +The sparse-prefill interface does not promise to sanitize that exceptional +case. -The pinned source separates these roles cleanly: the +The implementation source separates these roles cleanly: the [K producer is at lines 608--676](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L608-L676), the [V producer is at lines 679--729](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L679-L729), and [validity packing is at lines 841--865](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L841-L865). -## Why does QK use both SS and TS? +## Why is Q split between SMEM and TMEM? -The next source excerpt answers how the kernel keeps only part of Q in SMEM. The -QK dot product is split at $d_{sq}=d_{qk}-384$: +The gather path has turned irregular K rows into a regular SMEM tile. Q must now +meet that tile without occupying all of the aliased SMEM workspace. Using the +SS/TS terms defined with the residency map, the QK dot product is split at +$d_{sq}=d_{qk}-384$: ```python if d_sq > 0: @@ -756,9 +917,21 @@ coordinates. ## How does online softmax avoid needless O rescaling? -For a stream of score tiles, the usual online-softmax recurrence stores a row -origin $m$, denominator $\ell$, and unnormalized output $\widetilde O$. In base -2, when the next tile has scaled scores $r$, +QK has produced raw logits $L$; softmax must now turn each tile into $W$ while +preserving state from earlier selected tiles. Let $x$ be one raw QK dot product. +The kernel first places it in the base-2 exponent domain: + +$$ +r=x\cdot\text{semantic\_QK\_scale}\cdot\log_2(e). +$$ + +The TIRx specialization binds the multiplier named `sm_scale_div_log2` to +`(1 / sqrt(d_qk)) * log2(e)`. Despite that source name, $r$ is simply the +model-scaled score expressed in base-2 units so that the kernel can use `exp2`. + +For a stream of such score tiles, online softmax stores a base-2 row origin $m$, +denominator $\ell$, and unnormalized output $\widetilde O$. When the next tile +contains scores $r$, $$ m'=\max(m,\max r),\qquad @@ -770,14 +943,17 @@ $$ \widetilde O'=\alpha\widetilde O+\sum_j2^{r_j-m'}v_j. $$ -Conceptually, the implementation multiplies natural-unit logits by the model's -semantic QK scale and `log2(e)`, then uses `exp2`. In this fixed-scale port, the -compile-time `sm_scale_div_log2` is -`(1 / sqrt(d_qk)) * log2(e)`. This is the same softmax in a form that maps -directly to fast base-2 exponent instructions. - Rescaling the full 512-coordinate O tile whenever the row maximum increases -would be expensive. The head-128 kernel uses a lazy threshold: +would be expensive. Before reading the lazy-threshold excerpt, map its state back +to the recurrence: + +- `cur_pi_max` is the current tile's maximum in the base-2 exponent domain; +- `mi` is the retained numerical origin $m$; +- `real_mi` is the exact maximum retained for the reported `max_logits`; +- `li` is the running denominator $\ell$; and +- `attn_sink_log2` is the optional sink logit in the same base-2 domain. + +The head-128 kernel then makes one warp-uniform decision: ```python should_scale_o: T.bool = ( @@ -798,10 +974,9 @@ but the accumulated O does not need a rescale. Once the difference exceeds 6, it rebases and rescales both $\ell$ and, when it already exists, O. The warp-wide `any_sync` keeps the decision uniform for the participating rows. -`real_mi` is maintained separately as the exact maximum seen so far. Therefore -the optimization does not change `max_logits`; `mi` is the numerical origin for -the recurrence, while `real_mi` is the reported statistic. At the end, the two -64-token contributions to each logical row are combined, and the kernel emits +Because `real_mi` is maintained separately, the optimization does not change +`max_logits`. At the end, the two 64-token contributions to each logical row are +combined, and the kernel emits $$ \mathrm{lse}=m\ln 2+\ln\ell. @@ -817,7 +992,7 @@ output_scale: T.float32 = T.cuda.fdividef( but deliberately leaves the reported LSE untouched. All-invalid rows are special-cased to output zero with `max_logits=-inf` and `lse=+inf`, matching the -pinned reference. +executable reference. ## How can the stages overlap without racing? @@ -828,14 +1003,31 @@ V segment they need has become reusable. ```{figure} ../img/flashmla_pipeline_stages.png :width: 100% -:alt: Conceptual sparse-prefill stages and the dependencies that permit steady-state overlap - -In steady state, softmax($k-1$) may overlap QK($k$). The sole MMA issuer then -issues PV($k-1$) after QK($k$); once QK($k$) completes, softmax($k$) may overlap -that PV. Producer warpgroups gather the next safe K/V segments around this -serial issuer order. +:alt: Sparse-prefill pipeline fill, steady state, and drain, including the overlap among QK, softmax, and PV for adjacent tiles + +The fill iteration issues QK(0) without a previous PV, while the drain iteration +issues PV($N-1$) without a new QK before the final epilogue. In steady state, +softmax($k-1$) may overlap QK($k$). The sole MMA issuer then issues PV($k-1$) +after QK($k$); once QK($k$) completes, softmax($k$) may overlap that PV. +Producer warpgroups gather the next safe K/V segments around this serial issuer +order. ``` +At the coarsest level, four ownership handoffs repeat for each tile: + +1. WG1/WG2 publish gathered K/V segments, while warp 13 publishes validity; +2. WG3 completes QK, publishes $L$ to WG0, and returns consumed K segments; +3. WG0 masks $L$, updates online softmax, publishes $W$ to WG3, and releases the + raw-logit and validity storage; and +4. WG3 completes PV, returning V storage to WG2 and making O safe for WG0 to + rescale or finalize. + +An **mbarrier** is the hardware completion object behind these handoffs. It +tracks expected arrivals or TMA bytes and carries a phase, so a wait means that +the named production step has completed for the intended reuse of a slot. This +four-step view gives the causal chain; the exact table below splits K and V into +the finer parts needed for early reuse. + The kernel initializes its mbarriers in warp 0, performs a cluster sync, launches the Q prologue, allocates CTA-group TMEM, and then enters specialized loops. @@ -881,39 +1073,43 @@ is reusable. The two `bar_sv_*` edges do the analogous job for V. ```{figure} ../img/flashmla_pipeline.png :width: 100% -:alt: Sparse-prefill pipeline showing QK of the current tile and PV of the previous tile +:alt: Detailed sparse-prefill pipeline showing serial QK and PV issue, part-wise K and V reuse, the mask-slot ring, and the WG0 handoff The steady state interleaves QK($k$) and PV($k-1$) while other roles perform part-wise K/V gathers and softmax work. Barrier phases protect in-place storage reuse rather than selecting separate full-tile buffers. ``` -Two kinds of fences appear around these edges. `T.ptx.tcgen05.fence.*` orders -TMEM accesses relative to thread-visible work, while -`T.ptx.fence.proxy_async("shared::cta")` establishes cross-proxy ordering between -generic and asynchronous accesses to SMEM. +The memory model has one more distinction. Ordinary thread loads and stores see +SMEM through the **generic proxy**; TMA and tensor-core asynchronous accesses use +an **asynchronous proxy**. A barrier reports completion, but completion alone +does not establish the required visibility and ordering between those proxies. + +Two kinds of fences therefore appear around the barrier edges. +`T.ptx.tcgen05.fence.*` orders TMEM accesses relative to thread-visible work, +while `T.ptx.fence.proxy_async("shared::cta")` establishes cross-proxy ordering +between generic and asynchronous accesses to SMEM. Here the proxy fence is needed both when generic stores of $W$ or the epilogue tile precede tcgen05/TMA asynchronous reads, and after an asynchronous SMEM read completes before generic code overwrites aliased storage. -An mbarrier communicates completion and an ownership handoff; the proxy fence -orders memory effects across proxies. Neither is a substitute for the other. +Thus an mbarrier communicates completion and an ownership handoff, whereas the +proxy fence orders memory effects across proxies. Neither is a substitute for +the other. -## How do we compile and verify the entire path? +## How do we compile and verify the regular head-128 implementation? -The pinned module targets compute capability 10 and its TMA/tcgen05 forms require -an SM100-class GPU. Use B200, CUDA 12.9 or newer, and the official Apache TVM -0.26.0 package. The pinned kernel uses that release's TIRx API rather than the -spellings on a moving development checkout. +The regular head-128 specialization targets compute capability 10, and its +TMA/tcgen05 forms require an SM100-class GPU. Use B200, CUDA 12.9 or newer, and +the dependencies installed below. First install a CUDA-enabled PyTorch build that supports B200 using the [official PyTorch selector](https://pytorch.org/get-started/locally/). The companion repository imports PyTorch but does not declare it as a package dependency. -The following commands answer exactly which TVM release and kernel revision the -examples require: +Install TVM and the companion kernel repository as follows: ```bash python -m pip install "apache-tvm==0.26.0" cuda-bindings @@ -951,7 +1147,7 @@ row at a time, and checks output, maximum logits, and LSE with explicit tolerances. This is the right default verification path; compiling generated PTX alone cannot find a wrong head partition or a missing validity bit. -The repository CLI can run the full registered configuration: +The repository CLI can run the registered regular-head128 configuration: ```bash python -m tirx_kernels.test \ @@ -962,18 +1158,19 @@ python -m tirx_kernels.test \ Useful negative tests are just as important. Set `inject_invalid_indices=True` to cover negative and too-large row IDs, and `have_topk_length=True` to exercise the position predicate. Test an all-invalid row and confirm the documented -zero/-infinity/+infinity convention. Finally, call the unified dispatch entry -for head-64 and small-top-k shapes so that a successful regular-head128 run is -not mistaken for full API coverage. +zero/-infinity/+infinity convention. Finally, call the TIRx dispatch entry for +head-64 and small-top-k shapes so that a successful regular-head128 run is not +mistaken for coverage of every prefill specialization. Even that broader +dispatch check does not establish parity with the complete FlashMLA interface. -## Which five invariants define this path? +## Which invariants belong to the operator and the specialization? -1. **The cache invariant.** One `h_kv=1` latent KV row can serve 128 query heads - because key up-projection is absorbed into each query and value up-projection - is moved after core attention. The RoPE channel stays explicit, and the QK - scale remains the model's semantic scale. +1. **The cache invariant.** One `h_kv=1` latent KV row can serve multiple query + heads because key up-projection is absorbed into each query and value + up-projection is moved after core attention. The RoPE channel stays explicit, + and the QK scale remains the model's semantic scale. -2. **The sparse-contract invariant.** Selection happens before this kernel. +2. **The sparse-contract invariant.** Selection happens before this operator. `indices` supplies the rows; duplicates remain duplicates; causal legality is the caller's responsibility; and every `topk_length` lies in `[0, topk]`. Sink and all-invalid conventions must remain identical in optimized and @@ -994,17 +1191,19 @@ not mistaken for full API coverage. optimization preserves the reported-maximum semantics and the online LSE recurrence. -The first two invariants define operator semantics; the last three define this -specialization's schedule contract. Another dispatch may change tile sizes, -register budgets, ownership, or barrier topology, but it must replace those -contracts explicitly rather than silently changing the operator it computes. +The first two invariants define the sparse-prefill operator semantics. The last +three define the regular head-128 specialization's schedule contract. Another +specialization selected by the dispatch bridge may change tile sizes, register +budgets, ownership, or barrier topology, but it must preserve the operator +semantics while defining its own schedule contract explicitly. ## What should you test next? -The regular head-128 kernel is one point in a dispatch space. The pinned tree -also contains a 64-head phase-1 kernel and a 128-head `d_qk=512` small-top-k -kernel. Their different schedules are evidence that sparse attention should be -dispatched by tile economics, not forced through one universal template. +The regular head-128 specialization is one point in a dispatch space. The +TIRx dispatch tree also contains a head-64 phase-1 specialization and a head-128 +`d_qk=512` small-top-k specialization. Their different schedules are evidence +that sparse attention should be dispatched by tile economics, not forced +through one universal template. 1. **Reproduce weight absorption.** Add a causal mask to the runnable absorption proof. 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zhOz2+S$iKmIIhdV(dK4Pvk$>JJBE0mBA->lbh09N?flN0L;8LH05Sm`@J*NBW5wXw;) zVR7H#@Sh_?*Wgx*nmNSvt%9kpcdG-oDLI!pq$V8RUXf;23_$Lg4pPi*a(`-oBCWsT z4r+a2nA@Pc(6jmn%#K1VVlePv1$beYX#>*qqEBT1OsJ^;nW_$RxD8;iVl0m}i=cj; z0y8JQwQE3E!quWTBG3o%e=8eH!%MEoK!S@c+^O^b4lYG+8n68NS0e_vK-Ej=l0gT&lT11^ zmJekK)6{y;9NYJ^9l0doTY{mF;_P(S-^#{tsmgzU)O@<3!T9I3{caIpaIW?O8g(0^S-g8akreaATTr(&xUYF5PJ(WEGt?z- - + @@ -20,252 +20,133 @@ - - - - - - - - - - - - - - - - - - + - - + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + - + - - + + - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + - - + + + + + + + + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + - - - - - + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + @@ -3396,9 +2645,310 @@ z - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - + + + + + + + + + + + + - - + + - + + - - - - - - - - - - + + + + + + + + + + + + + + + + - - - - - - + + + + + + + + + + + + + + + + + + + + + - - + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + - - - - + + - - - - - - - - - - - - + + + + + + + + + + + + - - - - - - - - - - - + + + - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + - - - + + + + + + + + + + + + + + + + + + + + + + + + @@ -3960,19 +4081,19 @@ z - - - - - - - - + + + + + + + + - - - + + + @@ -3980,433 +4101,389 @@ z - - - - - - - - + + + + + + + + - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - + + + + + + + + + + + + - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - + + + + + + + + + + + + - - - - - - - + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + - - - - - - - + + + + + + + + + + + + + + + - - - + @@ -4420,71 +4497,11 @@ z - - + + + + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + - - - + + + + + + + + + + + + + + + + + @@ -4647,57 +4961,54 @@ z - - - - - - - - - - + + + + + + + + - - - - - - - - - - - - + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + - - - + + + - + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + - - + - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - + + + - - + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - + + diff --git a/img/flashmla_sparse_story_zh.svg b/img/flashmla_sparse_story_zh.svg index bab3b367..39e34ab3 100644 --- a/img/flashmla_sparse_story_zh.svg +++ b/img/flashmla_sparse_story_zh.svg @@ -261,8 +261,8 @@ z " clip-path="url(#p897ed09e89)" style="fill: #64748b; stroke: #64748b; stroke-width: 1.25; stroke-linecap: round"/> - - + + - - - - - - - - + + + + + + @@ -953,25 +960,6 @@ C 2771 3373 2458 3565 2003 3565 C 1107 3565 333 2893 333 1734 C 333 582 1037 -83 1958 -83 z -" transform="scale(0.015625)"/> - None: 1.30, 4.45, 6.45, - tr(lang, "1 · MHA cache", "1 · MHA cache"), - tr(lang, "materialize K and V for every head", "为每个 head 物化 K 与 V"), + tr(lang, "1 · Ordinary MHA cache", "1 · 普通 MHA cache"), + tr( + lang, + "store a key and a value for every head", + "为每个 head 保存一份 key 和 value", + ), COLORS["cta0_dark"], ) _panel( @@ -103,11 +107,11 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 1.30, 5.05, 6.45, - tr(lang, "2 · MLA cache", "2 · MLA cache"), + tr(lang, "2 · MLA shared cache", "2 · MLA 共享 cache"), tr( lang, - "store one latent source per token", - "每个 token 只保存一份 latent source", + "compress once and store one shared state", + "压缩一次,只保存一份共享状态", ), "#7c3aed", ) @@ -117,11 +121,11 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 1.30, 7.10, 6.45, - tr(lang, "3 · Absorbed execution", "3 · Absorbed execution"), + tr(lang, "3 · Use the shared cache", "3 · 使用共享 cache"), tr( lang, - "head-specific work moves around the core", - "各 head 的特定计算移到 core 两侧", + "head-specific work happens before and after attention", + "各 head 的特定计算放在 attention 前后", ), COLORS["cta1_dark"], ) @@ -136,10 +140,22 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: weight="bold", ) row_entries = ( - ("head 0", "K_0", "V_0"), - ("head 1", "K_1", "V_1"), + ( + "head 0", + tr(lang, "cached\nkey", "缓存\nkey"), + tr(lang, "cached\nvalue", "缓存\nvalue"), + ), + ( + "head 1", + tr(lang, "cached\nkey", "缓存\nkey"), + tr(lang, "cached\nvalue", "缓存\nvalue"), + ), ("...", "...", "..."), - ("head 127", "K_127", "V_127"), + ( + "head 127", + tr(lang, "cached\nkey", "缓存\nkey"), + tr(lang, "cached\nvalue", "缓存\nvalue"), + ), ) for idx, (label, k_label, v_label) in enumerate(row_entries): y = 5.70 - idx * 0.83 @@ -152,7 +168,7 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: k_label, ha="center", va="center", - fontsize=8.0, + fontsize=7.4, weight="bold", ) ax.text( @@ -161,7 +177,7 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: v_label, ha="center", va="center", - fontsize=8.0, + fontsize=7.4, weight="bold", ) rounded_box( @@ -172,8 +188,8 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 0.88, tr( lang, - "cache stores a separate K/V slice\nfor every head", - "cache 为每个 head 保存\n独立的 K/V slice", + "cache stores a separate key/value slice\nfor every head", + "cache 为每个 head 保存\n独立的 key/value slice", ), COLORS["note"], fontsize=8.5, @@ -181,38 +197,67 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: edgecolor="#ca8a04", ) - # MLA: down-project content once and store it with one shared RoPE key. - rounded_box(ax, 5.55, 5.83, 1.20, 0.72, "h_s", COLORS["neutral"], fontsize=9.2) - rounded_box(ax, 7.12, 5.83, 1.35, 0.72, "W_DKV", COLORS["projection"], fontsize=8.8) + # MLA: compress the token's content once and store it with one shared + # positional channel. Matrix names are intentionally deferred to the + # derivation that follows this introductory figure. + rounded_box( + ax, + 5.45, + 5.79, + 1.45, + 0.80, + tr(lang, "token\nrepresentation", "token\n表示"), + COLORS["neutral"], + fontsize=8.1, + ) + rounded_box( + ax, + 7.12, + 5.79, + 1.42, + 0.80, + tr(lang, "compress\ncontent once", "只压缩一次\ncontent"), + COLORS["projection"], + fontsize=8.0, + ) rounded_box( ax, 8.78, 5.69, 1.05, 1.00, - "c_KV\nlatent\n512", + tr(lang, "shared\ncontent state\n512 numbers", "共享\ncontent 状态\n512 个数"), COLORS["smem"], - fontsize=8.0, + fontsize=7.4, ) - arrow(ax, (6.75, 6.19), (7.12, 6.19)) - arrow(ax, (8.47, 6.19), (8.78, 6.19)) + arrow(ax, (6.90, 6.19), (7.12, 6.19)) + arrow(ax, (8.54, 6.19), (8.78, 6.19)) rounded_box( ax, 5.55, 4.47, 2.05, 0.78, - tr(lang, "shared RoPE key", "共享 RoPE key"), + tr(lang, "position information", "位置信息"), "#bfdbfe", fontsize=8.4, ) - rounded_box(ax, 8.02, 4.47, 1.81, 0.78, "k_R\nRoPE 64", "#bfdbfe", fontsize=8.4) + rounded_box( + ax, + 8.02, + 4.47, + 1.81, + 0.78, + tr(lang, "shared position part\n64 numbers", "共享位置信息\n64 个数"), + "#bfdbfe", + fontsize=7.8, + ) arrow(ax, (7.60, 4.86), (8.02, 4.86)) ax.text( 7.68, 3.94, - tr(lang, "stored once per token", "每个 token 只存一次"), + tr(lang, "one cache entry per token", "每个 token 只有一条 cache entry"), ha="center", va="center", fontsize=9.2, @@ -222,10 +267,22 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: plain_rect(ax, 5.82, 2.90, 2.76, 0.76, COLORS["gmem"]) plain_rect(ax, 8.58, 2.90, 1.20, 0.76, "#bfdbfe") ax.text( - 7.20, 3.28, "c_KV · 512", ha="center", va="center", fontsize=9.0, weight="bold" + 7.20, + 3.28, + tr(lang, "shared compressed\ncontent · 512", "共享压缩 content\n· 512"), + ha="center", + va="center", + fontsize=7.8, + weight="bold", ) ax.text( - 9.18, 3.28, "k_R · 64", ha="center", va="center", fontsize=8.4, weight="bold" + 9.18, + 3.28, + tr(lang, "position\npart · 64", "位置信息\n· 64"), + ha="center", + va="center", + fontsize=7.5, + weight="bold", ) rounded_box( ax, @@ -235,8 +292,8 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 0.72, tr( lang, - "one shared entry · not 128 expanded pairs", - "一份 shared entry · 不是 128 份展开 pair", + "one shared entry · not 128 key/value pairs", + "一份共享 cache entry,而不是 128 组 key/value", ), COLORS["note"], fontsize=8.2, @@ -245,16 +302,20 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: ) arrow(ax, (9.78, 3.28), (11.15, 4.09), color="#7c3aed", linewidth=1.6, rad=-0.05) - # Absorbed execution: q_C alone crosses W_UK; q_R remains explicit. + # Head-specific query/output work surrounds attention over the shared cache. rounded_box( ax, 10.92, 5.89, 1.46, 0.70, - "q_C,i\nper head", + tr( + lang, + "content part of query\nfor one head", + "某个 head query 的\ncontent 部分", + ), COLORS["neutral"], - fontsize=8.1, + fontsize=7.8, ) rounded_box( ax, @@ -262,9 +323,9 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 5.89, 1.66, 0.70, - "(W_UK,i)^T\ncontent only", + tr(lang, "head-specific\nquery transform", "该 head 的\nquery 变换"), COLORS["projection"], - fontsize=7.8, + fontsize=7.7, ) rounded_box( ax, @@ -272,9 +333,9 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 4.93, 1.46, 0.70, - "q_R,i\nRoPE 64", + tr(lang, "position part of query\nfor that head", "该 head query 的\n位置信息"), "#bfdbfe", - fontsize=8.1, + fontsize=7.7, ) rounded_box( ax, @@ -282,9 +343,13 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 5.34, 2.28, 1.02, - "Q_i = [q_abs,i ; q_R,i]\n512 + 64", + tr( + lang, + "query used by attention\ncontent view + position", + "attention 使用的 query\ncontent 视图 + 位置信息", + ), COLORS["tmem"], - fontsize=8.1, + fontsize=7.8, ) arrow(ax, (12.38, 6.24), (12.78, 6.24)) arrow(ax, (14.44, 6.24), (14.88, 6.03)) @@ -292,7 +357,7 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: ax, (12.38, 5.28), (14.88, 5.62), - label=tr(lang, "bypass W_UK", "绕过 W_UK"), + label=tr(lang, "position stays separate", "位置信息保持独立"), color=COLORS["cta0_dark"], rad=-0.05, label_offset=(0.0, -0.14), @@ -304,9 +369,13 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 3.63, 2.56, 0.92, - "shared K = [c_KV ; k_R]\nshared V = c_KV", + tr( + lang, + "one shared cache entry\nkey side: content + position\nvalue side: content", + "一条共享 cache entry\nkey 侧:压缩 content + 位置信息\nvalue 侧:压缩 content", + ), COLORS["gmem"], - fontsize=8.0, + fontsize=7.6, ) rounded_box( ax, @@ -314,7 +383,7 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 3.48, 2.12, 1.10, - tr(lang, "shared-cache\nattention core", "shared-cache\nattention core"), + tr(lang, "attention over\nthe shared cache", "在共享 cache 上\n计算 attention"), COLORS["mma"], fontsize=8.7, ) @@ -326,9 +395,9 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 2.22, 1.60, 0.72, - "latent out_i\n512", + tr(lang, "shared-space result\n512 numbers", "共享空间结果\n512 个数"), COLORS["tmem"], - fontsize=8.0, + fontsize=7.6, ) rounded_box( ax, @@ -338,8 +407,8 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 0.72, tr( lang, - "per-head output path\nW_UV,i / W_O", - "per-head output 路径\nW_UV,i / W_O", + "head-specific\noutput transform", + "该 head 的\noutput 变换", ), COLORS["projection"], fontsize=7.6, @@ -351,8 +420,8 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 1.74, tr( lang, - "repeat the query/output paths for i=0…127\n→ 128 distinct head outputs", - "query/output 路径对 i=0…127 各自执行\n→ 128 份不同的 head output", + "repeat the query/output work for all 128 heads\n→ 128 distinct head outputs", + "对全部 128 个 heads 重复 query/output 处理\n→ 128 份不同的 head output", ), ha="center", va="center", @@ -369,8 +438,8 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: 0.66, tr( lang, - "Only [c_KV ; k_R] is cached. Per-head K/V need not be materialized; head-specific projections survive by reassociation around attention.", - "Cache 中只有 [c_KV ; k_R]。无需物化 per-head K/V;通过在 attention 两侧重新结合运算,仍保留各 head 的特定 projection。", + "MLA caches one shared compressed state per token. Head-specific transformations happen around attention, so the cache does not store 128 key/value pairs.", + "MLA 为每个 token 只缓存一份共享压缩状态。各 head 的特定变换放在 attention 两侧,因此 cache 无需保存 128 组 key/value。", ), COLORS["note"], fontsize=8.4, diff --git a/img/scripts/gen_flashmla_cta_ownership.py b/img/scripts/gen_flashmla_cta_ownership.py index e5f6679e..db3e9b81 100644 --- a/img/scripts/gen_flashmla_cta_ownership.py +++ b/img/scripts/gen_flashmla_cta_ownership.py @@ -285,12 +285,30 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: ) arrow(ax, (6.15, 3.1), (6.70, 3.1), label="L") arrow(ax, (9.30, 3.1), (9.85, 3.1), label="W") - # Ownership-to-logical-tile guide arrows. - arrow(ax, (2.72, 5.76), (2.72, 4.68), color=COLORS["cta0_dark"], linewidth=1.0) - arrow( - ax, (7.77, 5.76), (5.4, 4.7), color=COLORS["cta1_dark"], linewidth=1.0, rad=0.08 + # Route ownership guides around the logical-matrix titles, then terminate + # on the tile boundaries. A direct downward arrow would cross the long + # QK/PV headings and make the target ambiguous at the inline HTML width. + guide_specs = ( + ((2.72, 5.76), 0.42, (0.85, 4.34), COLORS["cta0_dark"]), + ((7.77, 5.76), 6.55, (6.15, 4.34), COLORS["cta1_dark"]), + ((12.82, 5.76), 15.58, (15.15, 4.34), COLORS["cta1_dark"]), ) - arrow(ax, (12.82, 5.76), (12.82, 4.68), color=COLORS["cta1_dark"], linewidth=1.0) + for start, corridor_x, target, color in guide_specs: + ax.plot( + [start[0], corridor_x, corridor_x], + [start[1], start[1], 4.53], + color=color, + linewidth=1.0, + zorder=1, + ) + arrow( + ax, + (corridor_x, 4.53), + target, + color=color, + linewidth=1.0, + zorder=2, + ) rounded_box( ax, diff --git a/img/scripts/gen_flashmla_dataflow.py b/img/scripts/gen_flashmla_dataflow.py index 2650a6db..1534affa 100644 --- a/img/scripts/gen_flashmla_dataflow.py +++ b/img/scripts/gen_flashmla_dataflow.py @@ -10,25 +10,112 @@ from flashmla_diagram_common import ( COLORS, - arrow, + arrow as _arrow, configure_style, plain_rect, - rounded_box, + rounded_box as _rounded_box, save_figure, tr, ) +def box(ax, x, y, w, h, text, color, *, fontsize=11.0, **kwargs): + """Draw a node sized for the book's roughly 790 px content column.""" + + return _rounded_box( + ax, + x, + y, + w, + h, + text, + color, + fontsize=fontsize, + **kwargs, + ) + + +def edge( + ax, + start, + end, + *, + label=None, + label_offset=(0.0, 0.14), + fontsize=10.0, + **kwargs, +): + """Draw an edge and place its label in surrounding whitespace.""" + + line_color = kwargs.get("color") or COLORS["line"] + zorder = kwargs.get("zorder", 2) + patch = _arrow(ax, start, end, label=None, **kwargs) + if label: + ax.text( + (start[0] + end[0]) / 2 + label_offset[0], + (start[1] + end[1]) / 2 + label_offset[1], + label, + ha="center", + va="center", + fontsize=fontsize, + color=line_color, + bbox=dict( + boxstyle="round,pad=0.10", + facecolor="white", + edgecolor="none", + alpha=0.94, + ), + zorder=zorder + 1, + ) + return patch + + +def panel(ax, x, y, w, h, title, subtitle): + """Draw one readable layer of the single data-flow figure.""" + + patch = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.05,rounding_size=0.06", + linewidth=1.15, + linestyle="--", + edgecolor="#c4b5fd", + facecolor="#ffffff", + zorder=0, + ) + ax.add_patch(patch) + ax.text( + x + 0.20, + y + h - 0.24, + title, + ha="left", + va="center", + fontsize=13.0, + weight="bold", + color="#6d28d9", + ) + ax.text( + x + w - 0.20, + y + h - 0.24, + subtitle, + ha="right", + va="center", + fontsize=10.0, + color=COLORS["muted"], + ) + + def draw(lang: str, output: str, font_path: str | None = None) -> None: configure_style(lang, font_path) - fig, ax = plt.subplots(figsize=(19.0, 9.4)) - ax.set_xlim(0, 19) - ax.set_ylim(0, 9.4) + fig, ax = plt.subplots(figsize=(12.0, 13.0)) + ax.set_xlim(0, 14) + ax.set_ylim(0, 13) ax.axis("off") ax.text( - 9.5, - 9.08, + 7, + 12.62, tr( lang, "Sparse FlashMLA Head128 Regular: Data Residency", @@ -36,439 +123,378 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: ), ha="center", va="center", - fontsize=18, + fontsize=19, weight="bold", ) ax.text( - 9.5, - 8.68, + 7, + 12.25, tr( lang, - "one CTA's view; cta_group::2 combines the pair's operand halves", - "单个 CTA 的视图;cta_group::2 会组合 CTA pair 的 operand halves", + "one CTA's logical view; cta_group::2 combines the pair's operand halves", + "单个 CTA 的 logical view;cta_group::2 组合 CTA pair 的 operand halves", ), ha="center", va="center", - fontsize=9.5, + fontsize=11.0, color=COLORS["muted"], ) - # Q path: one prefix remains in SMEM while the fixed 384-column suffix moves to TMEM. - rounded_box(ax, 0.35, 6.63, 1.65, 0.86, "Q\nGMEM", COLORS["gmem"], fontsize=9.5) - rounded_box( + panel( ax, - 2.55, - 6.43, - 2.35, - 1.25, + 0.25, + 8.20, + 13.50, + 3.55, + tr(lang, "1 · QK and online softmax", "1 · QK 与 online softmax"), + tr(lang, "BF16 operands → FP32 L → BF16 W", "BF16 operands → FP32 L → BF16 W"), + ) + + box(ax, 0.48, 9.20, 0.78, 0.92, "Q\nGMEM", COLORS["gmem"], fontsize=12.0) + box( + ax, + 1.52, + 9.08, + 1.55, + 1.16, tr( lang, - "q_full · SMEM\n64 × d_qk per CTA", - "q_full · SMEM\n每个 CTA 为 64 × d_qk", + "q_full\nSMEM · TMA\n64×d_qk / CTA", + "q_full\nSMEM · TMA\n64×d_qk / CTA", ), COLORS["smem"], - fontsize=9, + fontsize=10.5, ) - rounded_box( + box( ax, - 5.63, - 7.02, - 2.18, - 0.78, - tr( - lang, - "Q prefix · SMEM\nd_sq = d_qk − 384", - "Q prefix · SMEM\nd_sq = d_qk − 384", - ), + 3.35, + 9.86, + 1.90, + 0.80, + "Q prefix\nSMEM\nd_sq columns", COLORS["smem"], - fontsize=8.5, + fontsize=10.2, ) - rounded_box( + box( ax, - 5.63, - 5.94, - 2.18, - 0.78, - tr(lang, "q_tmem · TMEM\nfixed suffix 384", "q_tmem · TMEM\n固定 suffix 384"), + 3.35, + 8.66, + 1.90, + 0.80, + tr(lang, "Q suffix · TMEM\n384 columns", "Q suffix · TMEM\n384 列"), COLORS["tmem"], - fontsize=8.5, + fontsize=10.2, ) - rounded_box( + box( ax, - 8.48, - 6.34, - 1.92, - 1.18, - tr(lang, "QK MMA\nSS prefix + TS suffix", "QK MMA\nSS prefix + TS suffix"), + 5.57, + 9.01, + 1.42, + 1.30, + "QK MMA\nSS prefix\n+ TS suffix", COLORS["mma"], - fontsize=9, + fontsize=10.5, ) - arrow(ax, (2.0, 7.06), (2.55, 7.06), label="TMA") - arrow(ax, (4.9, 7.2), (5.63, 7.4), label=tr(lang, "stays", "保留"), rad=-0.05) - arrow(ax, (4.9, 6.86), (5.63, 6.33), label="SMEM→TMEM", rad=0.08) - arrow(ax, (7.81, 7.4), (8.48, 7.18)) - arrow(ax, (7.81, 6.33), (8.48, 6.68)) - - # Sparse gather path and validity mask. - rounded_box(ax, 0.35, 4.66, 1.65, 0.82, "indices\nGMEM", COLORS["gmem"], fontsize=9) - rounded_box( + box( ax, - 0.35, - 3.34, - 1.65, - 0.92, - "KV cache\nGMEM\n[s_kv, 1, d_qk]", - COLORS["gmem"], - fontsize=8.5, + 7.37, + 9.01, + 1.42, + 1.30, + "L (tmem_p)\nFP32 · TMEM\n64×128", + COLORS["tmem"], + fontsize=9.5, ) - rounded_box( + box( ax, - 2.65, - 4.56, - 2.5, - 0.92, + 9.17, + 8.93, + 1.90, + 1.46, tr( lang, - "WG1 gathered K · SMEM\n64 slots × d_qk per CTA", - "WG1 gather K · SMEM\n每个 CTA:64 slots × d_qk", + "WG0 softmax\nmask · max\nexp · row sum", + "WG0 softmax\nmask · max\nexp · row sum", ), - COLORS["smem"], - fontsize=8.3, + COLORS["softmax"], + fontsize=10.5, ) - rounded_box( + box( ax, - 2.65, - 3.10, - 2.5, - 0.98, + 11.42, + 9.83, + 2.05, + 0.78, tr( lang, - "WG2 gathered V · SMEM\n128 slots × 256 features per CTA", - "WG2 gather V · SMEM\n每个 CTA:128 slots × 256 features", + "max_logits / lse\nGMEM\nsink excluded", + "max_logits / lse\nGMEM\n不含 sink", ), - COLORS["smem"], - fontsize=8.1, + COLORS["gmem"], + fontsize=9.5, + ) + box( + ax, + 11.42, + 8.69, + 2.05, + 0.78, + "mi / real_mi / li\nWG0 registers", + COLORS["neutral"], + fontsize=10.0, ) - rounded_box( + + edge(ax, (1.26, 9.66), (1.52, 9.66)) + edge(ax, (3.07, 9.82), (3.35, 10.26)) + edge(ax, (3.07, 9.48), (3.35, 9.06)) + edge(ax, (5.25, 10.26), (5.57, 9.98)) + edge(ax, (5.25, 9.06), (5.57, 9.34)) + edge(ax, (6.99, 9.66), (7.37, 9.66)) + edge(ax, (8.79, 9.66), (9.17, 9.66)) + edge(ax, (11.07, 9.86), (11.42, 10.22)) + edge(ax, (11.07, 9.40), (11.42, 9.08)) + + panel( ax, - 5.72, - 4.45, - 1.82, - 0.93, + 0.25, + 3.20, + 13.50, + 4.70, tr( lang, - "is_k_valid · SMEM\n2 slots × 16 bytes", - "is_k_valid · SMEM\n2 个 slot × 16 bytes", + "2 · Sparse gather, PV, and epilogue", + "2 · Sparse gather、PV 与 epilogue", + ), + tr( + lang, + "indices + KV feed both gather4 paths; O~ / (li + sink)", + "indices + KV 同时送入两条 gather4;O~ / (li + sink)", ), - COLORS["barrier"], - fontsize=8.1, - ) - arrow(ax, (2.0, 5.08), (2.65, 5.08), label=tr(lang, "selected slots", "选中 slots")) - arrow( - ax, - (2.0, 4.76), - (2.65, 3.83), - color=COLORS["line"], - rad=-0.05, - ) - # Route mask metadata above the K box so the dependency does not cut through its label. - ax.plot( - [2.0, 2.25, 5.28], [5.32, 5.76, 5.76], color=COLORS["line"], lw=1.25, zorder=2 - ) - arrow(ax, (5.28, 5.76), (6.22, 5.38), color=COLORS["line"], rad=0.05) - ax.text( - 3.82, - 5.86, - tr(lang, "bounds + topk_length", "边界 + topk_length"), - ha="center", - va="center", - fontsize=7.3, - color=COLORS["line"], - ) - arrow(ax, (2.0, 3.72), (2.65, 4.83), label="gather4", rad=-0.12) - arrow(ax, (2.0, 3.72), (2.65, 3.59), label="gather4", rad=0.05) - # K takes a low elbow under q_tmem, then enters QK from below. - ax.plot( - [5.15, 5.5, 7.82], [5.32, 5.61, 5.61], color=COLORS["line"], lw=1.25, zorder=2 ) - arrow(ax, (7.82, 5.61), (8.82, 6.34), label="K", color=COLORS["line"], rad=-0.05) - # Logits, online softmax, weights, and public statistics. - rounded_box( + box(ax, 0.52, 6.00, 1.05, 0.88, "indices\nGMEM", COLORS["gmem"], fontsize=11.5) + box( ax, - 10.92, - 6.36, - 1.86, + 0.52, + 4.00, 1.15, - "tmem_p · TMEM\nL logits\n64 × 128 view", - COLORS["tmem"], - fontsize=8.5, + 1.05, + "KV cache\nGMEM\n[s_kv,1,\nd_qk]", + COLORS["gmem"], + fontsize=8.8, ) - rounded_box( + box( ax, - 13.25, - 6.10, - 1.94, - 1.48, + 2.15, + 5.90, + 2.05, + 1.08, tr( lang, - "WG0 online softmax\nmask · max · exp · sum", - "WG0 online softmax\nmask · max · exp · sum", + "WG1 K · SMEM\ngather4\n64×d_qk / CTA", + "WG1 K · SMEM\ngather4\n64×d_qk / CTA", ), - COLORS["softmax"], - fontsize=8.7, - ) - rounded_box( - ax, - 13.18, - 4.42, - 2.08, - 0.95, - "s_smem_gemm · SMEM\nW weights · 64 × 128", COLORS["smem"], - fontsize=8.3, + fontsize=10.2, ) - rounded_box( + box( ax, - 16.0, - 6.29, + 2.15, + 4.00, 2.05, - 1.08, + 1.05, tr( lang, - "max_logits / lse\nGMEM · sink excluded", - "max_logits / lse\nGMEM · 不含 sink", + "WG2 V · SMEM\ngather4\n128×256 / CTA", + "WG2 V · SMEM\ngather4\n128×256 / CTA", ), - COLORS["gmem"], - fontsize=8.2, + COLORS["smem"], + fontsize=10.2, ) - rounded_box( + box( ax, - 15.62, - 5.12, - 2.35, - 0.75, + 4.55, + 5.90, + 1.85, + 1.08, tr( lang, - "mi · real_mi · li\nWG0 registers", - "mi · real_mi · li\nWG0 registers", + "validity · SMEM\nbounds + length\n2 × 16 bytes", + "validity · SMEM\nbounds + length\n2 × 16 bytes", ), - COLORS["neutral"], - fontsize=8.0, - ) - rounded_box( - ax, - 16.10, - 4.22, - 1.87, - 0.64, - tr(lang, "optional attn_sink\nGMEM", "可选 attn_sink\nGMEM"), - COLORS["gmem"], - fontsize=7.7, - ) - arrow(ax, (10.4, 6.93), (10.92, 6.93)) - arrow(ax, (12.78, 6.93), (13.25, 6.93)) - arrow( - ax, - (7.54, 4.92), - (13.25, 6.42), - label=tr(lang, "mask ready", "mask 就绪"), - rad=-0.10, - ) - arrow( - ax, (14.22, 6.10), (14.22, 5.37), label=tr(lang, "cast/store W", "转换/写入 W") + COLORS["barrier"], + fontsize=10.0, ) - arrow(ax, (15.19, 6.93), (16.0, 6.93)) - arrow(ax, (15.10, 6.36), (15.78, 5.76), color=COLORS["line"], rad=0.05) - - # PV path and epilogue. - rounded_box( + box( ax, - 8.52, - 2.96, - 1.78, + 6.55, + 5.90, + 1.95, 1.08, - tr(lang, "PV MMA\nW × V", "PV MMA\nW × V"), - COLORS["mma"], - fontsize=9.2, + "W · BF16\ns_smem_gemm\n64 × 128", + COLORS["smem"], + fontsize=9.4, ) - rounded_box( + box(ax, 6.82, 4.00, 1.40, 1.05, "PV MMA\nW × V", COLORS["mma"], fontsize=11.4) + box( ax, - 10.92, - 2.92, - 1.86, - 1.14, - "o_tmem · TMEM\nO accumulator\n64 × 512 view", + 8.62, + 4.00, + 1.42, + 1.05, + "O~ · FP32\nTMEM\n64×512", COLORS["tmem"], - fontsize=8.4, + fontsize=9.8, ) - rounded_box( + box( ax, - 13.25, - 2.92, - 1.94, - 1.14, + 10.30, + 3.90, + 1.75, + 1.25, tr( lang, - "WG0 epilogue\nO~ / (li + sink term)\n→ bf16", - "WG0 epilogue\nO~ /(li + sink 项)\n→ bf16", + "WG0 epilogue\nO~/(li + sink)\n→ BF16", + "WG0 epilogue\nO~/(li + sink)\n→ BF16", ), COLORS["softmax"], - fontsize=7.7, + fontsize=9.5, ) - rounded_box( + box( ax, - 15.65, - 2.92, + 8.85, + 5.95, 1.55, - 1.14, - "o_smem\nSMEM\n64 × 512", - COLORS["smem"], - fontsize=8.3, - ) - rounded_box(ax, 17.64, 3.04, 1.05, 0.9, "out\nGMEM", COLORS["gmem"], fontsize=8.7) - arrow(ax, (5.15, 3.59), (8.52, 3.50), label="V") - arrow(ax, (13.18, 4.86), (10.0, 4.04), label="W", rad=0.10) - arrow(ax, (10.3, 3.5), (10.92, 3.5)) - arrow(ax, (12.78, 3.5), (13.25, 3.5), label="O~") - arrow( - ax, - (16.05, 5.12), - (14.84, 4.06), - label="li", - color=COLORS["line"], - rad=0.05, + 0.95, + tr( + lang, + "attn_sink\nGMEM", + "attn_sink\nGMEM", + ), + COLORS["gmem"], + fontsize=9.5, ) - arrow( + box( ax, - (16.10, 4.54), - (15.19, 3.75), - label=tr(lang, "denominator only", "仅进入分母"), - color=COLORS["line"], - rad=0.03, - label_offset=(0.30, -0.04), - ) - arrow(ax, (15.19, 3.5), (15.65, 3.5), label="TMEM→SMEM") - arrow(ax, (17.2, 3.5), (17.64, 3.5), label="TMA") - - # Exact lifetime aliasing from the pinned SharedMemoryPlan. - outer = FancyBboxPatch( - (0.42, 0.22), - 18.16, - 1.82, - boxstyle="round,pad=0.05,rounding_size=0.06", - linewidth=1.2, - linestyle="--", - edgecolor="#7c3aed", - facecolor="#faf5ff", - zorder=1, - ) - ax.add_patch(outer) - ax.text( - 0.72, - 1.80, + 12.34, + 3.96, + 1.20, + 1.13, tr( lang, - "Per-CTA SMEM union: the same address range is reused by lifetime", - "每个 CTA 的 SMEM union:同一地址范围按生命周期复用", + "o_smem\nBF16\n64×512\nTMA → out", + "o_smem\nBF16\n64×512\nTMA → out", ), - ha="left", - va="center", - fontsize=10, - weight="bold", - color="#6d28d9", - zorder=3, + COLORS["smem"], + fontsize=9.2, ) - rounded_box( + + # Both gather producers consume both the sparse row coordinates and KV source. + # The junction makes that all-to-all relationship explicit without four labels. + shared = (1.82, 5.48) + edge(ax, (1.57, 6.25), shared) + edge(ax, (1.67, 4.78), shared) + edge(ax, shared, (2.15, 6.25)) + edge(ax, shared, (2.15, 4.78)) + ax.plot(*shared, marker="o", markersize=4.0, color=COLORS["line"], zorder=4) + edge(ax, (4.20, 6.44), (4.55, 6.44)) + + # K enters the QK panel; validity and W cross the layer boundary separately. + ax.plot([4.20, 4.38, 6.28], [6.56, 8.02, 8.02], color=COLORS["line"], lw=1.25) + edge(ax, (6.28, 8.02), (6.28, 9.01)) + ax.plot([6.40, 6.40, 10.10], [6.62, 7.98, 7.98], color=COLORS["line"], lw=1.25) + edge(ax, (10.10, 7.98), (10.10, 8.93)) + ax.plot([9.60, 9.60, 7.52], [8.93, 8.08, 8.08], color=COLORS["line"], lw=1.25) + edge(ax, (7.52, 8.08), (7.52, 6.98)) + edge(ax, (4.20, 4.52), (6.82, 4.52)) + edge(ax, (7.52, 5.90), (7.52, 5.05)) + edge(ax, (8.22, 4.52), (8.62, 4.52)) + edge(ax, (10.04, 4.52), (10.30, 4.52)) + edge(ax, (10.40, 6.28), (10.88, 5.15)) + edge(ax, (12.05, 4.52), (12.34, 4.52)) + + panel( ax, - 0.72, - 0.52, - 3.0, - 0.88, + 0.25, + 0.35, + 13.50, + 2.45, tr( lang, - "prologue\nq_full = prefix | suffix384", - "prologue\nq_full = prefix | suffix384", + "3 · Per-CTA SMEM lifetime aliasing", + "3 · 每个 CTA 的 SMEM 生命周期复用", + ), + tr( + lang, + "one in-place K/V region; o_smem later reuses its base", + "单份原位 K/V 区域;随后 o_smem 复用其基址", ), - COLORS["smem"], - fontsize=8.3, ) - arrow( - ax, (3.72, 0.96), (4.36, 0.96), label=tr(lang, "reuse", "复用"), color="#7c3aed" + box( + ax, + 0.55, + 0.77, + 2.10, + 0.92, + "q_full · SMEM\nprefix | suffix384", + COLORS["smem"], + fontsize=10.2, ) - plain_rect(ax, 4.42, 0.52, 1.65, 0.88, COLORS["smem"], edgecolor=COLORS["ink"]) - plain_rect(ax, 6.07, 0.52, 2.0, 0.88, "#ddd6fe", edgecolor=COLORS["ink"]) - plain_rect(ax, 8.07, 0.52, 2.0, 0.88, "#c4b5fd", edgecolor=COLORS["ink"]) + edge(ax, (2.65, 1.23), (3.08, 1.23)) + + plain_rect(ax, 3.08, 0.77, 1.45, 0.92, COLORS["smem"], edgecolor=COLORS["ink"]) + plain_rect(ax, 4.53, 0.77, 1.75, 0.92, "#ddd6fe", edgecolor=COLORS["ink"]) + plain_rect(ax, 6.28, 0.77, 1.75, 0.92, "#c4b5fd", edgecolor=COLORS["ink"]) ax.text( - 5.24, - 0.96, + 3.80, + 1.23, tr(lang, "Q prefix\nlive", "Q prefix\n存活"), ha="center", va="center", - fontsize=8, + fontsize=11.0, weight="bold", - zorder=4, ) ax.text( - 7.07, - 0.96, + 5.40, + 1.23, tr(lang, "one V\nworkspace", "单份 V\nworkspace"), ha="center", va="center", - fontsize=8, + fontsize=11.0, weight="bold", - zorder=4, ) ax.text( - 9.07, - 0.96, + 7.15, + 1.23, tr(lang, "one K\nworkspace", "单份 K\nworkspace"), ha="center", va="center", - fontsize=8, + fontsize=11.0, weight="bold", - zorder=4, ) - ax.text( - 7.24, - 0.32, - tr( - lang, - "steady-state views are adjacent, not duplicate stages", - "稳态 views 相邻,并非复制的 stages", - ), - ha="center", - fontsize=7.3, - color=COLORS["muted"], - ) - arrow( - ax, - (10.07, 0.96), - (10.75, 0.96), - label=tr(lang, "reuse", "复用"), - color="#7c3aed", - ) - rounded_box( + + edge(ax, (8.03, 1.23), (8.46, 1.23)) + box( ax, - 10.82, - 0.52, - 2.72, - 0.88, - tr(lang, "epilogue\no_smem · 64 × 512", "epilogue\no_smem · 64 × 512"), + 8.46, + 0.77, + 1.95, + 0.92, + "o_smem · BF16\n64×512", COLORS["smem"], - fontsize=8.3, + fontsize=10.2, ) ax.text( - 14.0, - 0.96, + 10.82, + 1.23, tr( lang, - "K and V are adjacent in the steady-state region.\nThat region reuses Q's tail; later o_smem reuses the union base for the O epilogue.", - "K 与 V 位于相邻的稳态区域。\n该区域复用 Q tail;随后 o_smem 再复用 union base 完成 O epilogue。", + "Adjacent K/V workspaces\nbegin at Q's released suffix.", + "相邻的 K/V workspace\n从已释放的 Q suffix 开始。", ), ha="left", va="center", - fontsize=8.1, + fontsize=11.0, color=COLORS["muted"], ) diff --git a/img/scripts/gen_flashmla_pipeline.py b/img/scripts/gen_flashmla_pipeline.py index 64eebcb9..38ddeefe 100644 --- a/img/scripts/gen_flashmla_pipeline.py +++ b/img/scripts/gen_flashmla_pipeline.py @@ -6,25 +6,124 @@ import argparse import matplotlib.pyplot as plt +from matplotlib.patches import FancyBboxPatch from flashmla_diagram_common import ( COLORS, - arrow, + arrow as _arrow, configure_style, - rounded_box, + rounded_box as _rounded_box, save_figure, tr, ) -def _row(ax, y: float, title: str, role: str) -> None: - rounded_box( - ax, 0.12, y, 2.05, 0.82, f"{title}\n{role}", COLORS["neutral"], fontsize=8.4 +def box(ax, x, y, w, h, text, color, *, fontsize=10.8, **kwargs): + """Draw a timeline node sized for the book's content column.""" + + return _rounded_box( + ax, + x, + y, + w, + h, + text, + color, + fontsize=fontsize, + **kwargs, ) - ax.plot([2.42, 18.7], [y + 0.41, y + 0.41], color="#e5e7eb", lw=1.0, zorder=0) -def _barrier_note(ax, x: float, y: float, text: str, *, fontsize: float = 7.0) -> None: +def edge( + ax, + start, + end, + *, + label=None, + label_offset=(0.0, 0.14), + fontsize=10.0, + **kwargs, +): + """Draw a dependency edge with an HTML-readable label.""" + + line_color = kwargs.get("color") or COLORS["line"] + zorder = kwargs.get("zorder", 2) + patch = _arrow(ax, start, end, label=None, **kwargs) + if label: + ax.text( + (start[0] + end[0]) / 2 + label_offset[0], + (start[1] + end[1]) / 2 + label_offset[1], + label, + ha="center", + va="center", + fontsize=fontsize, + color=line_color, + bbox=dict( + boxstyle="round,pad=0.10", + facecolor="white", + edgecolor="none", + alpha=0.94, + ), + zorder=zorder + 1, + ) + return patch + + +def panel(ax, x, y, w, h, title, subtitle): + """Draw one layer of the steady-state dependency story.""" + + patch = FancyBboxPatch( + (x, y), + w, + h, + boxstyle="round,pad=0.05,rounding_size=0.06", + linewidth=1.15, + linestyle="--", + edgecolor="#c4b5fd", + facecolor="#ffffff", + zorder=0, + ) + ax.add_patch(patch) + ax.text( + x + 0.20, + y + h - 0.24, + title, + ha="left", + va="center", + fontsize=13.0, + weight="bold", + color="#6d28d9", + ) + ax.text( + x + w - 0.20, + y + h - 0.24, + subtitle, + ha="right", + va="center", + fontsize=10.0, + color=COLORS["muted"], + ) + + +def lane(ax, y, title, role): + """Draw a named warpgroup lane and its baseline.""" + + box( + ax, + 0.48, + y - 0.38, + 1.42, + 0.76, + f"{title}\n{role}", + COLORS["neutral"], + fontsize=10.2, + ) + ax.plot([2.08, 13.45], [y, y], color="#e5e7eb", lw=1.0, zorder=0) + + +def tag(ax, x, y, text, *, fontsize=9.8): + """Place a completion/ready barrier name away from node text.""" + ax.text( x, y, @@ -34,7 +133,9 @@ def _barrier_note(ax, x: float, y: float, text: str, *, fontsize: float = 7.0) - fontsize=fontsize, color="#92400e", bbox=dict( - boxstyle="round,pad=0.14", facecolor=COLORS["barrier"], edgecolor="#d97706" + boxstyle="round,pad=0.10", + facecolor=COLORS["barrier"], + edgecolor="#d97706", ), zorder=7, ) @@ -42,14 +143,14 @@ def _barrier_note(ax, x: float, y: float, text: str, *, fontsize: float = 7.0) - def draw(lang: str, output: str, font_path: str | None = None) -> None: configure_style(lang, font_path) - fig, ax = plt.subplots(figsize=(19.0, 10.5)) - ax.set_xlim(0, 19) - ax.set_ylim(0, 10.5) + fig, ax = plt.subplots(figsize=(14.0, 13.2)) + ax.set_xlim(0, 14) + ax.set_ylim(0, 13.2) ax.axis("off") ax.text( - 9.5, - 10.16, + 7, + 12.84, tr( lang, "Sparse FlashMLA Head128 Regular: Steady-State Pipeline", @@ -57,381 +158,283 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: ), ha="center", va="center", - fontsize=18, + fontsize=20, weight="bold", ) ax.text( - 9.5, - 9.76, + 7, + 12.30, tr( lang, - "softmax(k−1) may overlap QK(k); after QK(k) is issued, softmax(k) may overlap asynchronous PV(k−1); widths are not cycle measurements", - "softmax(k−1) 可与 QK(k) 重叠;QK(k) 发出后,softmax(k) 可与异步 PV(k−1) 重叠;方框宽度不表示 cycle 数", + "softmax(k−1) may overlap QK(k); once QK(k) completes,\nsoftmax(k) may overlap asynchronous PV(k−1) · box widths are not cycle measurements", + "softmax(k−1) 可与 QK(k) 重叠;QK(k) 完成后,\nsoftmax(k) 可与异步 PV(k−1) 重叠 · 方框宽度不表示 cycle 数", ), ha="center", va="center", - fontsize=9.4, - color=COLORS["muted"], - ) - arrow(ax, (2.42, 9.24), (18.62, 9.24), color="#9ca3af", linewidth=1.0) - ax.text( - 10.5, - 9.31, - tr(lang, "time", "时间"), - ha="center", - va="bottom", - fontsize=8, + fontsize=11.5, color=COLORS["muted"], - style="italic", + linespacing=1.25, ) - y_k = 7.83 - y_v = 6.23 - y_mma = 4.63 - y_mask = 3.17 - y_soft = 1.57 - _row(ax, y_k, "WG1", tr(lang, "K gather producer", "K gather producer")) - _row(ax, y_v, "WG2", tr(lang, "V gather producer", "V gather producer")) - _row(ax, y_mma, "WG3 · CTA0 warp 12", tr(lang, "QK / PV issue", "发起 QK / PV")) - _row(ax, y_mask, "WG3 · warp 13", tr(lang, "validity mask", "有效性 mask")) - _row(ax, y_soft, "WG0", tr(lang, "softmax + O rescale", "softmax + O 重缩放")) - - # Current K was gathered earlier into the one in-place K workspace. - rounded_box( + panel( ax, - 2.54, - y_k + 0.06, - 1.18, - 0.70, - "K(k) part0\nready", - "#dbeafe", - fontsize=7.5, - edgecolor="#60a5fa", - ) - rounded_box( - ax, - 3.92, - y_k + 0.06, - 1.18, - 0.70, - "K(k) part1\nready", - "#dbeafe", - fontsize=7.5, - edgecolor="#60a5fa", + 0.25, + 6.55, + 13.50, + 5.25, + tr( + lang, + "A · One issuer order; four independent part handshakes", + "A · 唯一 issuer 的顺序与四个独立分段握手", + ), + tr(lang, "box widths are not cycle measurements", "方框宽度不表示 cycle 数"), ) - # The leader issues two QK segments, then two PV segments for the prior tile. - rounded_box( - ax, - 5.40, - y_mma + 0.03, - 1.26, - 0.76, - "QK(k)\nSS prefix", - COLORS["mma"], - fontsize=8.0, - ) - rounded_box( - ax, - 7.35, - y_mma + 0.03, - 1.26, - 0.76, - "QK(k)\nTS suffix384", - COLORS["mma"], - fontsize=8.0, - ) - rounded_box( - ax, - 10.28, - y_mma + 0.03, - 1.35, - 0.76, - "PV(k−1)\npart0", - COLORS["mma"], - fontsize=8.0, - ) - rounded_box( - ax, - 12.36, - y_mma + 0.03, - 1.35, - 0.76, - "PV(k−1)\npart1", - COLORS["mma"], - fontsize=8.0, + ax.text( + 1.05, + 10.72, + tr( + lang, + "WG3 · CTA0 warp 12\nsole MMA issuer", + "WG3 · CTA0 warp 12\n唯一 MMA issuer", + ), + ha="center", + va="center", + fontsize=10.5, + weight="bold", + color=COLORS["ink"], ) - arrow(ax, (6.66, y_mma + 0.41), (7.35, y_mma + 0.41), color=COLORS["line"]) - arrow(ax, (8.61, y_mma + 0.41), (10.28, y_mma + 0.41), color=COLORS["line"]) - arrow(ax, (11.63, y_mma + 0.41), (12.36, y_mma + 0.41), color=COLORS["line"]) + issuer_boxes = [ + (2.25, "wait p_free[k−1]\nQK(k) · SS prefix"), + (5.10, "QK(k) · TS suffix384"), + (7.95, "wait so_ready[k−1]\nPV(k−1) · part0"), + (10.80, "PV(k−1) · part1"), + ] + for x, text in issuer_boxes: + box(ax, x, 10.25, 2.25, 0.90, text, COLORS["mma"], fontsize=10.4) + for x0, x1 in ((4.50, 5.10), (7.35, 7.95), (10.20, 10.80)): + edge(ax, (x0, 10.70), (x1, 10.70), color=COLORS["ink"]) ax.text( - 9.42, - y_mma + 0.18, - tr(lang, "same issue warp · source order", "同一个 issue warp · 源码顺序"), + 7.0, + 9.93, + tr(lang, "strict issue order", "严格串行发起顺序"), ha="center", va="center", - fontsize=6.9, + fontsize=10.0, color=COLORS["muted"], style="italic", ) - # Current K readiness gates each QK segment; score-TMEM reuse has its own gate. - arrow(ax, (3.72, y_k + 0.39), (5.73, y_mma + 0.79), color="#2563eb", rad=-0.06) - _barrier_note(ax, 4.55, 6.74, "k_part0_ready[k]") - arrow(ax, (5.10, y_k + 0.39), (7.68, y_mma + 0.79), color="#2563eb", rad=-0.08) - _barrier_note(ax, 6.42, 6.98, "k_part1_ready[k]") - rounded_box( + handshakes = [ + ( + 0.70, + 8.33, + tr( + lang, + "WG1: k_part0_ready[k]\n→ QK SS prefix\n→ qk_part_done[k]\n→ gather K(k+1) part0", + "WG1:k_part0_ready[k]\n→ QK SS prefix\n→ qk_part_done[k]\n→ gather K(k+1) part0", + ), + "#dbeafe", + ), + ( + 7.10, + 8.33, + tr( + lang, + "WG1: k_part1_ready[k]\n→ QK TS suffix384\n→ qk_done[k]\n→ gather K(k+1) part1", + "WG1:k_part1_ready[k]\n→ QK TS suffix384\n→ qk_done[k]\n→ gather K(k+1) part1", + ), + "#dbeafe", + ), + ( + 0.70, + 6.88, + tr( + lang, + "WG2: v_part0_ready[k−1]\n→ PV part0\n→ sv_part_done[k−1]\n→ gather V(k) part0", + "WG2:v_part0_ready[k−1]\n→ PV part0\n→ sv_part_done[k−1]\n→ gather V(k) part0", + ), + COLORS["tma"], + ), + ( + 7.10, + 6.88, + tr( + lang, + "WG2: v_part1_ready[k−1]\n→ PV part1\n→ sv_done[k−1]\n→ gather V(k) part1", + "WG2:v_part1_ready[k−1]\n→ PV part1\n→ sv_done[k−1]\n→ gather V(k) part1", + ), + COLORS["tma"], + ), + ] + for x, y, text, color in handshakes: + box(ax, x, y, 6.20, 1.12, text, color, fontsize=10.3, weight="normal") + + panel( ax, - 4.92, - 4.06, - 2.10, - 0.43, + 0.25, + 1.05, + 13.50, + 5.15, tr( lang, - "incoming from prior WG0(k−1) · p_free[k−1]", - "来自前一轮 WG0(k−1) · p_free[k−1]", + "B · Tile k: mask-slot reuse and WG0 handoff", + "B · Tile k:mask slot 复用与 WG0 交接", + ), + tr( + lang, + "arrows name the barrier that guards reuse", + "箭头标出保护复用的 barrier", ), - "#f3e8ff", - fontsize=6.5, - weight="normal", - edgecolor="#7c3aed", - linestyle="--", - ) - arrow( - ax, - (5.97, 4.49), - (5.97, y_mma + 0.03), - color="#7c3aed", - linestyle="--", - linewidth=1.1, - ) - - # QK segment completion releases the same K workspace for k+1, part by part. - rounded_box( - ax, - 6.70, - y_k + 0.06, - 1.42, - 0.70, - "gather K(k+1)\npart0", - COLORS["tma"], - fontsize=7.6, - ) - rounded_box( - ax, - 8.68, - y_k + 0.06, - 1.42, - 0.70, - "gather K(k+1)\npart1", - COLORS["tma"], - fontsize=7.6, - ) - arrow(ax, (6.03, y_mma + 0.79), (7.12, y_k + 0.06), color="#059669", rad=0.04) - _barrier_note(ax, 6.72, 7.25, "qk_part_done[k]") - arrow(ax, (7.98, y_mma + 0.79), (9.10, y_k + 0.06), color="#059669", rad=0.04) - _barrier_note(ax, 8.64, 7.32, "qk_done[k]") - - # The prior V parts are already ready for PV(k-1). - rounded_box( - ax, - 8.18, - y_v + 0.06, - 1.15, - 0.70, - "V(k−1)\npart0 ready", - "#dbeafe", - fontsize=7.2, - edgecolor="#60a5fa", ) - rounded_box( + box( ax, - 9.48, - y_v + 0.06, - 1.15, 0.70, - "V(k−1)\npart1 ready", - "#dbeafe", - fontsize=7.2, - edgecolor="#60a5fa", + 4.35, + 2.45, + 0.92, + tr(lang, "WG3 warp 13\npack mask(k)", "WG3 warp 13\npack mask(k)"), + COLORS["barrier"], + fontsize=10.8, ) - arrow(ax, (9.33, y_v + 0.38), (10.62, y_mma + 0.79), color="#2563eb", rad=-0.04) - arrow(ax, (10.63, y_v + 0.28), (12.70, y_mma + 0.79), color="#2563eb", rad=-0.08) - rounded_box( + box( ax, - 9.88, - 4.06, - 2.14, - 0.43, + 5.35, + 4.35, + 3.10, + 0.92, tr( lang, - "incoming from prior WG0(k−1) · so_ready[k−1]", - "来自前一轮 WG0(k−1) · so_ready[k−1]", + "WG0 consumes mask(k)\nwhile processing L(k)", + "WG0 处理 L(k) 时\n读取 mask(k)", ), - "#f3e8ff", - fontsize=6.4, - weight="normal", - edgecolor="#7c3aed", - linestyle="--", + COLORS["softmax"], + fontsize=10.8, ) - arrow( + box( ax, - (10.95, 4.49), - (10.95, y_mma + 0.03), - color="#7c3aed", - linestyle="--", - linewidth=1.1, + 10.35, + 4.35, + 2.95, + 0.92, + "WG3 warp 13\npack mask(k+2)\nreuse slot k%2", + COLORS["barrier"], + fontsize=10.6, ) - - # Each completed PV half releases the one V workspace for the matching k half. - rounded_box( + edge( ax, - 11.72, - y_v + 0.06, - 1.38, - 0.70, - "gather V(k)\npart0", - COLORS["tma"], - fontsize=7.6, + (3.15, 4.81), + (5.35, 4.81), + label="k_valid_ready[k]", + label_offset=(0.0, 0.22), + fontsize=9.7, + color="#d97706", ) - rounded_box( + edge( ax, - 13.80, - y_v + 0.06, - 1.38, - 0.70, - "gather V(k)\npart1", - COLORS["tma"], - fontsize=7.6, + (8.45, 4.81), + (10.35, 4.81), + label="k_valid_free[k]", + label_offset=(0.0, 0.22), + fontsize=9.7, + color="#d97706", + linestyle="--", ) - arrow(ax, (10.95, y_mma + 0.79), (12.12, y_v + 0.06), color="#059669", rad=0.04) - _barrier_note(ax, 11.78, 5.94, "sv_part_done[k−1]") - arrow(ax, (13.03, y_mma + 0.79), (14.20, y_v + 0.06), color="#059669", rad=0.04) - _barrier_note(ax, 13.87, 5.94, "sv_done[k−1]") - # Mask production runs on a separate warp and feeds WG0. - rounded_box( + box( ax, - 5.72, - y_mask + 0.06, - 1.92, 0.70, - tr( - lang, - "pack mask(k)\n8 indices / lane", - "pack mask(k)\n每个 lane 处理 8 indices", - ), - COLORS["barrier"], - fontsize=7.6, - ) - - # WG0 consumes L(k), computes W in registers while PV(k-1) is active, then safely reuses W/O. - rounded_box( - ax, - 8.72, - y_soft + 0.03, - 1.55, - 0.76, - tr(lang, "load L(k)\nfrom TMEM", "从 TMEM\n读取 L(k)"), + 2.35, + 2.45, + 1.00, + tr(lang, "qk_done[k]\nload L(k) from TMEM", "qk_done[k]\n从 TMEM 读取 L(k)"), COLORS["tmem"], - fontsize=7.8, + fontsize=10.8, ) - rounded_box( + box( ax, - 10.55, - y_soft + 0.03, - 2.22, - 0.76, - tr( - lang, - "mask L(k)\nmax / exp / row sum", - "mask L(k)\nmax / exp / row sum", - ), + 5.05, + 2.35, + 3.25, + 1.00, + tr(lang, "WG0: mask · max\nexp · row sum", "WG0:mask · max\nexp · row sum"), COLORS["softmax"], - fontsize=7.8, + fontsize=10.8, ) - rounded_box( + box( ax, - 13.78, - y_soft + 0.03, - 3.05, - 0.76, + 9.65, + 2.20, + 3.65, + 1.30, tr( lang, - "after sv_done(k−1): write W(k)\noptional O rescale · so_ready[k]", - "等待 sv_done(k−1) 后:写入 W(k)\n按需重缩放 O · so_ready[k]", + "wait sv_done(k−1)\nwrite W(k) · optional O rescale\narrive so_ready[k]", + "等待 sv_done(k−1)\n写 W(k) · 按需重缩放 O\narrive so_ready[k]", ), COLORS["softmax"], - fontsize=7.7, + fontsize=10.5, ) - arrow(ax, (8.0, y_mma + 0.03), (9.32, y_soft + 0.79), color="#7c3aed", rad=0.05) - _barrier_note(ax, 8.50, 3.76, "qk_done[k]") - arrow(ax, (7.64, y_mask + 0.41), (10.90, y_soft + 0.79), color="#d97706", rad=0.07) - _barrier_note(ax, 8.35, 2.86, "k_valid_ready[k]") - arrow(ax, (12.77, y_soft + 0.41), (13.78, y_soft + 0.41), color="#7c3aed") - _barrier_note(ax, 13.25, y_soft + 0.72, "wait sv_done[k−1]") - arrow(ax, (13.03, y_mma + 0.03), (14.30, y_soft + 0.79), color="#059669", rad=-0.05) - arrow( + edge( ax, - (9.49, y_soft + 0.03), - (9.49, 0.94), - label=tr( - lang, - "TMEM L load complete → p_free[k] → future QK(k+1)", - "TMEM L 读取完成 → p_free[k] → 后续 QK(k+1)", - ), + (3.15, 2.85), + (5.05, 2.85), + color=COLORS["line"], + ) + edge( + ax, + (8.30, 2.85), + (9.65, 2.85), color="#7c3aed", - linestyle="--", - label_offset=(1.45, 0.0), ) - arrow( + ax.text( + 2.0, + 1.65, + "p_free[k] → QK(k+1)", + ha="center", + va="center", + fontsize=10.3, + color="#7c3aed", + weight="bold", + ) + edge( ax, - (16.35, y_soft + 0.03), - (17.52, 0.94), - label=tr(lang, "so_ready[k] → future PV(k)", "so_ready[k] → 后续 PV(k)"), + (1.95, 2.35), + (1.95, 1.87), color="#7c3aed", linestyle="--", - label_offset=(0.10, 0.0), - rad=0.05, ) - rounded_box( - ax, - 15.42, - y_mask + 0.06, - 2.08, - 0.70, - tr( - lang, - "pack mask(k+2)\nreuse slot k%2", - "pack mask(k+2)\n复用 slot k%2", - ), - COLORS["barrier"], - fontsize=7.4, + ax.text( + 11.5, + 1.65, + "so_ready[k] → PV(k)", + ha="center", + va="center", + fontsize=10.3, + color="#7c3aed", + weight="bold", ) - arrow( + edge( ax, - (11.35, y_soft + 0.79), - (15.80, y_mask + 0.06), - color="#d97706", + (11.5, 2.20), + (11.5, 1.87), + color="#7c3aed", linestyle="--", - rad=-0.08, ) - _barrier_note(ax, 13.55, 2.88, "k_valid_free[k]", fontsize=6.6) - # Exact scope of the two-slot ring in the pinned regular kernel. - rounded_box( + box( ax, - 0.62, - 0.18, - 17.76, - 0.62, + 0.52, + 0.10, + 12.96, + 0.72, tr( lang, - "NUM_BUFS=2 is a barrier/phase ring: slot=k%2, phase=(k//2)&1. K, V, and s_smem_gemm are single in-place workspaces (plus two small mask slots), not two complete K/V stages.", - "NUM_BUFS=2 是 barrier/phase ring:slot=k%2,phase=(k//2)&1。K、V 与 s_smem_gemm 都是单份原位 workspace(另有两个小型 mask slots),并非两份完整 K/V stages。", + "NUM_BUFS=2 is a barrier/phase ring: slot=k%2, phase=(k//2)&1.\nK, V, and W use one in-place workspace each; only the small validity mask has two data slots.", + "NUM_BUFS=2 是 barrier/phase ring:slot=k%2,phase=(k//2)&1。\nK、V、W 各自只有一份原位 workspace;只有小型 validity mask 有两个 data slots。", ), COLORS["note"], - fontsize=8.3, + fontsize=9.8, weight="normal", edgecolor="#ca8a04", ) diff --git a/img/scripts/gen_flashmla_sparse_story.py b/img/scripts/gen_flashmla_sparse_story.py index a7b6b6bf..3ad3d617 100644 --- a/img/scripts/gen_flashmla_sparse_story.py +++ b/img/scripts/gen_flashmla_sparse_story.py @@ -66,7 +66,7 @@ def draw(lang: str, output: str, font_path: str | None = None) -> None: tr( lang, "Who Chooses the Tokens in Sparse FlashMLA?", - "Sparse FlashMLA 中由谁选择 Tokens?", + "Sparse FlashMLA 中由谁选择 token?", ), ha="center", va="center", diff --git a/zh/chapter_flashmla/index.md b/zh/chapter_flashmla/index.md index 22eecfab..b4dc4ca0 100644 --- a/zh/chapter_flashmla/index.md +++ b/zh/chapter_flashmla/index.md @@ -1,51 +1,43 @@ (chap_flashmla)= # FlashMLA -先看一个表面上的矛盾。普通 MHA 会为每个 token 保存 $n_h$ 份互不相同的 -head 切片;K 或 V 的总宽度各为 $n_h d_h$。本章研究的 Blackwell kernel -接受 128 个 query heads,但它的 KV tensor 却只有一个 head。一条 cached KV -entry 必须同时服务这 128 个 heads,保留各 head 不同的 attention 行为,并 -产生 128 份各含 512 个 coordinates 的 output。 +:::{admonition} 概览 +:class: overview -这个问题分为三层。MLA 解释 cache 为何可以共享;weight absorption 解释各 head -的 projection 去了哪里;FlashMLA kernel 则解释如何把共享 cache rows 的稀疏 -列表变成 2-CTA 协作的 dense tensor-core computation。 +- 从普通 MHA 的 KV cache 出发,理解 MLA 为什么只需为每个 token 保存一份共享的压缩状态,以及各 head 特有的 K/V 变换被移到了哪里。 +- 理解 FlashMLA sparse-prefill operator 的输入:外部 indexer 先选出 KV rows,FlashMLA 再对这些 rows 完成 attention;随后用一个可执行 reference 明确其数值语义和边界条件。 +- 通过 TIRx `flash_mla_sparse_fwd` 入口理解 shape dispatch 与 QK scale 的 API 差异,再沿 regular head-128 specialization 分析 2-CTA 分工、数据驻留、warpgroup 角色与 pipeline,最后在 B200 上编译并验证。 +::: -```{figure} ../../img/flashmla_cache_story_zh.svg -:width: 100% -:alt: 一条 latent KV cache entry 通过吸收投影服务 128 个 query heads +在介绍 MLA 之前,先回顾普通 attention 为什么需要 **KV cache**。计算一个新的 query 时,attention 需要读取更早 tokens 的 key 和 value。如果每次都重新计算这些 K/V,就会产生大量重复工作,因此系统会把已经得到的 K/V 缓存起来,供后续 query 直接读取。 -缓存为每个 token 保存一份 latent content vector 和一份共享 RoPE key。各 -head 的行为保留在 query 与 output 路径中,而不是展开成 128 份 K/V cache -entries。 -``` +普通 multi-head attention(MHA)中,每个 attention head 都有自己的 K 和 V。因此,KV cache 必须为每个已经处理过的 token 保存各个 head 的 K/V。上下文越长,需要保存和读取的数据就越多。MLA 要解决的第一个问题,就是怎样缩小这部分 cache。 -:::{admonition} 概览 -:class: overview +这种方法称为 **Multi-head Latent Attention(MLA)**。它的核心做法是换一种 cache 表示:不再保存各个 head 展开后的 K/V,而只为每个 token 保存一份由所有 heads 共享的压缩状态。这并不是把所有 heads 合并成一个 head。每个 head 仍有自己的变换,只是 cache 不再需要长期保存这些变换产生的 K/V。至于一份共享状态怎样保留各 head 的差异,后面会用公式逐步推导。 -- 理解 MLA 如何共享 latent KV cache、MHA/MQA 两种执行模式,以及 weight absorption。 -- 从 sparse contract 追踪到 Blackwell 上由 2 个 CTA 协作完成的数据流程序。 -- 运行可执行 reference,并在 B200 上编译、验证固定版本的 TIRx 实现。 -::: +MLA 说明的是 cache 中保存什么,以及 attention 应该怎样计算;FlashMLA 解决的则是怎样在 GPU 上高效完成这些计算。DeepSeek 将这套高性能 GPU kernel library 称为 **FlashMLA**。其中包含适用于不同 attention 阶段和 cache 格式的多类算子。 -*FlashMLA* 这个名字包含两个容易混淆的概念。MLA 是一种 attention 架构, -它将 key-value 状态压缩成 latent vector;FlashMLA 则是 DeepSeek 提供的 -高性能 attention kernel library,其中既包含 dense 和 sparse operator,也 -覆盖 prefill 与 decode。 +本章先以 FlashMLA `flash_mla_sparse_fwd` 的 sparse-prefill contract 为语义主线。Prefill 表示并行处理 prompt 中的 query tokens;sparse 表示先由外部 indexer 选出需要关注的 KV rows,再对选中的 rows 计算 attention。 -本章会先推导 MLA 架构,再让 sparse contract 真正运行起来,最后沿用 FA4 -从算法深入 schedule 的分析方式,研究一条具体的 library 路径:Blackwell 上 -regular 128-query-head sparse-prefill forward kernel。 +TIRx 也注册了一个同名的 `flash_mla_sparse_fwd` 入口。它是一座实现桥梁:按 shape dispatch 到 head-64、regular head-128 和 small-top-k head-128 三个 SM100 specializations,但其 QK scale 已 specialize 为 `1 / sqrt(d_qk)`。后半章再以其中的 regular head-128 specialization 为实现主线,分析它在 Blackwell 上的 schedule。这样,FlashMLA sparse-prefill contract 回答“算什么”,TIRx 入口回答“选哪条实现”,被选中的 specialization 回答“怎样在 GPU 上执行”。其他实现只在后文比较算子族、dispatch 和设计取舍时出现。 -本章实现固定使用 -[`mlc-ai/tirx-kernels@5be39749`](https://github.com/mlc-ai/tirx-kernels/tree/5be39749e7dfd2c4bdae9b4d396f8ec35af07126)。 -下文所有 TIRx API 写法和代码摘录都来自这个 revision。这一点很重要: -compiler API 仍在演进,而教材示例必须能够复现。 +先预告后半章的 regular head-128 案例:一个 query token 对应一行 query,这一行包含 128 个 query heads;每个 cached token 则对应 cache 中的一行共享 KV。于是问题变成了:128 个 heads 读取同一行 KV,为什么仍能得到不同的结果?下面这张图先给出直观线索:共享的是生成 K/V 所需的源状态,而不是各 head 最终参与 attention 的表示。各 head 特有的变换仍然位于点积、softmax 和加权求和这些核心 attention 计算的两侧。精确的 tensor shapes 会在完成 MLA 推导后统一列出。 -## 为什么 MHA 要为每个 head 分别缓存 K/V 状态? +```{figure} ../../img/flashmla_cache_story_zh.svg +:width: 100% +:alt: 普通 MHA 为每个 head 分别缓存 key 和 value;MLA 只保存一份共享压缩状态,并把各 head 特有的计算放在 attention 两侧 -设 $h_t\in\mathbb{R}^{d_{model}}$ 是 token $t$ 的 hidden state。普通 -multi-head attention(MHA)会为每个 head $i$ 分别做 projection: +普通 MHA 为每个 head 分别保存一份 key/value。MLA 为每个 token 只保存一份共享的压缩内容状态和位置信息;各 head 特有的 query 与 output 变换分别在 attention 前后完成。 +``` + +这张图只给出了直觉,还没有说明共享状态怎样保留各 head 的差异,也没有证明移动这些变换为什么不改变计算结果。下面先算清普通 MHA 的 cache 开销,再推导 MLA 到底缓存了什么,以及各 head 的变换为什么可以移动。等 cache 表示和等价变换都讲清楚之后,我们再进入 FlashMLA sparse-prefill contract 和 regular head-128 schedule。 + +## 先从普通 MHA 的 KV cache 算起 + +上面的直观描述还没有回答 cache 到底有多大。设 +$h_t\in\mathbb{R}^{d_{model}}$ 是 token $t$ 的 hidden state,$n_h$ 是 head +数量,$d_h$ 是每个 head 的宽度;$i$ 表示某个 head,$s$ 表示一个已经缓存的 +key-token 位置。普通 MHA 会为每个 head $i$ 分别生成 query、key 和 value: $$ q_{t,i}=W_i^Q h_t,\qquad @@ -80,7 +72,7 @@ cache 一个共享的低维数据源,需要时可以从中恢复各 head 的 ### MLA 如何只缓存一次,却恢复 per-head 行为? 最初的 [DeepSeek-V2 MLA 推导](https://arxiv.org/abs/2405.04434)先定义一个 -joint latent KV vector: +联合潜在 KV 向量(joint latent KV vector): $$ c_t^{KV}=W^{DKV}h_t, @@ -97,20 +89,8 @@ $$ 每个 head 保存展开后的 $k^C$ 和 $v^C$,只需为每个 token 保存一份 $c^{KV}$。 -MLA 还可以引入一个独立的低秩 latent,对 query projection 做分解: - -$$ -c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. -$$ - -Query 侧的这项分解会降低训练时的 activation memory,但不会进一步缩小 KV -cache。 - -它也发生在 core-attention API 之前:传给 FlashMLA 的 `q` tensor 已经是 -projection 后的 query。因此,下文把 $q^C$ 视为输入,重点讨论决定 cache 与 -kernel operands 的 KV 侧 compression。 - -RoPE 让这幅简单图景变得复杂。如果在 $W^{UK}$ 与 dot product 之间加入 +Rotary positional embedding(RoPE)会旋转 Q/K 中负责表示位置的子空间。 +这让上面的简单图景变得复杂:如果在 $W^{UK}$ 与 dot product 之间加入这种 position-dependent rotation,矩阵就无法再重新结合。为此,MLA 使用 decoupled positional channel:每个 query head 有自己的 $q_{t,i}^{R}$, 而所有 heads 共享一个 cached $k_t^R$。真正以 MHA 形式计算的 score 使用: @@ -123,10 +103,27 @@ $$ 此时 cache 保存的是 $[c_s^{KV};k_s^R]$,仍然由所有 heads 共享。 Positional channel 保持显式,weight absorption 只作用于 content channel。 +:::{admonition} Query 侧也可以压缩,但它不是本章的主线 +:class: note + +MLA 还可以通过一个独立的低秩 latent 分解 query projection: + +$$ +c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +$$ + +这项分解主要降低训练时的 activation memory,不会进一步缩小 KV cache。 +而且,它发生在 FlashMLA core attention 之前:传给 kernel 的 `q` 已经是 +projection 后的 query。所以下文把 $q^C$ 当作输入,继续沿着 KV cache 这条 +主线分析。 +::: + ### 各 head 的 up-projection 去了哪里? -MLA 的 core attention 可以用两种代数上相关的模式执行。不能因为其中一种 -叫 MQA mode,就把所有 MLA 模型都理解成普通 MQA 模型。 +到这里,我们知道了 cache 里保存什么,但还没有回答一个关键问题:各 head 的 +$W_i^{UK}$ 和 $W_i^{UV}$ 是否仍要在 attention 前显式执行?MLA 的 core +attention 可以用两种代数上等价的模式执行。这里的 “MQA mode” 是一种执行 +方式,不能据此把所有 MLA 模型都理解成普通 MQA 模型。 | MLA 执行模式 | 提交给 kernel 的 core-attention K/V | Up-projection 发生的位置 | | --- | --- | --- | @@ -161,16 +158,10 @@ $$ 因此,$W_i^{UV}$ 可以与模型的 output projection 合并。Attention kernel 不必真正 materialize 展开的 per-head K 或 per-head V。 -这个区别体现在实际执行上,而不只是记号不同。 -[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) -Appendix A 说明,DeepSeek-V3.1-Terminus 在 training 和 prefill 时使用 MHA -mode,在 decode 时使用 MQA mode。相比之下,DeepSeek Sparse Attention -(DSA)即使在 sparse prefill 中也采用 MLA 的 MQA mode,因为每个被选中的 -latent KV entry 会由所有 query heads 共享。因此,这条 sparse-prefill 路径 -中常见的 $d_{qk}=576$、$d_v=512$ contract 表示吸收权重后的 MQA -representation:576 这一变体由 512 个 latent content coordinates 和 64 个 -RoPE coordinates 组成。它不是所有 MLA 或 FlashMLA operator 的通用 shape; -实现还支持 $d_{qk}=512$ 变体。 +本章研究的 DeepSeek Sparse Attention(DSA)sparse-prefill 路径采用的正是 +这个 MQA mode:每个被选中的 latent KV entry 由所有 query heads 共享。因此, +下面先用一个小程序验证两种计算确实等价。具体模型为什么选择不同 mode, +以及 512/576 等实现 shapes 的含义,留到进入 kernel contract 时再说明。 ### 一个小程序能否证明两种模式一致? @@ -227,21 +218,24 @@ print("weight absorption: exact up to float64 roundoff") 吸收权重后的 dot product 恰好有 $D_{latent}$ 个 coordinates,就把它改成 $1/\sqrt{D_{latent}}$。 -## Sparse kernel 会自己选择 token 吗? +Weight absorption 回答了“一条共享 KV row 如何服务多个 query heads”。接下来 +还要回答另一个独立问题:sparse-prefill operator 收到的 KV row list 究竟由谁选择? + +## Sparse-prefill operator 会自己选择 token 吗? Dense attention 会访问每个合法的 KV token。DSA 先用轻量的 *lightning -indexer* 为候选 tokens 打分,并为每个 query 选出一个 top-$k$ 集合;sparse +indexer* 为候选 token 打分,并为每个 query 选出一个 top-$k$ 集合;sparse core attention 随后只读取这些 latent KV entries。若原始 context length 为 $L$,prefill 的 core-attention 计算量会从 $O(L^2)$ 变成 $O(Lk)$,不过 indexer 自身也有开销。 ```{figure} ../../img/flashmla_sparse_story_zh.svg :width: 100% -:alt: Lightning indexer 先选择 token,sparse-prefill kernel 再执行 attention +:alt: Lightning indexer 先选择 token,sparse-prefill operator 再执行 attention -Token selection 与 sparse core attention 是两个相互独立的算子。Indexer -产生 row addresses;sparse-prefill kernel gather 这些 rows,再完成 -QK--softmax--PV 计算。 +Token 选择与 sparse core attention 是两个相互独立的算子。Indexer 输出 +row addresses;sparse-prefill operator 根据这些地址 gather 对应的 rows, +再完成 QK--softmax--PV 计算。 ``` 本章研究的 sparse-prefill operator 不计算 index scores,也不执行 top-k @@ -255,80 +249,51 @@ selection,而是直接接收 `indices` tensor。因此它的语义 contract 这个 interface 没有 causal flag。若 caller 需要 causal attention,就必须生成 一个只含允许访问的 keys 的 index list。稀疏性本身并不等同于 causal mask。 -如果提供 `topk_length`,每个 query 的值都必须满足 -`0 <= topk_length[q] <= topk`。这是 caller 应保证的前置条件,而不是 -kernel 会自动 clip 的输入;大于 `topk` 会让固定版本的 kernel 走到 +如果提供 `topk_length`,FlashMLA sparse-prefill contract 要求每个 query 的值 +都满足 `0 <= topk_length[q] <= topk`。这是 caller 应保证的前置条件。TIRx +prefill specializations 不会 clip 或逐项验证该值;大于 `topk` 会使它们读取到 `indices` storage 之外。 -这个 prefill interface 也没有 batch dimension。在下文研究的 port 中, -`h_kv=1`,所以 `indices` 的 shape 是 `[s_q, 1, topk]`:每个 query token -提供一份 selected-token list,它的 128 个 query heads 共用这份 list。Serving -system 必须在调用前 flatten batch,或用其他方式完成 batch mapping。 - -### FlashMLA 是一个 kernel,还是一族算子? +这个 prefill 接口也没有 batch 维度。每个 query token 提供一份 +selected-token list,它的 `h_q` 个 query heads 共用这份 list。Serving system +必须在调用前 flatten batch,或用其他方式完成 batch mapping。`s_q`、`h_kv` +和 `topk` 对应的精确 tensor shape 会在介绍 public call 时统一定义;后半章的 +regular specialization 再令 `h_q=128`。 -*Prefill* 并行处理 prompt 中的 query tokens;*decode* 则在复用 KV cache 的 -同时,每一步加入一个新 query(或一小组 speculative queries)。 -[FlashMLA 官方仓库](https://github.com/deepseek-ai/FlashMLA)将 kernel 组织成 -四类: - -| Selection | Sequence stage | 代表性用途 | -| --- | --- | --- | -| dense | prefill | MHA forward 与 backward | -| dense | decode | 为新生成的 queries 读取 MLA KV cache | -| token-sparse | prefill | 对 selected-token list 执行 DSA core attention | -| token-sparse | decode | 对 selected FP8 KV cache 执行 DSA inference | +这些规则已经回答了 operator 接受什么、拒绝什么。接下来把它们写成 CPU +reference,先验证语义能够独立运行,再讨论 FlashMLA 如何实现。 -所以,FlashMLA 既不等同于 sparse attention,也不等同于本章这个 kernel。 - -本章选择 sparse prefill operator,是因为它把一个系统问题展示得很清楚: -irregular TMA gather 如何为规则的 tensor-core tiles 供数?Sparse decode 有 -不同的 paged-cache、scheduling 和 reduction contract,不在本章范围内。 - -Upstream sparse-prefill public call 在概念上是: - -```text -out, max_logits, lse = flash_mla_sparse_fwd( - q, kv, indices, sm_scale, - d_v=512, - attn_sink=attn_sink, # optional [h_q], float32 - topk_length=topk_length, # optional [s_q], int32 -) -``` - -固定版本的 TIRx repository 在统一的 `flash_mla_sparse_fwd` registry entry 中 -沿用了这个 public name,再根据 shape dispatch 到三个 SM100 phase-1 modules -之一。 +## 能否先把 sparse contract 写成可执行 reference? -:::{admonition} Port 范围:`sm_scale` 已固定 -:class: warning +阅读优化实现之前,先把“应该算什么”写成可执行 reference。在吸收权重后的 +MQA contract 中,`kv[:, 0, :]` 同时提供 K 和 V:全部 `d_qk` 个坐标参与 QK, +前 `d_v` 个坐标则作为 latent value。 -上面的 upstream call 会在 runtime 接收 `sm_scale`。固定版本的 TIRx entry -保留了 registry name 和 shape dispatch,却**没有**保留完整的 call -signature:三个 prefill modules 都将 scale specialize 为 -`1 / sqrt(d_qk)`,launch ABI 中没有 scale argument。在这个 revision 中, -通过 `**kwargs` wrappers 传入 `sm_scale=...` 会被静默忽略。因此,下文 -的 B200 示例验证的是固定 scale 的教学 port,而不是 upstream -`flash_mla_sparse_fwd` 的 drop-in replacement。若模型语义中的 QK scale -不同,就必须将正确数值暴露为参数,或在编译时将其 specialize。 +这里还有两个容易在代码中突然出现的边界语义。第一,**attention sink** 可以 +看成额外加入一个 logit $a_i$,但它对应的 value vector 为 0。因此它只进入 +output 的 denominator: -Weight absorption 并不构成改变该 scale 的理由。 -::: +$$ +O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} +{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. +$$ -## 能否先把 sparse contract 写成可执行 reference? +Sink 不参与返回的 `max_logits` 或 `lse`。第二,如果一个 query 的 selected +rows 全部无效,reference 约定 `output=0`、`max_logits=-inf`、`lse=+inf`。 +显式写出这项约定,可以避免在 softmax 中计算 `(-inf)-(-inf)`。 -阅读 kernel 之前,先写一个明确处理各种边界情况的 reference。在吸收权重后的 -MQA contract 中,`kv[:, 0, :]` 同时提供 K 和 V:全部 `d_qk` coordinates -参与 QK,前 `d_v` 个 coordinates 则作为 latent value。PyTorch gather 之前 -必须先 clamp invalid indices,再将其 mask 掉;如果直接用 `-1` 做 index,就会 -错误地选择最后一行。 +下面的 CPU 程序按四步实现这个 contract: -越界地址对应的 V row 还要在 PV 前清零,因为按照 IEEE arithmetic,softmax -weight 为 0 并不能消除 NaN。对于只因 `topk_length` 而被 mask、地址本身仍合法的 -row,这里有意不做净化,以匹配后文说明的固定版本 kernel 行为。 +1. 将 `indices` clamp 成可安全读取的地址,再 gather 对应 KV rows; +2. 合并地址边界与 `topk_length`,得到 validity mask; +3. 计算 QK、mask、softmax 与 PV,并把 sink 加入最终 denominator; +4. 返回 output、maximum logit 和不含 sink 的 log-sum-exp。 -下面的完整 CPU block 回答这些规则、attention sink 和全 invalid 约定能否共存 -于一个可执行 oracle 中: +第一步只解决“地址可以安全读取”,不能代替后面的 mask。越界地址对应的 V row +还要在 PV 前清零:按照 IEEE arithmetic,softmax weight 为 0 并不能消除 NaN。 +对于只因 `topk_length` 而被 mask、地址本身仍合法的 row,这里有意不做净化; +FlashMLA sparse-prefill contract 和三个 TIRx prefill specializations 都没有 +承诺净化这种异常输入。完整代码如下: ```python import math @@ -425,53 +390,110 @@ torch.testing.assert_close(nan_out, torch.tensor([[[2.0, 3.0]]])) print(out.shape, max_logits.shape, lse.shape) ``` -Attention sink 等价于额外加入一个 logit,并令与它关联的 value vector 为 0。 -它只改变 output denominator: +这段 reference 明确了 FlashMLA sparse-prefill operator 对合法输入和返回值的 +数值 contract。上面对异常 NaN 输入的处理与 TIRx specializations 一致,但不会 +为接口增加额外的净化保证。所有由 TIRx 入口选中的 specializations 都必须在其 +QK scale 能力边界内复现已经定义的结果;tile 切分、storage reuse 和 pipeline +overlap 则属于实现,而不属于 operator contract。 -$$ -O_i=\frac{\sum_j e^{x_{ij}-m_i}v_j} -{\sum_j e^{x_{ij}-m_i}+e^{a_i-m_i}}. -$$ +## Sparse prefill 在 FlashMLA 算子族中的位置 -其中 $a_i$ 是 per-head sink logit。它不影响 `max_logits` 或返回的 `lse`; -编写独立 oracle 时很容易漏掉这个细节。 +前面已经明确了 sparse-prefill operator 的语义。现在把它放回完整的算子族: +*decode* 会在复用 KV cache 的同时,每一步加入一个新 query(或一小组 +speculative queries),与前面处理整段 prompt 的 *prefill* 不同。 +[FlashMLA 官方仓库](https://github.com/deepseek-ai/FlashMLA)将相关实现组织成 +四类: -## 本章具体研究哪一个 Blackwell 案例? +| Selection | Sequence stage | 代表性用途 | +| --- | --- | --- | +| dense | prefill | MHA forward 与 backward | +| dense | decode | 为新生成的 queries 读取 MLA KV cache | +| token-sparse | prefill | 对 selected-token list 执行 DSA core attention | +| token-sparse | decode | 对 selected FP8 KV cache 执行 DSA inference | -下面聚焦 -[`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py)。 -虽然内部的 `phase1` 名称继承自 upstream FlashMLA,但这条 prefill 路径会在 -一个 kernel 中生成完整的 `(out, max_logits, lse)`;它不是等待 combine -kernel 的 partial split-KV output。 +所以,FlashMLA 不等同于本章研究的 sparse-prefill operator,更不等同于后半章 +聚焦的 regular head-128 specialization。本章选择 sparse prefill,是因为它能把 +算子语义与一个关键的实现问题连起来:如何将不规则 row addresses 整理成规则的 +tensor-core tiles?Sparse decode 有自己的 paged-cache、scheduling 和 reduction +contract,不在本章范围内。在 TIRx 中,它是单独注册的实现,内部 +先运行 split-KV main kernel,再运行独立的 combine kernel;它不是 +`flash_mla_sparse_fwd` 的第四个 dispatch target。 + +FlashMLA sparse-prefill public call 在概念上是: + +```text +out, max_logits, lse = flash_mla_sparse_fwd( + q, kv, indices, sm_scale, + d_v=512, + attn_sink=attn_sink, # optional [h_q], float32 + topk_length=topk_length, # optional [s_q], int32 +) +``` + +这些参数对应前面 reference 明确的语义:`h_q` 是 query-head 数,`s_q` 是 +query-row 数,`sm_scale` 用来缩放 QK scores,`d_v` 决定 value 和 output 的 +宽度,`attn_sink` 可以为每个 query head 加入一个 value 为 0 的额外 logit, +`topk_length` 则限定每个 query 中有效 indices 的前缀长度。这个调用返回归一化 +后的 output、经过 scale 的最大 logit,以及不包含 sink 的 log-sum-exp。 + +这段 public call 定义 FlashMLA sparse-prefill API;前面的 reference 则把其中 +与本章相关的数值语义写成了可执行形式。TIRx 中同名的 +`flash_mla_sparse_fwd` 是 registry/dispatch bridge,而不是这个 Python API 的 +完整复刻:它按 shape 选择三个 SM100 phase-1 specializations 之一,并把调用 +转交给相应实现。 + +:::{admonition} TIRx 入口中的 `sm_scale` +:class: warning + +FlashMLA public call 会在 runtime 接收 `sm_scale`。TIRx 入口保留了 registry +name 和 shape dispatch,却**没有**保留完整的 call signature:三个 prefill +specializations 都将 `sm_scale` specialize 为 `1 / sqrt(d_qk)`,launch ABI 中 +没有 scale argument。通过 `**kwargs` wrappers 传入 `sm_scale=...` 会被静默 +忽略。因此,下文的 B200 示例验证的是 TIRx 入口所覆盖的 QK scale;它不是 +FlashMLA `flash_mla_sparse_fwd` 的 drop-in replacement。若模型语义中的 QK +scale 不同,就必须将正确数值暴露为参数,或在编译时将其 specialize。 + +Weight absorption 并不构成改变该 scale 的理由。 +::: + +明确 operator family、FlashMLA API 与 TIRx 入口的边界后,下一步才是选择一条 +具体 specialization。 + +## 本章具体研究哪一个 Blackwell 案例? Regular head-128 案例可以自然衔接前面的 FlashAttention 章节:它保留熟悉的 QK--softmax--PV 主链,再加入 irregular gather、吸收权重后的 latent KV 和 2-CTA cooperative ownership,让读者不必同时面对所有新概念。 +下面聚焦 TIRx regular head-128 实现中的 +[`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py)。 +TIRx 是建立在 TVM 0.26 TIR 之上的 Python DSL 扩展;代码里的 `T` 是 TIR +script namespace,`Tx` 是 GPU kernel helpers。 + +虽然文件名中含有 `phase1`,这个 regular head-128 specialization 仍会在一个 +kernel 中生成完整的 `(out, max_logits, lse)`;它不是等待 combine kernel 的 +partial split-KV output。 + +后文还会频繁使用三个执行层级。一个 **CTA**(cooperative thread array)就是 +一个 CUDA thread block(线程块);相邻两个 CTA 组成一个 **cluster**,可以 +共同发起 CTA-group tensor-core operation。一个 **warpgroup** 由 4 个 warps、 +共 128 个 threads 组成,并在这条 kernel 中承担一个专门角色。这里的一个 +cluster 将负责一个 query row。 + 先明确一组命名,避免后文混淆。在数学推导中,$p$ 表示归一化后的 softmax -probability;而在固定版本的源码里,`tmem_p` 和 register 变量 `p` 保存的是 +probability;而在源码里,`tmem_p` 和 register 变量 `p` 保存的是 **原始 QK logits**,下文将它们记作 $L$。源码中的 `s_frag` 和 `s_smem_gemm` 保存 BF16 **未归一化指数权重**,下文记作 $W$。只有在 epilogue 中用 `li`(以及可选的 sink term)除 accumulated output 后, 最终 output 才完成归一化。 -下面较短的 TIRx 代码块都是固定版本 kernel 的上下文摘录,不是 standalone +下面较短的 TIRx 代码块都是 regular head-128 kernel 的上下文摘录,不是 standalone program。最后一节会编译并做数值验证;可以独立执行的 blocks 会显式说明。 ### 哪些 shape 会进入 regular head-128 路径? -Regular head-128 module 固定使用以下 tile constants: - -```python -B_H = 128 -B_TOPK = 128 -D_V = 512 -NUM_BUFS = 2 -NUM_THREADS = 512 -D_TQ = 384 -``` - -它的输入输出 contract 是: +算法部分只需要知道“共享 latent KV”;现在进入具体实现,才需要把每个 tensor +的 shape 写完整。Regular head-128 specialization 的输入输出 contract 是: | Tensor | Shape | Type | 含义 | | --- | --- | --- | --- | @@ -484,18 +506,48 @@ D_TQ = 384 | `max_logits` | `[s_q, 128]` | FP32 | 最大 scaled logit | | `lse` | `[s_q, 128]` | FP32 | 不含 sink 的 natural-log sum-exp | -这个 module 接受 512 或 576 的 `d_qk`,要求 `h_kv=1`、`d_v=512`,并要求 +这里的 128 正是开篇问题中的 query-head 数,而 `kv` 中的 1 表示所有 heads +共享同一条 KV row。常见的 $d_{qk}=576$ 由 512 个 latent-content coordinates +和 64 个 RoPE coordinates 组成,`d_v=512` 则对应 latent value 宽度。这是本章 +absorbed MQA representation 的 shape,不是所有 MLA operator 的通用 shape。 + +这个区别也会随模型和阶段变化。 +[DeepSeek-V3.2 report](https://github.com/deepseek-ai/DeepSeek-V3.2-Exp/blob/main/DeepSeek_V3_2.pdf) +Appendix A 说明,DeepSeek-V3.1-Terminus 在 training 和 prefill 时使用 MHA +mode,在 decode 时使用 MQA mode;DSA sparse prefill 则使用 MQA mode。 + +Tensor contract 确定后,再看决定一次 tile 如何执行的常量: + +```python +B_H = 128 +B_TOPK = 128 +D_V = 512 +NUM_BUFS = 2 +NUM_THREADS = 512 +D_TQ = 384 +``` + +这些名字分别对应后文会反复出现的结构:`B_H=128` 是每个 logical tile 的 +query-head 数,`B_TOPK=128` 是每次处理的 selected-token 数,`D_V=512` 是 +output feature 宽度,`NUM_THREADS=512` 表示每个 CTA 有四个 warpgroups, +`D_TQ=384` 是移入 Blackwell tensor memory(TMEM)的 Q suffix 宽度。 +`NUM_BUFS=2` 只为 barrier phases +和小型 validity mask 提供两个循环槽位,并不表示有两份完整 K/V tile;数据 +驻留与 pipeline 两节会说明这一点。 + +这个 specialization 接受 512 或 576 的 `d_qk`,要求 `h_kv=1`、`d_v=512`,并要求 regular path 的 `topk` 是 128 的正整数倍。对于 128 heads,统一 front door 还会 -多做一次选择:`d_qk=512` 且 `topk<=1280` 时进入 small-top-k 实现;其他 -支持的 head-128 shapes 进入本章的 regular 实现。Head-64 shapes 使用另一个 -kernel。 +多做一次选择:`d_qk=512` 且 `topk<=1280` 时进入 small-top-k specialization; +其他支持的 head-128 shapes 进入本章的 regular specialization。Head-64 shapes +使用 head-64 specialization。 `topk > 0` 是调用者必须满足的前置条件。统一 front door 会拒绝 -`topk<=0`,但固定版本各 specialization 的 `_cfg().validate()` 只检查整除性, +`topk<=0`,但各 specialization 的 `_cfg().validate()` 只检查整除性, 没有检查正数条件。因此,直接 import 某个 specialization 时仍须拒绝或避开 非正的 `topk`;local validator 接受它并不意味着这种 launch 有效。 -无需 launch GPU kernel 就能检查 dispatch: +无需 launch GPU kernel 就能检查 dispatch。下面的代码块本身可独立执行,但 +需要先按本章末节安装 `tirx-kernels`: ```python from tirx_kernels.flashmla.flash_mla_sparse_fwd import ( @@ -509,26 +561,37 @@ print(dispatch_reason(**shape)) # sm100 h_q=128 dispatches to regular head128 phase1 ``` -Dispatch 本身记录在固定版本的 +Dispatch 本身记录在 [`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120) 中。把 dispatch 与 device schedule 分开,可以避免把一个 specialization 错当成 整个 operator。 -### 为什么一个 query row 需要两个 CTA? - -Launch grid 包含 `2 * s_q` 个 CTA,并将相邻 CTA 两两组成 cluster: +在分配硬件角色之前,先把 selected tokens 如何流过 kernel 化成六步。对每个 +包含 128 个 selected tokens 的 tile,重复前五步;所有 tiles 都处理完后,才 +执行第六步: -```python -block_idx = T.cta_id([2 * s_q]) -T.cta_id_in_cluster([2]) -cta_idx: T.let = block_idx % 2 -s_q_idx: T.let = block_idx // 2 -thread_idx = T.thread_id([512]) -T.warpgroup_id([4]) +```text +对每个包含 128 个 selected tokens 的 tile: + 1. gather 该 tile 的 K rows + 2. gather 该 tile 的 V rows,并构造 validity mask + 3. QK:128 个 query heads × 128 个 selected tokens → logits L + 4. 更新 mask 后的 online softmax,得到 W、参考值 mi 和分母 li + 5. 必要时 rescale running state,再累加 O~ += W @ V +所有 selected tiles 完成后: + 6. 用 li + sink 归一化 O~,写回 out、max_logits 和 lse ``` -因此,一个 cluster 负责一个 query row。每个 CTA 含 4 个 warpgroups。先看 -ownership 图。这里最不寻常的是,QK 与 PV 之间的切分轴会发生变化。 +现在算术主线已经清楚了。下一个问题是:两个 thread blocks 怎样协作完成这六步, +又不重复搬运整个 tile? + +### 为什么一个 query row 需要两个 CTA? + +难点出现在第 3、5 步的切分轴不同:QK 要形成所有 head 与 selected token 的 +两两组合,PV 又要沿 token 维归约,产生 512 个 value coordinates。Regular +head-128 实现让两个 CTA 通过 `cta_group=2` 共同形成这块 logical tile,并在 +QK 与 PV 之间旋转切分轴。 + +这个关系先用所有权图(ownership map)表示: ```{figure} ../../img/flashmla_cta_ownership_zh.svg :width: 100% @@ -548,24 +611,45 @@ coordinates。 | V-feature gather ownership | value columns 0--255 | value columns 256--511 | 所以,2-CTA tensor-core operation 不只是“两个 CTA 各做同一个循环的一半”。 -QK 需要形成 128 heads 与 128 selected tokens 的 cross-product,PV 再沿 token -维度做 contraction,得到 512 个 value coordinates。这两次 GEMM 之间的 partition -会发生旋转;collective `cta_group=2` MMA、配对的 SMEM/TMEM layouts 和 -cross-CTA barriers 共同组成一个 logical tile。 +QK 形成 128 个 heads 与 128 个 selected tokens 的两两组合,PV 再沿 token 维 +归约,得到 512 个 value coordinates。Collective `cta_group=2` MMA、配对的 +SMEM/TMEM layouts 和 cross-CTA barriers 共同组成一个 logical tile。 + +现在再回到源码验证 launch topology。Launch grid 包含 `2 * s_q` 个 CTA,并将 +相邻 CTA 两两组成 cluster: -这个划分可以直接从固定版本源码看出:Q 按 `cta_idx` chunk,K producer 选择 +```python +block_idx = T.cta_id([2 * s_q]) +T.cta_id_in_cluster([2]) +cta_idx: T.let = block_idx % 2 +s_q_idx: T.let = block_idx // 2 +thread_idx = T.thread_id([512]) +T.warpgroup_id([4]) +``` + +因此,一个 cluster 负责一个 query row,每个 CTA 含 4 个 warpgroups。这个 +划分还可以从后面的数据索引直接看出:Q 按 `cta_idx` chunk,K producer 选择 每个 top-k block 的 `cta_idx` 半块,V producer 则从 `cta_idx * 256` 开始。 ## 各个 tile 放在哪里? -Blackwell tensor memory(TMEM)让 `tcgen05` 可以把大型 accumulator 放在 -tensor cores 附近,但它不会取代 shared memory(SMEM)。TMA gather 的数据先 -到达 SMEM,softmax warpgroup 也必须在 SMEM 中 materialize BF16 未归一化 -权重,供 PV GEMM 使用。 +进入数据驻留图之前,先统一硬件词汇。**Global memory(GMEM)** 保存 kernel +的输入输出;**shared memory(SMEM)** 是 CTA 内线程和异步搬运共同访问的片上 +存储;**tensor memory(TMEM)** 是 Blackwell tensor cores 附近用于 operands +与 accumulators 的专用片上存储;registers 则归当前线程所有。**Tensor Memory +Accelerator(TMA)** 负责在 GMEM 与 SMEM 之间异步搬运规则 tile,也能根据 +地址列表执行 gather。`tcgen05` tensor-core operation 则从 SMEM/TMEM 读取 +operands,并把大型 accumulators 留在 TMEM。 + +后文还会用两个简写描述 QK 的 operand 来源:**SS** 表示 Q、K 都从 SMEM +读取;**TS** 表示 Q 从 TMEM 读取、K 仍从 SMEM 读取。这条 kernel 将 Q 的 +384-column suffix 搬到 TMEM,只把 prefix 留在 SMEM,所以 QK 要先做 SS +prefix,再做 TS suffix。Softmax 产生的 BF16 未归一化权重则要写入 SMEM,供 +后面的 PV GEMM 使用。 ```{figure} ../../img/flashmla_dataflow_zh.svg :width: 100% -:alt: Global memory、shared memory、tensor memory 与 registers 之间的数据移动 +:alt: QK、softmax、PV 与 epilogue 期间,global memory、shared memory、tensor memory 和 WG0 registers 中的数据驻留与生命周期复用 Q 被拆成 SMEM prefix 和 TMEM suffix。Gather 后的 K/V 进入 SMEM;原始 QK logits 与 output 在 TMEM 中累积;未归一化 softmax weights 再经过 SMEM 交给 @@ -585,9 +669,11 @@ PV。 | TMEM `o_tmem` | `64 x 512` FP32 logical view | running unnormalized output | | SMEM `o_smem` | `64 x 512` BF16 | TMA store 前的 epilogue staging | -这些都是 logical views;CTA-group TMEM layout 和 rearrangement 决定 MMA 与 -load/store instructions 的实际 lane mapping。源码分配一个 512-column -CTA-group TMEM pool,再从中切出 O、raw-logit 和 Q views。 +这些都是逻辑视图(logical views);CTA-group TMEM layout 和 rearrangement +决定 MMA 与 load/store instructions 的实际 lane mapping。源码中的 +`SMEMPool` 是共享内存分配器,用来从同一片动态 SMEM 中切出带对齐和生命周期 +约束的 views。源码还另行分配一个 512-column CTA-group TMEM pool,再从中 +切出 O、raw-logit 和 Q views。 SMEM 采用激进的 alias 与复用策略。只要 lifetime 允许,`q_full`、gather 后的 K/V region 和 output epilogue 就会复用类似 union 的 base。最后 384 个 Q columns 移到 @@ -605,7 +691,8 @@ storage。 ## 每次数据交接由哪个 warpgroup 负责? -四个 warpgroups 各做不同工作,而不是 lockstep 前进: +数据放置确定后,下一问是谁生产每块 tile、谁消费它,以及谁归还可复用空间。 +四个 warpgroups 各做不同工作,而不是齐步推进: | Warpgroup | Warps | 职责 | | --- | --- | --- | @@ -619,10 +706,14 @@ WG3 中剩下的 warps 并没有承担另一个隐藏 stage。这种不对称 ro 而 exponentiation、row reduction、packing 和 epilogue conversion 则适合使用 较多 lanes。 -Register budget 也与 role 对应。WG0 将上限提高到 144 registers,WG3 提高到 -168;producer groups 则降到 96。固定版本 API 用 -`T.ptx.setmaxnreg(True, ...)` 表示提高,用 -`T.ptx.setmaxnreg(False, ...)` 表示降低。 +:::{admonition} Register budget 也跟着角色分配 +:class: note + +WG0 将上限提高到 144 registers,WG3 提高到 168;producer groups 则降到 +96。TIRx API 用 `T.ptx.setmaxnreg(True, ...)` 表示提高,用 +`T.ptx.setmaxnreg(False, ...)` 表示降低。这个配额解释了为什么不同 +warpgroups 适合承担不同工作,但不改变下面的数据交接顺序。 +::: ### 不规则的 rows 如何变成规则的 tiles? @@ -632,8 +723,10 @@ WG1 和 WG2 使用显式 TMA `gather4`:一次 issue 提供恰好 4 个 row coo CTA-pair policy。 下面的上下文摘录回答两个具体问题:一次 `gather4` issue 读取哪些 addresses, -它的 completion 又交给哪个 barrier。Index names 和 slices 与固定 revision -完全相同: +它的 completion 又交给哪个 barrier。读代码时先记住三个名字:`cur_buf` 是 +当前 tile 在两槽 barrier ring 中使用的槽位;`bar` 是 producer 与 consumer +共享的 completion barrier;`leader_mbar(...)` 取得 CTA pair 中负责汇总 TMA +completion 的 leader 地址。Index names 和 slices 与链接源码一致: ```python _kv_gather_tma = partial( @@ -675,20 +768,25 @@ WG0 等待 packed mask,再把对应的原始 logit $L$ 替换成 negative infi attention 的是 packed mask,而不是假设 gather 会填 0。Mask 必须发生在 online-softmax state 更新之前。 -与 upstream API 相同,caller 仍应避免让 `topk_length` 之后的 in-range KV -rows 含有 NaN;优化后的数据路径不保证屏蔽这类异常输入。 +对于 TIRx regular head-128 specialization,caller 应避免让 `topk_length` +之后的 in-range KV rows 含有 NaN;这条优化数据路径不保证屏蔽这类异常输入。 -固定版本源码清楚分开了这些 roles:[K producer 位于 lines +源码清楚分开了这些 roles:[K producer 位于 lines 608--676](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L608-L676), [V producer 位于 lines 679--729](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L679-L729), [validity packing 位于 lines 841--865](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L841-L865)。 -## 为什么 QK 同时使用 SS 与 TS? +至此,不规则的 addresses 已经变成规则的 K/V SMEM tiles。下一问是 tensor core +为什么要从两个 memory spaces 读取同一个 QK dot product。 + +## 为什么 QK 要拆成 SMEM--SMEM 与 TMEM--SMEM 两段? -下面的源码摘录回答 kernel 如何只让一部分 Q 留在 SMEM。QK dot product 在 -$d_{sq}=d_{qk}-384$ 处分成两部分: +前面的驻留图已经定义了 SS 与 TS。拆分的目的,是让 Q 的大块 suffix 尽早离开 +SMEM,从而给 K/V 和 epilogue 让出可复用空间,同时仍让 tensor core 完成完整 +dot product。QK 在 $d_{sq}=d_{qk}-384$ 处分成两部分;下面的源码摘录展示这 +两个 partial products 如何写入同一个 accumulator: ```python if d_sq > 0: @@ -721,9 +819,20 @@ Softmax 之后,PV 是 SS GEMM:BF16 $W$ 和 V 都在 SMEM,FP32 O accumulato ## Online softmax 如何避免不必要的 O 重缩放? -对于连续到来的 score tiles,普通 online-softmax recurrence 会保存 row origin -$m$、denominator $\ell$ 和未归一化 output $\widetilde O$。使用 base 2 时, -若下一块 tile 含有 scaled scores $r$,则: +当 `topk` 大于 `B_TOPK=128` 时,一个 query row 会连续处理多个 selected-token +tiles。每个 tile 都只看到一部分 scores,不能各自独立做完整 softmax;kernel +必须把前面 tiles 的状态带到下一轮。 + +为了直接使用硬件 `exp2`,先把原始 QK dot product $x$ 乘以模型规定的 QK +scale,再转换到以 2 为底的指数单位: + +$$ +r=x\cdot\text{semantic\_QK\_scale}\cdot\log_2(e). +$$ + +对于连续到来的 score tiles,普通 online-softmax recurrence 会保存指数参考值 +$m$、denominator $\ell$ 和未归一化 output $\widetilde O$。若下一块 tile 含有 +base-2 scaled scores $r$,则: $$ m'=\max(m,\max r),\qquad @@ -735,12 +844,16 @@ $$ \widetilde O'=\alpha\widetilde O+\sum_j2^{r_j-m'}v_j. $$ -概念上,实现会将 natural-unit logits 乘以模型语义中的 QK scale 与 -`log2(e)`,再使用 `exp2`。在本章的固定 scale port 中,编译期 +在 TIRx regular head-128 specialization 中,编译期 `sm_scale_div_log2` 就是 `(1 / sqrt(d_qk)) * log2(e)`。这与原来的 softmax 相同,只是改写成直接映射到快速 base-2 exponential instructions 的形式。 +对应到源码,`cur_pi_max` 是当前 128-token tile 的 base-2 最大值,`mi` 是递推 +中实际采用的指数参考值,`li` 是相对于 `mi` 累积的 denominator。`real_mi` +则单独保存迄今为止真实的最大值,用于最终报告 `max_logits`。区分 `mi` 与 +`real_mi`,正是下面 lazy rescaling 能不改变输出统计量的关键。 + 每次 row maximum 增加时都重缩放完整的 512-coordinate O tile,代价会很高。 Head-128 kernel 因此使用 lazy threshold: @@ -757,15 +870,14 @@ else: scale_for_old = T.ptx.exp2(mi - new_max) ``` -如果新 tile maximum 比保存的 origin 至多高 6 个 base-2 units,kernel 会继续 -保留旧 origin。新的 exponential 此时最大可能达到 $2^6=64$,但 accumulated -O 无需 rescale。一旦差值超过 6,kernel 就执行 rebase,同时 rescale $\ell$ +如果当前 tile 的最大值比保存的指数参考值至多高 6 个 base-2 units,kernel +会继续保留旧参考值。新的 exponential 此时最大可能达到 $2^6=64$,但已累积 +的 O 无需 rescale。一旦差值超过 6,kernel 就更新参考值,同时 rescale $\ell$ 和已经存在的 O。Warp-wide `any_sync` 让参与计算的 rows 使用一致的决策。 -`real_mi` 单独维护截至当前看到的精确 maximum,所以这项优化不会改变 -`max_logits`:`mi` 是 recurrence 使用的 numerical origin,`real_mi` 则是 -最终报告的统计量。结束时,两个 64-token half 对每个 logical row 的贡献会被 -合并,kernel 输出: +`real_mi` 始终维护迄今为止真实的最大值,所以这项优化不会改变 +`max_logits`。结束时,两个 64-token half 对每个 logical row 的贡献会被合并, +kernel 输出: $$ \mathrm{lse}=m\ln 2+\ln\ell. @@ -780,31 +892,39 @@ output_scale: T.float32 = T.cuda.fdividef( ``` 但它有意不改变报告的 LSE。对于全 invalid row,特殊分支会输出 0,同时令 -`max_logits=-inf`、`lse=+inf`,与固定版本 reference 一致。 +`max_logits=-inf`、`lse=+inf`,与前面的 reference 一致。 ## 各个阶段如何安全重叠? -把这个 schedule 看成一个依赖关系问题最容易理解。QK 必须先完成,softmax -才能消费它的 logits;softmax 必须先产生 weights,PV 才能开始。但是,只要 -原位复用的 K 或 V segment 已经安全释放,负责 gather 的 warpgroups 就应该 -继续向前推进。 +把这个 schedule 看成“数据所有权何时交给下一角色”最容易理解。宏观上,每个 +tile 依次经历 `K ready → QK done → L consumed → W ready → PV done → V/O +reusable`。QK 必须先完成,softmax 才能消费 logits;softmax 必须先产生 weights, +PV 才能开始。但是,只要原位复用的 K 或 V segment 已经安全释放,负责 gather +的 warpgroups 就应该继续向前推进。 + +源码用 **memory barrier(mbarrier)** 表示这些交接。Producer 在数据或异步 +操作完成时贡献 arrival,consumer 等待相应 phase;consumer 用完后,再通过 +done/free barrier 把覆盖这段 storage 的权利交还 producer。也就是说,ready +保护“不要过早读取”,done/free 保护“不要过早覆盖”。 ```{figure} ../../img/flashmla_pipeline_stages_zh.svg :width: 100% -:alt: QK、softmax 与 PV 在相邻 tile 之间的稳态重叠 +:alt: 相差一个 tile 的 pipeline 填充、稳态与排空,以及 QK、softmax、PV 的重叠 -Softmax($k-1$) 可与 QK($k$) 重叠;唯一的 MMA issuer 串行发出 QK($k$) 与 -PV($k-1$);随后 softmax($k$) 可与异步执行的 PV($k-1$) 重叠。这不是两条 -同时发射 QK 与 PV 的 tensor-core streams。 +填充阶段只发起 QK(0),没有上一块 PV;排空阶段只发起 PV($N-1$),随后进入 +最终 epilogue。稳态中,softmax($k-1$) 可与 QK($k$) 重叠;唯一的 MMA issuer +串行发出 QK($k$) 与 PV($k-1$);QK($k$) 完成后,softmax($k$) 可与仍在异步 +执行的 PV($k-1$) 重叠。这不是两条同时发射 QK 与 PV 的 tensor-core streams。 ``` -Kernel 先由 warp 0 初始化 mbarriers,执行 cluster sync,launch Q prologue, -分配 CTA-group TMEM,再进入 specialized loops。 +有了这张宏观时间线,再看初始化和具体 barrier 名称。Kernel 先由 warp 0 初始化 +mbarriers,执行 cluster sync,launch Q prologue,分配 CTA-group TMEM,再进入 +specialized loops。 CTA-group gather 的 TMA completion 会被路由到指定的 leader barrier,使 CTA pair 发出的操作共同满足同一 expected byte count。 -把主要 barrier edges 写成 ownership transfer 会更容易理解: +把主要 barrier edges 写成 storage ownership transfer 会更容易理解: | Barrier | Producer 到 consumer | 保护的 storage | | --- | --- | --- | @@ -827,14 +947,14 @@ tensor-core streams。 QK($k$) 之后发出 PV($k-1$);QK($k$) 完成后,softmax($k$) 又可以与仍在异步 执行的 PV($k-1$) 重叠。所有这些重叠仍受上述 part-level edges 约束。 -Ring index 是: +Barrier 槽位按下面的方式循环使用: ```python cur_buf = k % 2 cur_phase = (k // 2) & 1 ``` -这样,复用的 barrier slot 可以区分本轮的新 arrival 与两轮之前的旧 arrival。 +这样,复用的 barrier slot 可以区分本轮到达与两轮之前的旧到达。 再次强调,这是一条 two-slot *barrier/phase ring*,并不是让两个完整 KV tiles 同时 resident。 @@ -844,38 +964,43 @@ cur_phase = (k // 2) & 1 ```{figure} ../../img/flashmla_pipeline_zh.svg :width: 100% -:alt: Sparse-prefill pipeline,其中当前 tile 执行 QK,前一个 tile 执行 PV +:alt: Sparse-prefill 详细 pipeline,展示 QK 与 PV 的串行发起、K/V 分段复用、mask-slot ring 和 WG0 交接 在稳态中,QK($k$) 与 PV($k-1$) 交错发起,其他 roles 同时执行分段 K/V gather 和 softmax。Barrier phase 保护 in-place storage reuse,而不是选择两份 完整 tile buffer。 ``` -这些 edges 周围会出现两类 fence。`T.ptx.tcgen05.fence.*` 对 TMEM access 与 -thread-visible work 做 ordering;`T.ptx.fence.proxy_async("shared::cta")` 则在 -SMEM 的 generic access 与 asynchronous access 之间建立 cross-proxy ordering。 +Barrier 只说明“某项工作已经完成”,还要处理不同 memory proxy 的可见性。 +这里有两类 proxy:线程执行的普通 SMEM load/store 属于 **generic proxy**, +TMA 与 tcgen05 的异步访问属于 **async proxy**。如果一边写、另一边读同一片 +SMEM,仅有 barrier arrival 并不能自动约束两个 proxy 观察 memory effects 的 +先后关系。 -这里既包括 generic store 写入 $W$ 或 epilogue tile 后,tcgen05/TMA 执行 -asynchronous read,也包括 asynchronous SMEM read 完成后,generic code 覆写 -alias storage。 +因此,`T.ptx.tcgen05.fence.*` 约束 TMEM access 与线程可见操作的先后关系; +`T.ptx.fence.proxy_async("shared::cta")` 则在 SMEM 的 generic 与 async proxy +之间建立顺序。它既用于普通 store 写入 $W$ 或 epilogue tile 后、tcgen05/TMA +执行异步读取之前,也用于异步 SMEM read 完成后、普通代码覆写共用 storage +之前。 -Mbarrier 传达 completion 与 ownership handoff;proxy fence 则对不同 proxy 的 -memory effects 做 ordering,两者不能互相替代。 +Mbarrier 传达 completion 并移交 storage 使用权,proxy fence 则约束不同 proxy +的 memory effects;两者不能互相替代。 -## 如何编译并验证整条路径? +## 如何编译并验证 regular head-128 specialization? -固定版本 module 面向 compute capability 10,其 TMA/tcgen05 形式要求 SM100 -class GPU。环境应使用 B200、CUDA 12.9 或更高版本,以及官方 Apache TVM -0.26.0 package。 +到这里需要验证三件不同的事:regular head-128 实现能否用 TVM 0.26 +编译,生成的 kernel 能否在 B200 上实际 launch,以及它的 output、maximum +logits 和 LSE 是否与前面的 reference 一致。只完成第一项并不能证明后两项。 -Kernel 使用的是这个 release 的 TIRx API,而不是持续变化的 development -checkout 写法。 +这个 specialization 面向 compute capability 10,其 TMA/tcgen05 形式要求 +SM100 class GPU。环境应使用 B200、CUDA 12.9 或更高版本,以及官方 Apache +TVM 0.26.0 package。 首先通过 [PyTorch 官方选择器](https://pytorch.org/get-started/locally/)安装 支持 B200 的 CUDA-enabled PyTorch build。Companion repository 会 import PyTorch,但没有把它声明为 package dependency。 -随后安装 TVM、固定 kernel repository,再运行示例: +随后安装 TVM 和 kernel repository,再运行示例: ```bash python -m pip install "apache-tvm==0.26.0" cuda-bindings @@ -924,45 +1049,52 @@ Negative tests 同样重要。设置 `inject_invalid_indices=True` 可以覆盖 row ID,设置 `have_topk_length=True` 可以覆盖 position predicate。还应测试全 invalid row,并确认约定的 0/-infinity/+infinity 行为。最后,对 head-64 和 small-top-k shapes 调用统一 dispatch entry,避免把一次成功的 regular-head128 -运行误认为完整 API coverage。 +运行误认为已经覆盖全部 prefill specializations。即便这些 dispatch 都能通过, +也不能据此声称与完整 FlashMLA API 等价。 -## 哪五条不变量定义了这条路径? +这些正向与异常输入测试,分别对应下面要总结的 operator semantics 与 +specialization schedule contract。 + +## 哪些不变量属于 operator,哪些属于 specialization? 1. **缓存不变量(cache invariant)。** 一条 `h_kv=1` 的 latent KV row 可以 - 服务 128 个 query heads,是因为 key up-projection 已吸收到各 head 的 query - 路径,而 value up-projection 被移到 core attention 之后。RoPE channel 仍 - 保持显式,QK scale 仍是模型语义规定的 scale。 + 服务全部 `h_q` 个 query heads,是因为 key up-projection 已吸收到各 head 的 + query 路径,而 value up-projection 被移到 core attention 之后。RoPE channel + 仍保持显式,QK scale 仍是模型语义规定的 scale。 2. **稀疏契约不变量(sparse-contract invariant)。** Token selection 发生在 - 这个 kernel 之前;`indices` 提供 rows,重复项仍按重复项计算,因果合法性由 - caller 保证,并且每个 `topk_length` 都必须位于 `[0, topk]`。优化路径与 - reference path 必须保持相同的 attention sink 和全 invalid 约定。 - -3. **所有权不变量(ownership invariant)。** 一个 2-CTA cluster 负责一个 - query row。这对 CTA 沿不同的轴切分 Q/output heads、selected K rows 和 V - features;CTA 0 的 warp 12 是 CTA-group MMA 的唯一 issuer。 - -4. **驻留不变量(residency invariant)。** $L$ 表示 FP32 原始 logits,$W$ - 表示 BF16 未归一化指数权重。K、V、$L$ 和 $W$ 的大型 workspace 都是原位 - 复用的单份 tile,而 `NUM_BUFS=2` 驱动的是 barrier/phase ring。在数据缓冲区 - (data buffers)中,只有小型 packed-validity mask 才有两个 physical slots。 - -5. **交接不变量(handoff invariant)。** Ready/done barriers 转移每个可复用 - segment 的 ownership,proxy fences 则对 generic 与 asynchronous SMEM - access 排序。唯一 issuer 保证 QK($k$) 先于 PV($k-1$) 发射,而 threshold - 为 6 的优化保证上报 maximum 的语义不变,并保持 online LSE 的递推关系。 - -前两条不变量定义 operator semantics,后三条定义这个 specialization 的 -schedule contract。其他 dispatch 可以修改 tile sizes、register budgets、 -ownership 或 barrier topology,但必须显式给出替代 contract,而不能悄悄改变 -operator 所计算的结果。 + sparse-prefill operator 之前;`indices` 提供 rows,重复项仍按重复项计算, + 因果合法性由 caller 保证,并且每个 `topk_length` 都必须位于 `[0, topk]`。 + 优化路径与 reference path 必须保持相同的 attention sink 和全 invalid 约定。 + +3. **所有权不变量(ownership invariant)。** 在 regular head-128 + specialization 中,一个 2-CTA cluster 负责一个 query row。这对 CTA 沿 + 不同的轴切分 Q/output heads、selected K rows 和 V features;CTA 0 的 + warp 12 是 CTA-group MMA 的唯一 issuer。 + +4. **驻留不变量(residency invariant)。** 在这个 specialization 中,$L$ + 表示 FP32 原始 logits,$W$ 表示 BF16 未归一化指数权重。K、V、$L$ 和 $W$ + 的大型 workspace 都是原位复用的单份 tile,而 `NUM_BUFS=2` 驱动的是 + barrier/phase ring。在数据缓冲区(data buffers)中,只有小型 + packed-validity mask 才有两个 physical slots。 + +5. **交接不变量(handoff invariant)。** 在这个 specialization 中,ready/done + barriers 转移每个可复用 segment 的 ownership,proxy fences 则对 generic + 与 asynchronous SMEM access 排序。唯一 issuer 保证 QK($k$) 先于 + PV($k-1$) 发射,而 threshold 为 6 的优化保证上报 maximum 的语义不变, + 并保持 online LSE 的递推关系。 + +前两条不变量定义 FlashMLA sparse-prefill operator semantics,后三条定义 +regular head-128 specialization 的 schedule contract。另一条由 dispatch 选中的 +specialization 可以修改 tile sizes、register budgets、ownership 或 barrier +topology,但必须显式给出替代 contract,而不能悄悄改变 operator 所计算的结果。 ## 接下来应该测试什么? -Regular head-128 kernel 只是 dispatch space 中的一个点。固定版本源码树还包含 -64-head phase-1 kernel,以及 128-head `d_qk=512` small-top-k kernel。它们使用 -不同 schedule,这说明 sparse attention 应根据 tile economics 做 dispatch, -而不应被强行塞进一个 universal template。 +Regular head-128 specialization 只是 dispatch space 中的一个点。源码树还包含 +head-64 phase-1 specialization,以及 head-128 `d_qk=512` small-top-k +specialization。它们使用不同 schedule,这说明 sparse attention 应根据 tile +economics 做 dispatch,而不应被强行塞进一个 universal template。 1. **复现 weight absorption。** 给可执行的 absorption proof 加入 causal mask。 确认 MHA mode 与 MQA mode 仍然一致,再故意把 absorbed path 的 scale 改为 @@ -982,10 +1114,10 @@ Regular head-128 kernel 只是 dispatch space 中的一个点。固定版本源 5. **测量 threshold。** 对 random 和 adversarial logits 加入 instrumentation, 统计 `should_scale_o` 取 true 的频率。比较 threshold 6、always-rebase 和 - never-rebase 三个版本的 numerical error 与 TMEM O traffic。 + never-rebase 三种策略的 numerical error 与 TMEM O traffic。 6. **比较 dispatch。** 对 head count 64/128、`d_qk` 512/576,以及 1280 附近的 - top-k values 调用 `select_kernel`。运行前先预测选择的 module,再检查哪些 + top-k values 调用 `select_kernel`。运行前先预测选择的 specialization,再检查哪些 constraint 属于 front door,哪些由单个 specialization 强制执行。 7. **阅读 generated program。** 编译 smoke shape,在生成的 PTX 中找到 From 1931b94c497327984560435d1cb76e359f08ec1d Mon Sep 17 00:00:00 2001 From: tlopex <820958424@qq.com> Date: Wed, 12 Aug 2026 16:24:39 -0400 Subject: [PATCH 3/5] Restructure FlashMLA tutorial progression --- chapter_flashmla/index.md | 580 +++++++++++++++++---------- zh/chapter_flashmla/index.md | 754 ++++++++++++----------------------- 2 files changed, 630 insertions(+), 704 deletions(-) diff --git a/chapter_flashmla/index.md b/chapter_flashmla/index.md index 22d1cd15..5d361614 100644 --- a/chapter_flashmla/index.md +++ b/chapter_flashmla/index.md @@ -10,10 +10,8 @@ - Define the FlashMLA sparse-prefill operator: an external indexer selects KV rows, then FlashMLA attends over those rows. An executable reference fixes its numerical behavior and edge cases. -- Use the TIRx `flash_mla_sparse_fwd` entry to understand shape dispatch and how - it specializes the QK scale, then follow the regular head-128 - specialization through two-CTA ownership, data residency, specialized roles, - and the pipeline before compiling and verifying it on B200. +- Use a concrete implementation to understand how sparse attention maps to + Blackwell, then compile and verify it on B200. ::: Before introducing MLA, recall why ordinary attention needs a **KV cache**. To @@ -21,10 +19,17 @@ compute a new query, attention must read the keys and values of earlier tokens. Recomputing them every time would repeat a large amount of work, so the system caches the K/V states and lets later queries read them directly. +Those states remain reusable because generative models normally use causal +attention: the K/V at position $s$ depend only on tokens up to position $s$. +Appending later tokens cannot change them. Prefill computes the prompt tokens +in parallel and fills the cache; decode then reads that cache step by step and +appends the new token's K/V. A KV cache therefore trades storage capacity and +read bandwidth for avoiding repeated computation over the whole prefix. + In ordinary multi-head attention (MHA), every attention head has its own K and V. The KV cache must therefore store every head's K/V for every processed token. As the context grows, the amount of state that must be stored and read grows -with it. MLA's first goal is to reduce this cache. +with it. The next problem is how to reduce this cache. **Multi-head Latent Attention (MLA)** uses a different cache representation. Instead of storing expanded K/V for every head, it stores one compressed state @@ -38,29 +43,18 @@ addresses how to perform those computations efficiently on a GPU. **FlashMLA** is DeepSeek's library of optimized GPU kernels for MLA, with operators for different attention stages and cache formats. -This chapter begins with sparse prefill. *Prefill* means processing the prompt's -query tokens in parallel; *sparse* means that an external indexer first selects -the relevant KV rows and attention visits only those rows. - -The sparse-prefill operator does not map to one immutable kernel. This chapter -keeps three layers distinct. The FlashMLA `flash_mla_sparse_fwd` interface is -the semantic thread: it defines the inputs, outputs, and computation of sparse -prefill. The TIRx registry entry with the same name is a dispatch bridge with a -narrower call signature: its specializations bind `sm_scale` to -`1 / sqrt(d_qk)` and it selects a head-64, regular head-128, or small-top-k -head-128 specialization by shape. The regular head-128 specialization is the -implementation thread: it shows how Blackwell schedules that computation. -Other implementations appear only when comparing operator families, dispatch, -and design tradeoffs. - -In the regular head-128 specialization, MLA's sharing is especially visible. -One query token corresponds to a query row containing 128 query heads, while -each cached token contributes one shared KV row. How can 128 heads read the same -KV row and still produce different results? The next figure gives the first -clue. What is shared is the source state used to form K/V, not the final -representation consumed by every head. Head-specific transformations remain on -the two sides of the dot-product, softmax, and weighted-sum core. We will list -the exact tensor shapes after deriving MLA. +This chapter focuses on sparse attention during prefill. Unlike dense attention, +which visits the whole history, an external indexer first selects the relevant +KV rows and FlashMLA attends only to those rows. We will first establish the +shared operator semantics and postpone implementation choices until the +algorithm is clear. + +This raises the central MLA question: if multiple query heads read one shared +cached state, how can they still produce different results? The key is that only +the compressed source state is shared. Head-specific transformations do not +disappear; they move to the two sides of the core attention computation. The +next figure uses 128 heads to make the question concrete, while the derivation +that follows keeps the head count general. ```{figure} ../img/flashmla_cache_story.png :width: 100% @@ -72,12 +66,8 @@ head-specific query and output transformations happen before and after attention. ``` -The figure gives intuition, but it does not yet explain how a shared state -preserves head-specific behavior or prove why moving these transformations -leaves the computation unchanged. We will first quantify the ordinary MHA -cache, derive what MLA stores, and prove why the transformations can move. Only -then will we turn to the sparse operator and the regular head-128 -specialization's Blackwell schedule. +Why is the transformation in the figure valid? Start with the ordinary MHA KV +cache. ## Start with the ordinary MHA KV cache @@ -107,12 +97,29 @@ generation, however, every earlier $k_{s,i}$ and $v_{s,i}$ must remain available The cache therefore stores $2n_h d_h$ elements per token per layer: one K slice and one V slice for every head. +Batch size, sequence length, layer count, and dtype quickly amplify that number. +For a batch of $B$ equal-length sequences of length $S$, a model with +$N_{layer}$ layers, and $b_{elem}$ bytes per element, an ordinary MHA KV cache +occupies + +$$ +M_{MHA}=2N_{layer}BSn_hd_hb_{elem}\quad\text{bytes}. +$$ + +For a variable-length batch, replace $BS$ with $\sum_{j=1}^{B}S_j$, where $S_j$ +is the length of sequence $j$. As a concrete example, 32 layers, batch size 1, +context length 4096, 32 heads of width 128, and BF16 require 2 GiB for the KV +cache alone. This estimate excludes allocator metadata, model weights, and +other intermediate state. + For a fixed $d_{model}=n_h d_h$, changing only the head count need not change that total width. The structural cost is that the cache still materializes separate per-head state. -During a long decode, reading those slices for the growing token history can -dominate the step. +During dense decode, each new query reads the growing K/V history, so those +reads often become a bottleneck. A smaller representation not only permits a +longer context or larger batch; it also reduces HBM traffic on every decode +step. Multi-query attention (MQA) reduces the cache by sharing one K/V head across all query heads. Grouped-query attention shares within groups. Those are useful model @@ -120,10 +127,39 @@ architectures, but MLA takes a different route: retain the expressive per-head projections while caching a shared low-dimensional source from which they can be recovered. -### How does MLA cache once and recover per-head behavior? +### What if we cache one shared state first? + +Temporarily ignore RoPE and low-rank compression. Let $h_s$ denote the hidden +state fed to the attention projections at position $s$ in one layer. It is not +a token embedding from the vocabulary. The superscript $C$ denotes the +non-positional content channel; ordinary MHA content keys and values are + +$$ +k_{s,i}^{C}=W_i^Kh_s,\qquad v_{s,i}^{C}=W_i^Vh_s. +$$ + +If we cache one shared $h_s$, associativity and the distributivity of a linear +map over a sum let us change the evaluation order: + +$$ +(q_{t,i}^{C})^{\mathsf T}W_i^Kh_s +=\left((W_i^K)^{\mathsf T}q_{t,i}^{C}\right)^{\mathsf T}h_s, +\qquad +\sum_s p_{t,s,i}W_i^Vh_s +=W_i^V\left(\sum_s p_{t,s,i}h_s\right). +$$ + +The left side expands K/V for every key and every head. The right side moves +the key projection to the current query and the value projection after the +weighted sum. The values are identical, yet only one $h_s$ must persist. Think +of this as an uncompressed latent-cache thought experiment. -The original [DeepSeek-V2 MLA derivation](https://arxiv.org/abs/2405.04434) -introduces a joint latent KV vector +The problem is that $h_s$ is still $d_{model}$ coordinates wide. The cache is +shared across heads, but QK (the query--key dot product) and PV (the +probability--value weighted sum) now operate in that wide space, so this is +usually not a practical design. MLA adds a learned low-rank bottleneck that +shrinks the shared state to $d_c$ coordinates. The original +[DeepSeek-V2 MLA derivation](https://arxiv.org/abs/2405.04434) defines $$ c_t^{KV}=W^{DKV}h_t, @@ -136,49 +172,94 @@ k_{t,i}^{C}=W_i^{UK}c_t^{KV},\qquad v_{t,i}^{C}=W_i^{UV}c_t^{KV}. $$ -The superscript $C$ denotes the non-positional, or *content*, channel. The key -observation is that the cache need not store the expanded $k^C$ and $v^C$ for -every head. It stores one $c^{KV}$ per token instead. +Here $c^{KV}\in\mathbb{R}^{d_c}$ is the shared latent state. The thought +experiment above corresponds to $d_c=d_{model}$, $W^{DKV}=I$, $c^{KV}=h$, +$W_i^{UK}=W_i^K$, and $W_i^{UV}=W_i^V$; MLA learns a much narrower $c^{KV}$. + +This low-rank step is not a lossless compression of an arbitrary pretrained +MHA. It is a joint low-rank structure imposed during training. If we write the +MLA content path as an equivalent projection from $h_t$, its effective K/V +projection matrices factor as + +$$ +W_i^K=W_i^{UK}W^{DKV},\qquad +W_i^V=W_i^{UV}W^{DKV}. +$$ + +Thus every head's content K/V projections share the right factor $W^{DKV}$. +These $W_i^K$ and $W_i^V$ denote the effective MLA projections defined by this +factorization; the equations do not claim that arbitrary MHA projection +matrices can always be factored this way. Under the MLA training constraint, +the model learns what information to preserve in $c^{KV}$. + +The construction therefore has two steps: use associativity and linearity to +move per-head projections to the query and output paths so that one shared state +can participate directly in core attention, then use a learned bottleneck to +make that state narrow. The cache stores one $c^{KV}$ per token instead of +expanded $k^C$ and $v^C$ for every head. + +### Why does RoPE need a separate positional channel? Rotary positional embedding (RoPE) rotates a position-carrying subspace of Q -and K. This complicates the simple picture above: inserting that -position-dependent rotation between $W^{UK}$ and a dot product would prevent -the matrices from being reassociated. MLA therefore uses a decoupled positional -channel: each query head has -$q_{t,i}^{R}$, while all heads share a cached $k_t^R$. The actual MHA-form score -uses +and K. Let $R_u$ denote the RoPE rotation at position $u$. Suppose we applied +RoPE directly to the content query and key. Their dot product would become $$ -q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad -k_{s,i}=[k_{s,i}^{C};k_s^R]. +\left(R_tq_{t,i}^{C}\right)^{\mathsf T} +\left(R_sW_i^{UK}c_s^{KV}\right) += +(q_{t,i}^{C})^{\mathsf T}R_t^{\mathsf T}R_sW_i^{UK}c_s^{KV}. $$ -The cache is now $[c_s^{KV};k_s^R]$, still shared across heads. The positional -channel remains explicit; weight absorption applies to the content channel. +The factor $R_t^{\mathsf T}R_s$ changes with the relative query/key position. +Matrix multiplication can still be reassociated, of course, but $W_i^{UK}$ can +no longer be folded into one projection that the current query can reuse for +every key position. MLA therefore uses a decoupled positional channel: each query head has +$q_{t,i}^{R}$, while all heads share a cached $k_t^R$. The actual MHA-form query +and key are -:::{admonition} The query side can also be compressed -:class: note +$$ +q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad +k_{s,i}=[k_{s,i}^{C};k_s^R]. +$$ -MLA may factor the query projection through a separate low-rank latent, +The unscaled score therefore separates into $$ -c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +\operatorname{score}_{t,s,i} +=(q_{t,i}^{C})^{\mathsf T}W_i^{UK}c_s^{KV} ++(q_{t,i}^{R})^{\mathsf T}k_s^R. $$ -This factorization mainly reduces activation memory during training; it does -not shrink the KV cache further. It also happens before FlashMLA's core -attention: the `q` tensor presented to the sparse-prefill operator is already -projected. We therefore treat $q^C$ as an input and continue along the KV-cache -path. -::: +The cache is now $[c_s^{KV};k_s^R]$, still shared across heads. The positional +channel remains explicit; weight absorption applies to the content channel. + +This lets us compare MLA with ordinary MQA precisely. The table counts cached +elements per token per layer; it does not compare model quality or include dtype +and allocator metadata. + +| Mechanism | Cached elements per token per layer | Cached state | +| --- | ---: | --- | +| MHA | $2n_hd_h$ | $n_h$ expanded K/V heads | +| GQA | $2n_{kv}d_h$ | $n_{kv}$ expanded K/V heads, $1 logits L + 4. update masked online softmax, producing W, origin mi, and denominator li + 5. rescale the running state when needed, then accumulate O~ += W @ V +after all selected-index tiles: + 6. normalize O~ by li + sink; store out, max_logits, and lse +``` + +In the concrete example, the first five steps repeat 16 times before the sixth +step runs. With the arithmetic thread fixed, we can now ask how TIRx assigns +the hardware roles. + +We now focus on TIRx's regular head-128 implementation in +[`sparse_prefill_head128_phase1.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py). +TIRx extends TVM 0.26's TIR Python DSL: `T` denotes the TIR script namespace, +while `Tx` contains GPU-kernel helpers. Despite the internal `phase1` name, +this specialization produces the complete `(out, max_logits, lse)` result in +one kernel; it is not a partial split-KV output awaiting a combine kernel. + +Three execution levels recur below. A cooperative thread array (CTA) is one +CUDA thread block. Two adjacent CTAs form a cluster that can participate in +CTA-group tensor-core operations. A warpgroup is four warps, or 128 threads, +assigned one specialized role. Here one two-CTA cluster owns one query row. + +In the mathematical introduction, $p$ denoted a normalized softmax +probability. In the source, however, `tmem_p` and the register variable `p` +hold the raw QK logits already named $L$. The source's `s_frag` and +`s_smem_gemm` hold the unnormalized exponential weights already named $W$. +Only the epilogue divides the accumulated output by `li` plus the optional sink +term. + +All shorter TIRx code blocks below are contextual excerpts from the linked +implementation, not standalone programs. The complete module is compiled and +numerically verified in the final section. Blocks intended to run independently +are called out explicitly. -With the specialization's tensor shapes fixed, the following constants -determine one tile's execution: +With the tensor contract fixed, the following constants determine one tile's +execution: ```python B_H = 128 @@ -615,12 +776,12 @@ D_TQ = 384 ``` The names map directly to the work we will trace: `B_H` is the 128-head logical -tile, `B_TOPK` is the 128 selected rows processed per streaming tile, `D_V` is -the value/output width, and `D_TQ` is the 384-coordinate Q suffix placed in -Blackwell tensor memory. `NUM_THREADS=512` gives each CTA four warpgroups. -`NUM_BUFS=2` names two synchronization slots (and two small validity-mask -slots), not two full K/V data stages; the residency and pipeline sections will -make that distinction concrete. +tile, `B_TOPK` is the 128 selected-index slots processed per streaming tile, +`D_V` is the value/output width, and `D_TQ` is the 384-coordinate Q suffix moved +to dedicated on-chip storage. `NUM_THREADS=512` gives each CTA four +warpgroups. `NUM_BUFS=2` names two synchronization slots (and two small +validity-mask slots), not two full K/V data stages; the residency and pipeline +sections will make that distinction concrete. The regular head-128 specialization accepts `d_qk` 512 or 576, requires `h_kv=1`, `d_v=512`, and requires `topk` to be a positive multiple of 128. The @@ -655,22 +816,8 @@ The dispatch itself is documented in Keeping dispatch separate from the device schedule prevents a tutorial from mistaking one specialization for the entire operator. -Before assigning hardware roles, reduce one selected tile to six semantic -steps. This is the bridge between the CPU oracle and the schedule: - -```text -for each selected 128-row tile: - 1. gather the tile's K rows - 2. gather its V rows and build the validity mask - 3. compute raw logits L = Q @ K.T - 4. update masked online softmax, producing W, origin mi, and denominator li - 5. rescale the running state when needed, then accumulate O~ += W @ V -after all selected tiles: - 6. normalize O~ by li + sink; store out, max_logits, and lse -``` - -The arithmetic is now familiar. The next question is how two thread blocks can -cooperate on these six steps without duplicating the whole tile. +Dispatch has selected the implementation. The next question is how two thread +blocks cooperate on the six steps without duplicating the whole tile. ### Why does one query row need two CTAs? @@ -723,21 +870,13 @@ starts at `cta_idx * 256`. ## Where do the tiles live? The ownership map says *who* computes each piece; residency explains where a -piece waits between producers and consumers. Four hardware terms are enough to +piece waits between producers and consumers. Three storage terms are enough to read the next figure: - global memory (GMEM) holds the input and output tensors; - shared memory (SMEM) is the ordinary on-chip scratchpad visible to a CTA; -- the Tensor Memory Accelerator (TMA) moves data asynchronously between GMEM - and SMEM and provides the sparse `gather4` path used here; -- Blackwell tensor memory (TMEM) is a separate on-chip space used by the - `tcgen05` tensor-core instruction family for operands and accumulators. - -TMEM does not replace SMEM. TMA gathers arrive in SMEM, and the softmax -warpgroup must materialize BF16 unnormalized weights in SMEM for the PV GEMM. -In the source's MMA shorthand, **SS** means that both matrix operands come from -SMEM; **TS** means that the first comes from TMEM and the second from SMEM. The -Q prefix follows the SS path and its suffix follows the TS path. +- Blackwell tensor memory (TMEM) is a separate on-chip space near the tensor + cores, used for operands and large accumulators. ```{figure} ../img/flashmla_dataflow.png :width: 100% @@ -748,6 +887,18 @@ raw QK logits and the output accumulate in TMEM, and unnormalized softmax weights cross back through SMEM for PV. ``` +The arrows in the figure correspond to two Blackwell mechanisms. The Tensor +Memory Accelerator (TMA) moves data asynchronously between GMEM and SMEM and +provides the sparse `gather4` path used here. The `tcgen05` tensor-core +instruction family reads operands from SMEM or TMEM and keeps its large +accumulators in TMEM. TMEM therefore complements rather than replaces SMEM: +TMA gathers land in SMEM, and the softmax warpgroup materializes BF16 +unnormalized weights there for PV. + +The source abbreviates tensor-core operand residency as **SS** when both matrix +operands come from SMEM and **TS** when the first comes from TMEM and the second +from SMEM. The Q prefix follows the SS path; its suffix follows the TS path. + For one CTA, the important logical views are: | Storage | Logical tile | Lifetime and purpose | @@ -776,6 +927,11 @@ $d_{sq}=d_{qk}-384$ prefix must stay live for the first QK part. For The allocation plan is visible in [`sparse_prefill_head128_phase1.py` lines 302--365](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L302-L365). +A **completion barrier** is a small hardware state object that records when an +asynchronous producer has finished. Its phase bit distinguishes successive +uses of the same barrier slot; later sections will spell out the complete +producer--consumer protocol. + One important caveat is that `NUM_BUFS = 2` does **not** allocate two complete K, V, $L$, or $W$ tiles. Those arrays have no stage axis. `NUM_BUFS` drives the two-slot barrier/phase ring and also gives the small packed-validity mask two @@ -808,6 +964,13 @@ as `T.ptx.setmaxnreg(True, ...)` for an increase and `T.ptx.setmaxnreg(False, ...)` for a decrease. ::: +Before following a gather, keep one minimal synchronization model in mind. A +producer waits until a tile's storage is **free**, writes or asynchronously +fills the tile, and signals **ready**. The consumer waits for ready, uses the +tile, and signals free when the storage may be overwritten. These barriers +transfer ownership of storage; they do not imply that two complete data tiles +exist. + ### How do irregular rows become regular tiles? Sparse row addresses destroy the contiguous 2-D copy pattern used by dense @@ -868,10 +1031,6 @@ not an assumed zero value from the gather, decides whether a finite KV row participates in attention. Masking must happen before online-softmax state is updated. -Callers should avoid NaNs in in-range KV rows referenced beyond `topk_length`. -The sparse-prefill interface does not promise to sanitize that exceptional -case. - The implementation source separates these roles cleanly: the [K producer is at lines 608--676](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L608-L676), the [V producer is at lines 679--729](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L679-L729), @@ -918,7 +1077,8 @@ coordinates. ## How does online softmax avoid needless O rescaling? QK has produced raw logits $L$; softmax must now turn each tile into $W$ while -preserving state from earlier selected tiles. Let $x$ be one raw QK dot product. +preserving state from earlier selected tiles. In the running shape, this is why +the state must be merged across $N=16$ tiles. Let $x$ be one raw QK dot product. The kernel first places it in the base-2 exponent domain: $$ @@ -996,10 +1156,10 @@ executable reference. ## How can the stages overlap without racing? -The schedule is easiest to understand as a dependency puzzle. QK must finish -before softmax consumes its logits. PV must wait until softmax has produced its -weights. Yet the gather warpgroups should keep moving whenever the in-place K or -V segment they need has become reusable. +The ready/free ownership model introduced before gather now expands into a +pipeline. QK must finish before softmax consumes its logits, and PV must wait +until softmax has produced its weights. Meanwhile, the gather warpgroups move +forward whenever an in-place K or V segment becomes reusable. ```{figure} ../img/flashmla_pipeline_stages.png :width: 100% @@ -1010,7 +1170,7 @@ issues PV($N-1$) without a new QK before the final epilogue. In steady state, softmax($k-1$) may overlap QK($k$). The sole MMA issuer then issues PV($k-1$) after QK($k$); once QK($k$) completes, softmax($k$) may overlap that PV. Producer warpgroups gather the next safe K/V segments around this serial issuer -order. +order. For the running shape, $N=16$. ``` At the coarsest level, four ownership handoffs repeat for each tile: @@ -1023,10 +1183,9 @@ At the coarsest level, four ownership handoffs repeat for each tile: rescale or finalize. An **mbarrier** is the hardware completion object behind these handoffs. It -tracks expected arrivals or TMA bytes and carries a phase, so a wait means that -the named production step has completed for the intended reuse of a slot. This -four-step view gives the causal chain; the exact table below splits K and V into -the finer parts needed for early reuse. +tracks expected arrivals or TMA bytes and carries a phase, so a wait identifies +the intended reuse of a slot. This four-step view gives the causal chain; the +exact table below splits K and V into parts that can be released early. The kernel initializes its mbarriers in warp 0, performs a cluster sync, launches the Q prologue, allocates CTA-group TMEM, and then enters specialized loops. @@ -1048,15 +1207,6 @@ The main barrier edges are easier to read as ownership transfers: | `bar_v_part0_ready` / `bar_sv_part_done` | WG2 to/from WG3 | first V half | | `bar_v_part1_ready` / `bar_sv_done` | WG2 to WG3, then WG3 to WG2 and WG0 | second V half; PV/O completion before V reuse, O rescale, or epilogue | -For tile $k$, the sole MMA issuer first launches QK($k$). Once WG0 has turned -$L(k-1)$ into $W(k-1)$, that same issuer later launches PV($k-1$) in the serial -loop. - -QK and PV are therefore interleaved by one instruction stream, not issued as -two simultaneous tensor-core streams. Their asynchronous execution overlaps -the other warpgroups' gathers and scalar softmax work, subject to the part-level -edges above. - The ring index is ```python @@ -1075,9 +1225,9 @@ is reusable. The two `bar_sv_*` edges do the analogous job for V. :width: 100% :alt: Detailed sparse-prefill pipeline showing serial QK and PV issue, part-wise K and V reuse, the mask-slot ring, and the WG0 handoff -The steady state interleaves QK($k$) and PV($k-1$) while other roles perform -part-wise K/V gathers and softmax work. Barrier phases protect in-place storage -reuse rather than selecting separate full-tile buffers. +This detailed view names the part-level reuse edges and the mask-slot ring. +Barrier phases protect in-place storage reuse rather than selecting separate +full-tile buffers. ``` The memory model has one more distinction. Ordinary thread loads and stores see @@ -1106,10 +1256,10 @@ the dependencies installed below. First install a CUDA-enabled PyTorch build that supports B200 using the [official PyTorch selector](https://pytorch.org/get-started/locally/). The -companion repository imports PyTorch but does not declare it as a package +`tirx-kernels` repository imports PyTorch but does not declare it as a package dependency. -Install TVM and the companion kernel repository as follows: +Install TVM and `tirx-kernels` as follows: ```bash python -m pip install "apache-tvm==0.26.0" cuda-bindings @@ -1147,7 +1297,7 @@ row at a time, and checks output, maximum logits, and LSE with explicit tolerances. This is the right default verification path; compiling generated PTX alone cannot find a wrong head partition or a missing validity bit. -The repository CLI can run the registered regular-head128 configuration: +The `tirx-kernels` CLI can run the registered regular-head128 configuration: ```bash python -m tirx_kernels.test \ diff --git a/zh/chapter_flashmla/index.md b/zh/chapter_flashmla/index.md index b4dc4ca0..4c95e4e7 100644 --- a/zh/chapter_flashmla/index.md +++ b/zh/chapter_flashmla/index.md @@ -6,22 +6,22 @@ - 从普通 MHA 的 KV cache 出发,理解 MLA 为什么只需为每个 token 保存一份共享的压缩状态,以及各 head 特有的 K/V 变换被移到了哪里。 - 理解 FlashMLA sparse-prefill operator 的输入:外部 indexer 先选出 KV rows,FlashMLA 再对这些 rows 完成 attention;随后用一个可执行 reference 明确其数值语义和边界条件。 -- 通过 TIRx `flash_mla_sparse_fwd` 入口理解 shape dispatch 与 QK scale 的 API 差异,再沿 regular head-128 specialization 分析 2-CTA 分工、数据驻留、warpgroup 角色与 pipeline,最后在 B200 上编译并验证。 +- 以一个具体实现为例,理解 sparse attention 如何映射到 Blackwell,并在 B200 上完成编译与数值验证。 ::: 在介绍 MLA 之前,先回顾普通 attention 为什么需要 **KV cache**。计算一个新的 query 时,attention 需要读取更早 tokens 的 key 和 value。如果每次都重新计算这些 K/V,就会产生大量重复工作,因此系统会把已经得到的 K/V 缓存起来,供后续 query 直接读取。 -普通 multi-head attention(MHA)中,每个 attention head 都有自己的 K 和 V。因此,KV cache 必须为每个已经处理过的 token 保存各个 head 的 K/V。上下文越长,需要保存和读取的数据就越多。MLA 要解决的第一个问题,就是怎样缩小这部分 cache。 +这些状态能够安全复用,是因为生成模型通常采用因果(causal)attention:位置 $s$ 的 K/V 只依赖位置 $s$ 及其之前的 tokens,后来追加的 token 不会改变它们。Prefill 会并行计算 prompt 中的 tokens,并填充 cache;decode 随后逐步读取已有 cache,再追加新 token 的 K/V。KV cache 因而是在用存储容量和读取带宽换掉对整个 prefix 的重复计算。 -这种方法称为 **Multi-head Latent Attention(MLA)**。它的核心做法是换一种 cache 表示:不再保存各个 head 展开后的 K/V,而只为每个 token 保存一份由所有 heads 共享的压缩状态。这并不是把所有 heads 合并成一个 head。每个 head 仍有自己的变换,只是 cache 不再需要长期保存这些变换产生的 K/V。至于一份共享状态怎样保留各 head 的差异,后面会用公式逐步推导。 +普通 multi-head attention(MHA)中,每个 attention head 都有自己的 K 和 V。因此,KV cache 必须为每个已经处理过的 token 保存各个 head 的 K/V。上下文越长,需要保存和读取的数据就越多。接下来要解决的问题,就是怎样缩小这部分 cache。 -MLA 说明的是 cache 中保存什么,以及 attention 应该怎样计算;FlashMLA 解决的则是怎样在 GPU 上高效完成这些计算。DeepSeek 将这套高性能 GPU kernel library 称为 **FlashMLA**。其中包含适用于不同 attention 阶段和 cache 格式的多类算子。 +**Multi-head Latent Attention(MLA)** 的核心做法是换一种 cache 表示:不再保存各个 head 展开后的 K/V,而只为每个 token 保存一份由所有 heads 共享的压缩状态。这并不是把所有 heads 合并成一个 head。每个 head 仍有自己的变换,只是 cache 不再需要长期保存这些变换产生的 K/V。至于一份共享状态怎样保留各 head 的差异,后面会用公式逐步推导。 -本章先以 FlashMLA `flash_mla_sparse_fwd` 的 sparse-prefill contract 为语义主线。Prefill 表示并行处理 prompt 中的 query tokens;sparse 表示先由外部 indexer 选出需要关注的 KV rows,再对选中的 rows 计算 attention。 +MLA 说明的是 cache 中保存什么,以及 attention 应该怎样计算;FlashMLA 解决的则是怎样在 GPU 上高效完成这些计算。**FlashMLA** 是 DeepSeek 为 MLA 开发的高性能 GPU kernel library,包含适用于不同 attention 阶段和 cache 格式的多类算子。 -TIRx 也注册了一个同名的 `flash_mla_sparse_fwd` 入口。它是一座实现桥梁:按 shape dispatch 到 head-64、regular head-128 和 small-top-k head-128 三个 SM100 specializations,但其 QK scale 已 specialize 为 `1 / sqrt(d_qk)`。后半章再以其中的 regular head-128 specialization 为实现主线,分析它在 Blackwell 上的 schedule。这样,FlashMLA sparse-prefill contract 回答“算什么”,TIRx 入口回答“选哪条实现”,被选中的 specialization 回答“怎样在 GPU 上执行”。其他实现只在后文比较算子族、dispatch 和设计取舍时出现。 +本章关注 prefill 阶段的 sparse attention。与访问全部历史位置的 dense attention 不同,这里的外部 indexer 会先选出需要关注的 KV rows,FlashMLA 只对这些 rows 计算 attention。我们会先明确统一的算子语义,等算法讲清以后再选择具体实现。 -先预告后半章的 regular head-128 案例:一个 query token 对应一行 query,这一行包含 128 个 query heads;每个 cached token 则对应 cache 中的一行共享 KV。于是问题变成了:128 个 heads 读取同一行 KV,为什么仍能得到不同的结果?下面这张图先给出直观线索:共享的是生成 K/V 所需的源状态,而不是各 head 最终参与 attention 的表示。各 head 特有的变换仍然位于点积、softmax 和加权求和这些核心 attention 计算的两侧。精确的 tensor shapes 会在完成 MLA 推导后统一列出。 +这就引出了 MLA 的核心问题:多个 query heads 读取同一份缓存状态,为什么仍能得到不同的结果?答案的关键是:共享的只是压缩后的源状态。各 head 特有的变换并没有消失,而是移到了核心 attention 计算的两侧。下面这张图用 128 个 heads 把问题具体化,随后的推导仍保留一般的 head 数。 ```{figure} ../../img/flashmla_cache_story_zh.svg :width: 100% @@ -30,14 +30,11 @@ TIRx 也注册了一个同名的 `flash_mla_sparse_fwd` 入口。它是一座实 普通 MHA 为每个 head 分别保存一份 key/value。MLA 为每个 token 只保存一份共享的压缩内容状态和位置信息;各 head 特有的 query 与 output 变换分别在 attention 前后完成。 ``` -这张图只给出了直觉,还没有说明共享状态怎样保留各 head 的差异,也没有证明移动这些变换为什么不改变计算结果。下面先算清普通 MHA 的 cache 开销,再推导 MLA 到底缓存了什么,以及各 head 的变换为什么可以移动。等 cache 表示和等价变换都讲清楚之后,我们再进入 FlashMLA sparse-prefill contract 和 regular head-128 schedule。 +图中的变换为什么成立?我们先从普通 MHA 的 KV cache 算起。 ## 先从普通 MHA 的 KV cache 算起 -上面的直观描述还没有回答 cache 到底有多大。设 -$h_t\in\mathbb{R}^{d_{model}}$ 是 token $t$ 的 hidden state,$n_h$ 是 head -数量,$d_h$ 是每个 head 的宽度;$i$ 表示某个 head,$s$ 表示一个已经缓存的 -key-token 位置。普通 MHA 会为每个 head $i$ 分别生成 query、key 和 value: +上面的直观描述还没有回答 cache 到底有多大。设 $h_t\in\mathbb{R}^{d_{model}}$ 是 token $t$ 的 hidden state,$n_h$ 是 head 数量,$d_h$ 是每个 head 的宽度;$i$ 表示某个 head,$s$ 表示一个已经缓存的 key-token 位置。普通 MHA 会为每个 head $i$ 分别生成 query、key 和 value: $$ q_{t,i}=W_i^Q h_t,\qquad @@ -54,25 +51,43 @@ p_{t,s,i}=\operatorname{softmax}_s o_{t,i}=\sum_s p_{t,s,i}v_{s,i}. $$ -Output projection 会混合各个 head 的结果。但在 autoregressive generation -期间,所有更早位置的 $k_{s,i}$ 和 $v_{s,i}$ 都必须继续可用。因此,每层的 -cache 需要为每个 token 保存 $2n_h d_h$ 个元素,也就是为每个 head 分别保存 -一份 K slice 和一份 V slice。 +Output projection 会混合各个 head 的结果。但在 autoregressive generation 期间,所有更早位置的 $k_{s,i}$ 和 $v_{s,i}$ 都必须继续可用。因此,每层的 cache 需要为每个 token 保存 $2n_h d_h$ 个元素,也就是为每个 head 分别保存一份 K slice 和一份 V slice。 -若固定 $d_{model}=n_h d_h$,仅改变 head 数并不一定改变这项总宽度。结构上的 -代价在于 cache 仍需 materialize 各 head 的独立状态。 +把 batch、序列长度、层数和数据类型都计入后,cache 的实际容量会很快放大。若 batch size 为 $B$,每条序列长度均为 $S$,层数为 $N_{layer}$,每个元素占 $b_{elem}$ bytes,那么普通 MHA 的 KV cache 大小为 -在长序列 decode 中,读取这些随 token history 增长的 slices 会主导整个 step。 +$$ +M_{MHA}=2N_{layer}BSn_hd_hb_{elem}\quad\text{bytes}. +$$ + +对于变长 batch,只需将 $BS$ 换成 $\sum_{j=1}^{B}S_j$,其中 $S_j$ 是第 $j$ 条序列的长度。例如,32 层、batch size 为 1、context length 为 4096、32 个 heads、每个 head 128 维,并使用 BF16 时,仅 KV cache 就需要 2 GiB。这个估算未计入 allocator metadata、模型权重和其他中间状态。 + +若固定 $d_{model}=n_h d_h$,仅改变 head 数并不一定改变这项总宽度。结构上的代价在于 cache 仍需 materialize 各 head 的独立状态。 + +在 dense decode 中,每个新 query 都要读取不断增长的历史 K/V,因此这些读取常会成为瓶颈。缩小 cache 不仅能容纳更长的 context 或更大的 batch,也会减少每个 decode step 的 HBM 读取量。 + +Multi-query attention(MQA)让所有 query heads 共享一个 K/V head,以此减小 cache;grouped-query attention 则在组内共享。它们都是有用的模型架构,但 MLA 采用了另一条路径:保留具有表达能力的 per-head projection,同时只 cache 一个共享的低维数据源,需要时可以从中恢复各 head 的表示。 + +### 如果先缓存一份共享状态,会发生什么? -Multi-query attention(MQA)让所有 query heads 共享一个 K/V head,以此 -减小 cache;grouped-query attention 则在组内共享。它们都是有用的模型架构, -但 MLA 采用了另一条路径:保留具有表达能力的 per-head projection,同时只 -cache 一个共享的低维数据源,需要时可以从中恢复各 head 的表示。 +暂时忽略 RoPE,也不做低秩压缩。令 $h_s$ 表示位置 $s$ 在某一层送入 attention projections 的 hidden state。它不是词表中的 token embedding。上标 $C$ 表示不含位置信息的 content channel;普通 MHA 的 content key 和 value 可以写成 -### MLA 如何只缓存一次,却恢复 per-head 行为? +$$ +k_{s,i}^{C}=W_i^Kh_s,\qquad v_{s,i}^{C}=W_i^Vh_s. +$$ -最初的 [DeepSeek-V2 MLA 推导](https://arxiv.org/abs/2405.04434)先定义一个 -联合潜在 KV 向量(joint latent KV vector): +如果直接缓存一份共享的 $h_s$,矩阵结合律和线性变换对求和的分配性允许我们改变计算顺序: + +$$ +(q_{t,i}^{C})^{\mathsf T}W_i^Kh_s +=\left((W_i^K)^{\mathsf T}q_{t,i}^{C}\right)^{\mathsf T}h_s, +\qquad +\sum_s p_{t,s,i}W_i^Vh_s +=W_i^V\left(\sum_s p_{t,s,i}h_s\right). +$$ + +左边先为每个 key、每个 head 展开 K/V;右边则把 key projection 移到当前 query,把 value projection 移到加权求和之后。两边的数值完全相同,但右边只需长期保存一份 $h_s$。这可以看成一个尚未压缩的 latent cache 思想实验。 + +问题是,$h_s$ 的宽度仍然是 $d_{model}$。缓存虽然已经在 heads 之间共享,QK(query--key 点积)和 PV(probability--value 加权求和)却都要在这个较宽的空间中计算,因此这个方案通常并不实用。MLA 再加入一个训练得到的低秩 bottleneck,把共享状态压到 $d_c$ 维。原始 [DeepSeek-V2 MLA 推导](https://arxiv.org/abs/2405.04434)定义 $$ c_t^{KV}=W^{DKV}h_t, @@ -85,45 +100,61 @@ k_{t,i}^{C}=W_i^{UK}c_t^{KV},\qquad v_{t,i}^{C}=W_i^{UV}c_t^{KV}. $$ -上标 $C$ 表示不含位置信息的 *content* channel。关键在于,cache 不需要为 -每个 head 保存展开后的 $k^C$ 和 $v^C$,只需为每个 token 保存一份 -$c^{KV}$。 +这里 $c^{KV}\in\mathbb{R}^{d_c}$ 是共享的 latent state。可以把前面的思想实验理解为 $d_c=d_{model}$、$W^{DKV}=I$、$c^{KV}=h$,并令 $W_i^{UK}=W_i^K$、$W_i^{UV}=W_i^V$;真正的 MLA 则学习一个窄得多的 $c^{KV}$。 -Rotary positional embedding(RoPE)会旋转 Q/K 中负责表示位置的子空间。 -这让上面的简单图景变得复杂:如果在 $W^{UK}$ 与 dot product 之间加入这种 -position-dependent rotation,矩阵就无法再重新结合。为此,MLA 使用 -decoupled positional channel:每个 query head 有自己的 $q_{t,i}^{R}$, -而所有 heads 共享一个 cached $k_t^R$。真正以 MHA 形式计算的 score 使用: +这个低秩步骤不是把任意已经训练好的 MHA 无损压成 $d_c$ 维。它是模型训练时施加的 joint low-rank 结构。对 MLA 的 effective content K/V projections 来说, $$ -q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad -k_{s,i}=[k_{s,i}^{C};k_s^R]. +W_i^K=W_i^{UK}W^{DKV},\qquad +W_i^V=W_i^{UV}W^{DKV}. $$ -此时 cache 保存的是 $[c_s^{KV};k_s^R]$,仍然由所有 heads 共享。 -Positional channel 保持显式,weight absorption 只作用于 content channel。 +也就是说,所有 heads 的 content K/V projections 共享右侧因子 $W^{DKV}$。模型会在这个约束下学习怎样把需要的信息保存在 $c^{KV}$ 中。 -:::{admonition} Query 侧也可以压缩,但它不是本章的主线 -:class: note +于是思路分成两步:先利用结合律和线性性,把 per-head projections 移到 query 与 output 路径,让一份共享状态直接参与 core attention;再用学习到的 bottleneck 缩小这份状态。Cache 不需要保存展开后的 $k^C$ 和 $v^C$,只需为每个 token 保存一份 $c^{KV}$。 -MLA 还可以通过一个独立的低秩 latent 分解 query projection: +### RoPE 为什么需要单独的 positional channel? + +Rotary positional embedding(RoPE)会旋转 Q/K 中负责表示位置的子空间。记 $R_u$ 为位置 $u$ 对应的 RoPE rotation。这让上面的简单图景变得复杂。假设直接对 content query 和 key 使用 RoPE,它们的 dot product 会变成 $$ -c_t^Q=W^{DQ}h_t,\qquad q_t^C=W^{UQ}c_t^Q. +\left(R_tq_{t,i}^{C}\right)^{\mathsf T} +\left(R_sW_i^{UK}c_s^{KV}\right) += +(q_{t,i}^{C})^{\mathsf T}R_t^{\mathsf T}R_sW_i^{UK}c_s^{KV}. $$ -这项分解主要降低训练时的 activation memory,不会进一步缩小 KV cache。 -而且,它发生在 FlashMLA core attention 之前:传给 kernel 的 `q` 已经是 -projection 后的 query。所以下文把 $q^C$ 当作输入,继续沿着 KV cache 这条 -主线分析。 -::: +其中 $R_t^{\mathsf T}R_s$ 随 query 与 key 的相对位置变化。矩阵乘法当然仍可结合,但 $W_i^{UK}$ 无法再被预先合并成一个可供当前 query 对所有 key 位置共用的 projection。为此,MLA 使用 decoupled positional channel:每个 query head 有自己的 $q_{t,i}^{R}$,而所有 heads 共享一个 cached $k_t^R$。真正以 MHA 形式计算的 query 和 key 为: + +$$ +q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad +k_{s,i}=[k_{s,i}^{C};k_s^R]. +$$ + +因此,未乘 scale 的 score 可以拆成 + +$$ +\operatorname{score}_{t,s,i} +=(q_{t,i}^{C})^{\mathsf T}W_i^{UK}c_s^{KV} ++(q_{t,i}^{R})^{\mathsf T}k_s^R. +$$ + +此时 cache 保存的是 $[c_s^{KV};k_s^R]$,仍然由所有 heads 共享。Positional channel 保持显式,weight absorption 只作用于 content channel。 + +把几种机制放在一起,就能看出 MLA 与普通 MQA 的区别。下表只比较每个 token、每层需要缓存的元素数,不比较模型能力,也不计数据类型和 allocator metadata: + +| 机制 | 每个 token、每层的 cache 元素数 | 缓存的内容 | +| --- | ---: | --- | +| MHA | $2n_hd_h$ | $n_h$ 组展开后的 K/V | +| GQA | $2n_{kv}d_h$ | $n_{kv}$ 组展开后的 K/V,$1 0` 是调用者必须满足的前置条件。统一 front door 会拒绝 -`topk<=0`,但各 specialization 的 `_cfg().validate()` 只检查整除性, -没有检查正数条件。因此,直接 import 某个 specialization 时仍须拒绝或避开 -非正的 `topk`;local validator 接受它并不意味着这种 launch 有效。 +`topk > 0` 是调用者必须满足的前置条件。统一 front door 会拒绝 `topk<=0`,但各 specialization 的 `_cfg().validate()` 只检查整除性,没有检查正数条件。因此,直接 import 某个 specialization 时仍须拒绝或避开非正的 `topk`;local validator 接受它并不意味着这种 launch 有效。 -无需 launch GPU kernel 就能检查 dispatch。下面的代码块本身可独立执行,但 -需要先按本章末节安装 `tirx-kernels`: +无需 launch GPU kernel 就能检查 dispatch。下面的代码块本身可独立执行,但需要先按本章末节安装 `tirx-kernels`: ```python from tirx_kernels.flashmla.flash_mla_sparse_fwd import ( @@ -561,35 +535,13 @@ print(dispatch_reason(**shape)) # sm100 h_q=128 dispatches to regular head128 phase1 ``` -Dispatch 本身记录在 -[`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120) -中。把 dispatch 与 device schedule 分开,可以避免把一个 specialization 错当成 -整个 operator。 +Dispatch 本身记录在 [`flash_mla_sparse_fwd.py`](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/flash_mla_sparse_fwd.py#L66-L120) 中。把 dispatch 与 device schedule 分开,可以避免把一个 specialization 错当成整个 operator。 -在分配硬件角色之前,先把 selected tokens 如何流过 kernel 化成六步。对每个 -包含 128 个 selected tokens 的 tile,重复前五步;所有 tiles 都处理完后,才 -执行第六步: - -```text -对每个包含 128 个 selected tokens 的 tile: - 1. gather 该 tile 的 K rows - 2. gather 该 tile 的 V rows,并构造 validity mask - 3. QK:128 个 query heads × 128 个 selected tokens → logits L - 4. 更新 mask 后的 online softmax,得到 W、参考值 mi 和分母 li - 5. 必要时 rescale running state,再累加 O~ += W @ V -所有 selected tiles 完成后: - 6. 用 li + sink 归一化 O~,写回 out、max_logits 和 lse -``` - -现在算术主线已经清楚了。下一个问题是:两个 thread blocks 怎样协作完成这六步, -又不重复搬运整个 tile? +Dispatch 确定了实现入口。下一个问题是:两个 thread blocks 怎样协作完成前面的六步,又不重复搬运整个 tile? ### 为什么一个 query row 需要两个 CTA? -难点出现在第 3、5 步的切分轴不同:QK 要形成所有 head 与 selected token 的 -两两组合,PV 又要沿 token 维归约,产生 512 个 value coordinates。Regular -head-128 实现让两个 CTA 通过 `cta_group=2` 共同形成这块 logical tile,并在 -QK 与 PV 之间旋转切分轴。 +难点出现在第 3、5 步的切分轴不同:QK 要形成所有 head 与 selected token 的两两组合,PV 又要沿 token 维归约,产生 512 个 value coordinates。Regular head-128 实现让两个 CTA 通过 `cta_group=2` 共同形成这块 logical tile,并在 QK 与 PV 之间旋转切分轴。 这个关系先用所有权图(ownership map)表示: @@ -597,9 +549,7 @@ QK 与 PV 之间旋转切分轴。 :width: 100% :alt: 两个 CTA 对 query heads、selected K rows 和 V feature columns 的 ownership -对于每个 query row,CTA pair 会在 QK 与 PV 之间改变 logical partition。 -每个 CTA 最终写出 64 个完整的 output heads,每个 head 含 512 个 -coordinates。 +对于每个 query row,CTA pair 会在 QK 与 PV 之间改变 logical partition。每个 CTA 最终写出 64 个完整的 output heads,每个 head 含 512 个 coordinates。 ``` 这个 CTA pair 会用三种不同方式切分三个轴: @@ -610,13 +560,9 @@ coordinates。 | K-row gather ownership | selected tokens 0--63 | selected tokens 64--127 | | V-feature gather ownership | value columns 0--255 | value columns 256--511 | -所以,2-CTA tensor-core operation 不只是“两个 CTA 各做同一个循环的一半”。 -QK 形成 128 个 heads 与 128 个 selected tokens 的两两组合,PV 再沿 token 维 -归约,得到 512 个 value coordinates。Collective `cta_group=2` MMA、配对的 -SMEM/TMEM layouts 和 cross-CTA barriers 共同组成一个 logical tile。 +所以,2-CTA tensor-core operation 不只是“两个 CTA 各做同一个循环的一半”。QK 形成 128 个 heads 与 128 个 selected tokens 的两两组合,PV 再沿 token 维归约,得到 512 个 value coordinates。Collective `cta_group=2` MMA、配对的片上布局和跨 CTA 同步共同组成一个 logical tile。 -现在再回到源码验证 launch topology。Launch grid 包含 `2 * s_q` 个 CTA,并将 -相邻 CTA 两两组成 cluster: +现在再回到源码验证 launch topology。Launch grid 包含 `2 * s_q` 个 CTA,并将相邻 CTA 两两组成 cluster: ```python block_idx = T.cta_id([2 * s_q]) @@ -627,35 +573,23 @@ thread_idx = T.thread_id([512]) T.warpgroup_id([4]) ``` -因此,一个 cluster 负责一个 query row,每个 CTA 含 4 个 warpgroups。这个 -划分还可以从后面的数据索引直接看出:Q 按 `cta_idx` chunk,K producer 选择 -每个 top-k block 的 `cta_idx` 半块,V producer 则从 `cta_idx * 256` 开始。 +因此,一个 cluster 负责一个 query row,每个 CTA 含 4 个 warpgroups。这个划分还可以从后面的数据索引直接看出:Q 按 `cta_idx` chunk,K producer 选择每个 top-k block 的 `cta_idx` 半块,V producer 则从 `cta_idx * 256` 开始。 ## 各个 tile 放在哪里? -进入数据驻留图之前,先统一硬件词汇。**Global memory(GMEM)** 保存 kernel -的输入输出;**shared memory(SMEM)** 是 CTA 内线程和异步搬运共同访问的片上 -存储;**tensor memory(TMEM)** 是 Blackwell tensor cores 附近用于 operands -与 accumulators 的专用片上存储;registers 则归当前线程所有。**Tensor Memory -Accelerator(TMA)** 负责在 GMEM 与 SMEM 之间异步搬运规则 tile,也能根据 -地址列表执行 gather。`tcgen05` tensor-core operation 则从 SMEM/TMEM 读取 -operands,并把大型 accumulators 留在 TMEM。 - -后文还会用两个简写描述 QK 的 operand 来源:**SS** 表示 Q、K 都从 SMEM -读取;**TS** 表示 Q 从 TMEM 读取、K 仍从 SMEM 读取。这条 kernel 将 Q 的 -384-column suffix 搬到 TMEM,只把 prefix 留在 SMEM,所以 QK 要先做 SS -prefix,再做 TS suffix。Softmax 产生的 BF16 未归一化权重则要写入 SMEM,供 -后面的 PV GEMM 使用。 +进入数据驻留图之前,先统一三种硬件存储:**global memory(GMEM)** 保存 kernel 的输入输出;**shared memory(SMEM)** 是 CTA 内线程共同访问的片上存储;**tensor memory(TMEM)** 是 Blackwell tensor cores 附近用于 operands 与 accumulators 的专用片上存储。 ```{figure} ../../img/flashmla_dataflow_zh.svg :width: 100% :alt: QK、softmax、PV 与 epilogue 期间,global memory、shared memory、tensor memory 和 WG0 registers 中的数据驻留与生命周期复用 -Q 被拆成 SMEM prefix 和 TMEM suffix。Gather 后的 K/V 进入 SMEM;原始 QK -logits 与 output 在 TMEM 中累积;未归一化 softmax weights 再经过 SMEM 交给 -PV。 +Q 被拆成 SMEM prefix 和 TMEM suffix。Gather 后的 K/V 进入 SMEM;原始 QK logits 与 output 在 TMEM 中累积;未归一化 softmax weights 再经过 SMEM 交给 PV。 ``` +图中的 registers 归当前线程所有。**Tensor Memory Accelerator(TMA)** 负责在 GMEM 与 SMEM 之间异步搬运规则 tile,也能根据地址列表执行 gather;`tcgen05` tensor-core operation 则从 SMEM/TMEM 读取 operands,并把大型 accumulators 留在 TMEM。 + +后文还会用两个简写描述 QK 的 operand 来源:**SS** 表示 Q、K 都从 SMEM 读取;**TS** 表示 Q 从 TMEM 读取、K 仍从 SMEM 读取。这条 kernel 将 Q 的 384-column suffix 搬到 TMEM,只把 prefix 留在 SMEM,所以 QK 要先做 SS prefix,再做 TS suffix。Softmax 产生的 BF16 未归一化权重则要写入 SMEM,供后面的 PV GEMM 使用。 + 对一个 CTA 而言,重要的 logical views 如下: | Storage | Logical tile | Lifetime 与用途 | @@ -669,30 +603,17 @@ PV。 | TMEM `o_tmem` | `64 x 512` FP32 logical view | running unnormalized output | | SMEM `o_smem` | `64 x 512` BF16 | TMA store 前的 epilogue staging | -这些都是逻辑视图(logical views);CTA-group TMEM layout 和 rearrangement -决定 MMA 与 load/store instructions 的实际 lane mapping。源码中的 -`SMEMPool` 是共享内存分配器,用来从同一片动态 SMEM 中切出带对齐和生命周期 -约束的 views。源码还另行分配一个 512-column CTA-group TMEM pool,再从中 -切出 O、raw-logit 和 Q views。 - -SMEM 采用激进的 alias 与复用策略。只要 lifetime 允许,`q_full`、gather 后的 -K/V region 和 output epilogue 就会复用类似 union 的 base。最后 384 个 Q columns 移到 -TMEM 后,只有 $d_{sq}=d_{qk}-384$ 的 prefix 仍需保持 live,供 QK 第一部分 -使用。`d_qk=512` 时 $d_{sq}=128$;`d_qk=576` 时则为 192。具体 allocation -plan 见 -[`sparse_prefill_head128_phase1.py` lines 302--365](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L302-L365)。 - -这里要特别澄清一个容易误解的点:`NUM_BUFS = 2` **没有**分配两份完整的 K、V、 -$L$ 或 $W$ tile,这些 arrays 都没有 stage axis。`NUM_BUFS` 用于两槽 -barrier/phase ring,也为小型 packed-validity mask 提供两个 slots;completion -barrier 则保证可以安全地分段覆盖同一个大型 tile 的 physical storage。把这种 -layout 称作“double-buffered K/V”,就会让人误以为存在两份实际上并不存在的 -storage。 +这些都是逻辑视图(logical views);CTA-group TMEM layout 和 rearrangement 决定 MMA 与 load/store instructions 的实际 lane mapping。源码中的 `SMEMPool` 是共享内存分配器,用来从同一片动态 SMEM 中切出带对齐和生命周期约束的 views。源码还另行分配一个 512-column CTA-group TMEM pool,再从中切出 O、raw-logit 和 Q views。 + +SMEM 采用激进的 alias 与复用策略。只要 lifetime 允许,`q_full`、gather 后的 K/V region 和 output epilogue 就会复用类似 union 的 base。最后 384 个 Q columns 移到 TMEM 后,只有 $d_{sq}=d_{qk}-384$ 的 prefix 仍需保持 live,供 QK 第一部分使用。`d_qk=512` 时 $d_{sq}=128$;`d_qk=576` 时则为 192。具体 allocation plan 见 [`sparse_prefill_head128_phase1.py` lines 302--365](https://github.com/mlc-ai/tirx-kernels/blob/5be39749e7dfd2c4bdae9b4d396f8ec35af07126/tirx_kernels/flashmla/sparse_prefill_head128_phase1.py#L302-L365)。 + +**Completion barrier** 是一个小型硬件状态对象,记录异步 producer 何时完成;phase bit 则用来区分同一 barrier slot 的前后两次使用。后文再展开完整的 producer--consumer protocol。 + +这里要特别澄清一个容易误解的点:`NUM_BUFS = 2` **没有**分配两份完整的 K、V、$L$ 或 $W$ tile,这些 arrays 都没有 stage axis。`NUM_BUFS` 用于两槽 barrier/phase ring,也为小型 packed-validity mask 提供两个 slots;completion barrier 则保证可以安全地分段覆盖同一个大型 tile 的 physical storage。把这种 layout 称作“double-buffered K/V”,就会让人误以为存在两份实际上并不存在的 storage。 ## 每次数据交接由哪个 warpgroup 负责? -数据放置确定后,下一问是谁生产每块 tile、谁消费它,以及谁归还可复用空间。 -四个 warpgroups 各做不同工作,而不是齐步推进: +数据放置确定后,下一问是谁生产每块 tile、谁消费它,以及谁归还可复用空间。四个 warpgroups 各做不同工作,而不是齐步推进: | Warpgroup | Warps | 职责 | | --- | --- | --- | @@ -701,32 +622,21 @@ storage。 | WG2 | 8--11 | 加载 index fragments,并为 V 发起 gather4 TMA | | WG3 | 12--15 | CTA 0 的 warp 12 发起 CTA-group QK/PV MMA;每个 CTA 的 warp 13 构造 validity mask | -WG3 中剩下的 warps 并没有承担另一个隐藏 stage。这种不对称 role assignment -是有意设计的:一个 elected lane 就能为 CTA pair 发起 asynchronous MMA, -而 exponentiation、row reduction、packing 和 epilogue conversion 则适合使用 -较多 lanes。 +WG3 中剩下的 warps 并没有承担另一个隐藏 stage。这种不对称 role assignment 是有意设计的:一个 elected lane 就能为 CTA pair 发起 asynchronous MMA,而 exponentiation、row reduction、packing 和 epilogue conversion 则适合使用较多 lanes。 :::{admonition} Register budget 也跟着角色分配 :class: note -WG0 将上限提高到 144 registers,WG3 提高到 168;producer groups 则降到 -96。TIRx API 用 `T.ptx.setmaxnreg(True, ...)` 表示提高,用 -`T.ptx.setmaxnreg(False, ...)` 表示降低。这个配额解释了为什么不同 -warpgroups 适合承担不同工作,但不改变下面的数据交接顺序。 +WG0 将上限提高到 144 registers,WG3 提高到 168;producer groups 则降到 96。TIRx API 用 `T.ptx.setmaxnreg(True, ...)` 表示提高,用 `T.ptx.setmaxnreg(False, ...)` 表示降低。这个配额解释了为什么不同 warpgroups 适合承担不同工作,但不改变下面的数据交接顺序。 ::: ### 不规则的 rows 如何变成规则的 tiles? -稀疏的 row addresses 破坏了 dense attention 所用的 contiguous 2-D copy pattern。 -WG1 和 WG2 使用显式 TMA `gather4`:一次 issue 提供恰好 4 个 row coordinates, -让一个 warp 可以把不连续的 KV rows 搬进规则的 SMEM tile。共享 helper 固定了 -CTA-pair policy。 +稀疏的 row addresses 破坏了 dense attention 所用的 contiguous 2-D copy pattern。WG1 和 WG2 使用显式 TMA `gather4`:一次 issue 提供恰好 4 个 row coordinates,让一个 warp 可以把不连续的 KV rows 搬进规则的 SMEM tile。共享 helper 固定了 CTA-pair policy。 + +这里先使用 barrier 最基本的 producer--consumer 语义:producer 完成数据写入后,通过 ready/completion barrier 通知 consumer;consumer 等待后才能读取,使用完这段 storage 后再通过 done/free barrier 把复用权还给 producer。完整的 phase ring 会在 pipeline 一节说明。 -下面的上下文摘录回答两个具体问题:一次 `gather4` issue 读取哪些 addresses, -它的 completion 又交给哪个 barrier。读代码时先记住三个名字:`cur_buf` 是 -当前 tile 在两槽 barrier ring 中使用的槽位;`bar` 是 producer 与 consumer -共享的 completion barrier;`leader_mbar(...)` 取得 CTA pair 中负责汇总 TMA -completion 的 leader 地址。Index names 和 slices 与链接源码一致: +下面的上下文摘录回答两个具体问题:一次 `gather4` issue 读取哪些 addresses,它的 completion 又交给哪个 barrier。读代码时先记住三个名字:`cur_buf` 是当前 tile 在两槽 barrier ring 中使用的槽位;`bar` 是 producer 与 consumer 共享的 completion barrier;`leader_mbar(...)` 取得 CTA pair 中负责汇总 TMA completion 的 leader 地址。Index names 和 slices 与链接源码一致: ```python _kv_gather_tma = partial( @@ -753,9 +663,7 @@ for row_group in T.unroll(WG1_ROWS_PER_WARP): ) ``` -Gather 与 validity 相关,但两者是分开的。Warp 13 的每个 active lane 加载 8 个 -indices,并调用 `pack_valid_mask8`。当且仅当下面两个条件同时满足时,bit $i$ -才为 1: +Gather 与 validity 相关,但两者是分开的。Warp 13 的每个 active lane 加载 8 个 indices,并调用 `pack_valid_mask8`。当且仅当下面两个条件同时满足时,bit $i$ 才为 1: $$ 0\leq\text{index}_i 0: @@ -807,32 +700,21 @@ Tx.gemm_async( ) ``` -第一步是 SS:Q 和 K operands 都由 SMEM 描述。第二步是 TS:Q 的 384-column -suffix 来自 TMEM,K 仍在 SMEM。两步写入同一个 FP32 raw-logit accumulator -(源码中的 `tmem_p`);第一步清零,第二步累加。这样拆分 Q 后,SMEM 中只需 -保留较小的 Q prefix,使 union allocation 成为可能,同时不必放弃较大 suffix -所使用的 TS path。 +第一步是 SS:Q 和 K operands 都由 SMEM 描述。第二步是 TS:Q 的 384-column suffix 来自 TMEM,K 仍在 SMEM。两步写入同一个 FP32 raw-logit accumulator(源码中的 `tmem_p`);第一步清零,第二步累加。这样拆分 Q 后,SMEM 中只需保留较小的 Q prefix,使 union allocation 成为可能,同时不必放弃较大 suffix 所使用的 TS path。 -Softmax 之后,PV 是 SS GEMM:BF16 $W$ 和 V 都在 SMEM,FP32 O accumulator -则留在 TMEM。Kernel 将 V rows 和 output columns 各分成两半,四种组合共同 -更新全部 512 个 value coordinates。 +Softmax 之后,PV 是 SS GEMM:BF16 $W$ 和 V 都在 SMEM,FP32 O accumulator 则留在 TMEM。Kernel 将 V rows 和 output columns 各分成两半,四种组合共同更新全部 512 个 value coordinates。 ## Online softmax 如何避免不必要的 O 重缩放? -当 `topk` 大于 `B_TOPK=128` 时,一个 query row 会连续处理多个 selected-token -tiles。每个 tile 都只看到一部分 scores,不能各自独立做完整 softmax;kernel -必须把前面 tiles 的状态带到下一轮。 +当 `topk` 大于 `B_TOPK=128` 时,一个 query row 会连续处理多个 selected-token tiles。每个 tile 都只看到一部分 scores,不能各自独立做完整 softmax;kernel 必须把前面 tiles 的状态带到下一轮。前面的具体例子在没有更短 `topk_length` 时有 $N=16$ 个 tiles,因此会递推合并 16 轮状态。 -为了直接使用硬件 `exp2`,先把原始 QK dot product $x$ 乘以模型规定的 QK -scale,再转换到以 2 为底的指数单位: +为了直接使用硬件 `exp2`,先把原始 QK dot product $x$ 乘以模型规定的 QK scale,再转换到以 2 为底的指数单位: $$ r=x\cdot\text{semantic\_QK\_scale}\cdot\log_2(e). $$ -对于连续到来的 score tiles,普通 online-softmax recurrence 会保存指数参考值 -$m$、denominator $\ell$ 和未归一化 output $\widetilde O$。若下一块 tile 含有 -base-2 scaled scores $r$,则: +对于连续到来的 score tiles,普通 online-softmax recurrence 会保存指数参考值 $m$、denominator $\ell$ 和未归一化 output $\widetilde O$。若下一块 tile 含有 base-2 scaled scores $r$,则: $$ m'=\max(m,\max r),\qquad @@ -844,18 +726,11 @@ $$ \widetilde O'=\alpha\widetilde O+\sum_j2^{r_j-m'}v_j. $$ -在 TIRx regular head-128 specialization 中,编译期 -`sm_scale_div_log2` 就是 `(1 / sqrt(d_qk)) * log2(e)`。这与原来的 -softmax 相同,只是改写成直接映射到快速 base-2 exponential instructions -的形式。 +在 TIRx regular head-128 specialization 中,编译期 `sm_scale_div_log2` 就是 `(1 / sqrt(d_qk)) * log2(e)`。这与原来的 softmax 相同,只是改写成直接映射到快速 base-2 exponential instructions 的形式。 -对应到源码,`cur_pi_max` 是当前 128-token tile 的 base-2 最大值,`mi` 是递推 -中实际采用的指数参考值,`li` 是相对于 `mi` 累积的 denominator。`real_mi` -则单独保存迄今为止真实的最大值,用于最终报告 `max_logits`。区分 `mi` 与 -`real_mi`,正是下面 lazy rescaling 能不改变输出统计量的关键。 +对应到源码,`cur_pi_max` 是当前 128-token tile 的 base-2 最大值,`mi` 是递推中实际采用的指数参考值,`li` 是相对于 `mi` 累积的 denominator。`real_mi` 则单独保存迄今为止真实的最大值,用于最终报告 `max_logits`。区分 `mi` 与 `real_mi`,正是下面 lazy rescaling 能不改变输出统计量的关键。 -每次 row maximum 增加时都重缩放完整的 512-coordinate O tile,代价会很高。 -Head-128 kernel 因此使用 lazy threshold: +每次 row maximum 增加时都重缩放完整的 512-coordinate O tile,代价会很高。Head-128 kernel 因此使用 lazy threshold: ```python should_scale_o: T.bool = ( @@ -870,14 +745,9 @@ else: scale_for_old = T.ptx.exp2(mi - new_max) ``` -如果当前 tile 的最大值比保存的指数参考值至多高 6 个 base-2 units,kernel -会继续保留旧参考值。新的 exponential 此时最大可能达到 $2^6=64$,但已累积 -的 O 无需 rescale。一旦差值超过 6,kernel 就更新参考值,同时 rescale $\ell$ -和已经存在的 O。Warp-wide `any_sync` 让参与计算的 rows 使用一致的决策。 +如果当前 tile 的最大值比保存的指数参考值至多高 6 个 base-2 units,kernel 会继续保留旧参考值。新的 exponential 此时最大可能达到 $2^6=64$,但已累积的 O 无需 rescale。一旦差值超过 6,kernel 就更新参考值,同时 rescale $\ell$ 和已经存在的 O。Warp-wide `any_sync` 让参与计算的 rows 使用一致的决策。 -`real_mi` 始终维护迄今为止真实的最大值,所以这项优化不会改变 -`max_logits`。结束时,两个 64-token half 对每个 logical row 的贡献会被合并, -kernel 输出: +`real_mi` 始终维护迄今为止真实的最大值,所以这项优化不会改变 `max_logits`。结束时,两个 64-token half 对每个 logical row 的贡献会被合并,kernel 输出: $$ \mathrm{lse}=m\ln 2+\ln\ell. @@ -891,38 +761,24 @@ output_scale: T.float32 = T.cuda.fdividef( ) ``` -但它有意不改变报告的 LSE。对于全 invalid row,特殊分支会输出 0,同时令 -`max_logits=-inf`、`lse=+inf`,与前面的 reference 一致。 +但它有意不改变报告的 LSE。对于全 invalid row,特殊分支会输出 0,同时令 `max_logits=-inf`、`lse=+inf`,与前面的 reference 一致。 ## 各个阶段如何安全重叠? -把这个 schedule 看成“数据所有权何时交给下一角色”最容易理解。宏观上,每个 -tile 依次经历 `K ready → QK done → L consumed → W ready → PV done → V/O -reusable`。QK 必须先完成,softmax 才能消费 logits;softmax 必须先产生 weights, -PV 才能开始。但是,只要原位复用的 K 或 V segment 已经安全释放,负责 gather -的 warpgroups 就应该继续向前推进。 +把这个 schedule 看成“数据所有权何时交给下一角色”最容易理解。宏观上,每个 tile 依次经历 `K ready → QK done → L consumed → W ready → PV done → V/O reusable`。QK 必须先完成,softmax 才能消费 logits;softmax 必须先产生 weights,PV 才能开始。但是,只要原位复用的 K 或 V segment 已经安全释放,负责 gather 的 warpgroups 就应该继续向前推进。 -源码用 **memory barrier(mbarrier)** 表示这些交接。Producer 在数据或异步 -操作完成时贡献 arrival,consumer 等待相应 phase;consumer 用完后,再通过 -done/free barrier 把覆盖这段 storage 的权利交还 producer。也就是说,ready -保护“不要过早读取”,done/free 保护“不要过早覆盖”。 +源码用 **memory barrier(mbarrier)** 表示这些交接。Producer 在数据或异步操作完成时贡献 arrival,consumer 等待相应 phase;consumer 用完后,再通过 done/free barrier 把覆盖这段 storage 的权利交还 producer。也就是说,ready 保护“不要过早读取”,done/free 保护“不要过早覆盖”。 ```{figure} ../../img/flashmla_pipeline_stages_zh.svg :width: 100% :alt: 相差一个 tile 的 pipeline 填充、稳态与排空,以及 QK、softmax、PV 的重叠 -填充阶段只发起 QK(0),没有上一块 PV;排空阶段只发起 PV($N-1$),随后进入 -最终 epilogue。稳态中,softmax($k-1$) 可与 QK($k$) 重叠;唯一的 MMA issuer -串行发出 QK($k$) 与 PV($k-1$);QK($k$) 完成后,softmax($k$) 可与仍在异步 -执行的 PV($k-1$) 重叠。这不是两条同时发射 QK 与 PV 的 tensor-core streams。 +填充阶段只发起 QK(0),没有上一块 PV;排空阶段只发起 PV($N-1$),随后进入最终 epilogue。稳态中,softmax($k-1$) 可与 QK($k$) 重叠;唯一的 MMA issuer 串行发出 QK($k$) 与 PV($k-1$);QK($k$) 完成后,softmax($k$) 可与仍在异步执行的 PV($k-1$) 重叠。这不是两条同时发射 QK 与 PV 的 tensor-core streams;前面的具体例子中 $N=16$。 ``` -有了这张宏观时间线,再看初始化和具体 barrier 名称。Kernel 先由 warp 0 初始化 -mbarriers,执行 cluster sync,launch Q prologue,分配 CTA-group TMEM,再进入 -specialized loops。 +有了这张宏观时间线,再看初始化和具体 barrier 名称。Kernel 先由 warp 0 初始化 mbarriers,执行 cluster sync,launch Q prologue,分配 CTA-group TMEM,再进入 specialized loops。 -CTA-group gather 的 TMA completion 会被路由到指定的 leader barrier,使 -CTA pair 发出的操作共同满足同一 expected byte count。 +CTA-group gather 的 TMA completion 会被路由到指定的 leader barrier,使 CTA pair 发出的操作共同满足同一 expected byte count。 把主要 barrier edges 写成 storage ownership transfer 会更容易理解: @@ -938,15 +794,6 @@ CTA pair 发出的操作共同满足同一 expected byte count。 | `bar_v_part0_ready` / `bar_sv_part_done` | WG2 到/从 WG3 | 第一半 V | | `bar_v_part1_ready` / `bar_sv_done` | WG2 到 WG3,再由 WG3 到 WG2 和 WG0 | 第二半 V;复用 V、rescale O 或执行 epilogue 前,PV/O 已完成 | -对于 tile $k$,唯一的 MMA issuer 先 launch QK($k$)。WG0 把 $L(k-1)$ 转成 -$W(k-1)$ 后,同一个 issuer 才在 serial loop 后部 launch PV($k-1$)。因此, -QK 与 PV 由同一 instruction stream 交错发起,而不是两条同时发射的 -tensor-core streams。 - -在 steady state 中,softmax($k-1$) 可以与 QK($k$) 重叠。唯一 issuer 在 -QK($k$) 之后发出 PV($k-1$);QK($k$) 完成后,softmax($k$) 又可以与仍在异步 -执行的 PV($k-1$) 重叠。所有这些重叠仍受上述 part-level edges 约束。 - Barrier 槽位按下面的方式循环使用: ```python @@ -956,49 +803,30 @@ cur_phase = (k // 2) & 1 这样,复用的 barrier slot 可以区分本轮到达与两轮之前的旧到达。 -再次强调,这是一条 two-slot *barrier/phase ring*,并不是让两个完整 KV tiles -同时 resident。 +再次强调,这是一条 two-slot *barrier/phase ring*,并不是让两个完整 KV tiles 同时 resident。 -`bar_qk_part_done` 允许 producer 在 K suffix 可以复用之前先替换 K prefix。 -两条 `bar_sv_*` edge 对 V 做同样的事。 +`bar_qk_part_done` 允许 producer 在 K suffix 可以复用之前先替换 K prefix。两条 `bar_sv_*` edge 对 V 做同样的事。 ```{figure} ../../img/flashmla_pipeline_zh.svg :width: 100% :alt: Sparse-prefill 详细 pipeline,展示 QK 与 PV 的串行发起、K/V 分段复用、mask-slot ring 和 WG0 交接 -在稳态中,QK($k$) 与 PV($k-1$) 交错发起,其他 roles 同时执行分段 K/V -gather 和 softmax。Barrier phase 保护 in-place storage reuse,而不是选择两份 -完整 tile buffer。 +在稳态中,QK($k$) 与 PV($k-1$) 交错发起,其他 roles 同时执行分段 K/V gather 和 softmax。Barrier phase 保护 in-place storage reuse,而不是选择两份完整 tile buffer。 ``` -Barrier 只说明“某项工作已经完成”,还要处理不同 memory proxy 的可见性。 -这里有两类 proxy:线程执行的普通 SMEM load/store 属于 **generic proxy**, -TMA 与 tcgen05 的异步访问属于 **async proxy**。如果一边写、另一边读同一片 -SMEM,仅有 barrier arrival 并不能自动约束两个 proxy 观察 memory effects 的 -先后关系。 +Barrier 只说明“某项工作已经完成”,还要处理不同 memory proxy 的可见性。这里有两类 proxy:线程执行的普通 SMEM load/store 属于 **generic proxy**,TMA 与 tcgen05 的异步访问属于 **async proxy**。如果一边写、另一边读同一片 SMEM,仅有 barrier arrival 并不能自动约束两个 proxy 观察 memory effects 的先后关系。 -因此,`T.ptx.tcgen05.fence.*` 约束 TMEM access 与线程可见操作的先后关系; -`T.ptx.fence.proxy_async("shared::cta")` 则在 SMEM 的 generic 与 async proxy -之间建立顺序。它既用于普通 store 写入 $W$ 或 epilogue tile 后、tcgen05/TMA -执行异步读取之前,也用于异步 SMEM read 完成后、普通代码覆写共用 storage -之前。 +因此,`T.ptx.tcgen05.fence.*` 约束 TMEM access 与线程可见操作的先后关系;`T.ptx.fence.proxy_async("shared::cta")` 则在 SMEM 的 generic 与 async proxy 之间建立顺序。它既用于普通 store 写入 $W$ 或 epilogue tile 后、tcgen05/TMA 执行异步读取之前,也用于异步 SMEM read 完成后、普通代码覆写共用 storage 之前。 -Mbarrier 传达 completion 并移交 storage 使用权,proxy fence 则约束不同 proxy -的 memory effects;两者不能互相替代。 +Mbarrier 传达 completion 并移交 storage 使用权,proxy fence 则约束不同 proxy 的 memory effects;两者不能互相替代。 ## 如何编译并验证 regular head-128 specialization? -到这里需要验证三件不同的事:regular head-128 实现能否用 TVM 0.26 -编译,生成的 kernel 能否在 B200 上实际 launch,以及它的 output、maximum -logits 和 LSE 是否与前面的 reference 一致。只完成第一项并不能证明后两项。 +到这里需要验证三件不同的事:regular head-128 实现能否用 TVM 0.26 编译,生成的 kernel 能否在 B200 上实际 launch,以及它的 output、maximum logits 和 LSE 是否与前面的 reference 一致。只完成第一项并不能证明后两项。 -这个 specialization 面向 compute capability 10,其 TMA/tcgen05 形式要求 -SM100 class GPU。环境应使用 B200、CUDA 12.9 或更高版本,以及官方 Apache -TVM 0.26.0 package。 +这个 specialization 面向 compute capability 10,其 TMA/tcgen05 形式要求 SM100 class GPU。环境应使用 B200、CUDA 12.9 或更高版本,以及官方 Apache TVM 0.26.0 package。 -首先通过 [PyTorch 官方选择器](https://pytorch.org/get-started/locally/)安装 -支持 B200 的 CUDA-enabled PyTorch build。Companion repository 会 import -PyTorch,但没有把它声明为 package dependency。 +首先通过 [PyTorch 官方选择器](https://pytorch.org/get-started/locally/)安装支持 B200 的 CUDA-enabled PyTorch build。`tirx-kernels` 仓库会 import PyTorch,但没有把它声明为 package dependency。 随后安装 TVM 和 kernel repository,再运行示例: @@ -1010,8 +838,7 @@ git checkout 5be39749e7dfd2c4bdae9b4d396f8ec35af07126 pip install -e . ``` -只用一个 query row 的 smoke test 仍会覆盖完整的 128-head、top-k-2048 -kernel,同时保持 reference 时间较短: +只用一个 query row 的 smoke test 仍会覆盖完整的 128-head、top-k-2048 kernel,同时保持 reference 时间较短: ```python from tirx_kernels.flashmla.sparse_prefill_head128_phase1 import run_test @@ -1032,12 +859,9 @@ run_test( print("compile, launch, and randomized reference check passed") ``` -`run_test` 不只是 compile。它会分配随机 BF16 Q/KV 和随机 indices,运行生成的 -kernel,逐个 query row 求 FP32 PyTorch oracle,再用明确的 tolerance 检查 -output、maximum logits 和 LSE。这才是默认应使用的验证路径;仅仅编译出 PTX -无法发现 head partition 错误或遗漏 validity bit。 +`run_test` 不只是 compile。它会分配随机 BF16 Q/KV 和随机 indices,运行生成的 kernel,逐个 query row 求 FP32 PyTorch oracle,再用明确的 tolerance 检查 output、maximum logits 和 LSE。这才是默认应使用的验证路径;仅仅编译出 PTX 无法发现 head partition 错误或遗漏 validity bit。 -Repository CLI 可以运行完整的 registered configuration: +`tirx-kernels` CLI 可以运行完整的 registered configuration: ```bash python -m tirx_kernels.test \ @@ -1045,88 +869,40 @@ python -m tirx_kernels.test \ --config bench_regular_dqk576_hq128_s4096_kv8192_topk2048 ``` -Negative tests 同样重要。设置 `inject_invalid_indices=True` 可以覆盖负数和过大的 -row ID,设置 `have_topk_length=True` 可以覆盖 position predicate。还应测试全 -invalid row,并确认约定的 0/-infinity/+infinity 行为。最后,对 head-64 和 -small-top-k shapes 调用统一 dispatch entry,避免把一次成功的 regular-head128 -运行误认为已经覆盖全部 prefill specializations。即便这些 dispatch 都能通过, -也不能据此声称与完整 FlashMLA API 等价。 +Negative tests 同样重要。设置 `inject_invalid_indices=True` 可以覆盖负数和过大的 row ID,设置 `have_topk_length=True` 可以覆盖 position predicate。还应测试全 invalid row,并确认约定的 0/-infinity/+infinity 行为。最后,对 head-64 和 small-top-k shapes 调用统一 dispatch entry,避免把一次成功的 regular-head128 运行误认为已经覆盖全部 prefill specializations。即便这些 dispatch 都能通过,也不能据此声称与完整 FlashMLA API 等价。 -这些正向与异常输入测试,分别对应下面要总结的 operator semantics 与 -specialization schedule contract。 +这些正向与异常输入测试,分别对应下面要总结的 operator semantics 与 specialization schedule contract。 ## 哪些不变量属于 operator,哪些属于 specialization? -1. **缓存不变量(cache invariant)。** 一条 `h_kv=1` 的 latent KV row 可以 - 服务全部 `h_q` 个 query heads,是因为 key up-projection 已吸收到各 head 的 - query 路径,而 value up-projection 被移到 core attention 之后。RoPE channel - 仍保持显式,QK scale 仍是模型语义规定的 scale。 - -2. **稀疏契约不变量(sparse-contract invariant)。** Token selection 发生在 - sparse-prefill operator 之前;`indices` 提供 rows,重复项仍按重复项计算, - 因果合法性由 caller 保证,并且每个 `topk_length` 都必须位于 `[0, topk]`。 - 优化路径与 reference path 必须保持相同的 attention sink 和全 invalid 约定。 - -3. **所有权不变量(ownership invariant)。** 在 regular head-128 - specialization 中,一个 2-CTA cluster 负责一个 query row。这对 CTA 沿 - 不同的轴切分 Q/output heads、selected K rows 和 V features;CTA 0 的 - warp 12 是 CTA-group MMA 的唯一 issuer。 - -4. **驻留不变量(residency invariant)。** 在这个 specialization 中,$L$ - 表示 FP32 原始 logits,$W$ 表示 BF16 未归一化指数权重。K、V、$L$ 和 $W$ - 的大型 workspace 都是原位复用的单份 tile,而 `NUM_BUFS=2` 驱动的是 - barrier/phase ring。在数据缓冲区(data buffers)中,只有小型 - packed-validity mask 才有两个 physical slots。 - -5. **交接不变量(handoff invariant)。** 在这个 specialization 中,ready/done - barriers 转移每个可复用 segment 的 ownership,proxy fences 则对 generic - 与 asynchronous SMEM access 排序。唯一 issuer 保证 QK($k$) 先于 - PV($k-1$) 发射,而 threshold 为 6 的优化保证上报 maximum 的语义不变, - 并保持 online LSE 的递推关系。 - -前两条不变量定义 FlashMLA sparse-prefill operator semantics,后三条定义 -regular head-128 specialization 的 schedule contract。另一条由 dispatch 选中的 -specialization 可以修改 tile sizes、register budgets、ownership 或 barrier -topology,但必须显式给出替代 contract,而不能悄悄改变 operator 所计算的结果。 +1. **缓存不变量(cache invariant)。** 一条 `h_kv=1` 的 latent KV row 可以服务全部 `h_q` 个 query heads,是因为 key up-projection 已吸收到各 head 的 query 路径,而 value up-projection 被移到 core attention 之后。RoPE channel 仍保持显式,QK scale 仍是模型语义规定的 scale。 + +2. **稀疏契约不变量(sparse-contract invariant)。** Token selection 发生在 sparse-prefill operator 之前;`indices` 提供 rows,重复项仍按重复项计算,因果合法性由 caller 保证,并且每个 `topk_length` 都必须位于 `[0, topk]`。优化路径与 reference path 必须保持相同的 attention sink 和全 invalid 约定。 + +3. **所有权不变量(ownership invariant)。** 在 regular head-128 specialization 中,一个 2-CTA cluster 负责一个 query row。这对 CTA 沿不同的轴切分 Q/output heads、selected K rows 和 V features;CTA 0 的 warp 12 是 CTA-group MMA 的唯一 issuer。 + +4. **驻留不变量(residency invariant)。** 在这个 specialization 中,$L$ 表示 FP32 原始 logits,$W$ 表示 BF16 未归一化指数权重。K、V、$L$ 和 $W$ 的大型 workspace 都是原位复用的单份 tile,而 `NUM_BUFS=2` 驱动的是 barrier/phase ring。在数据缓冲区(data buffers)中,只有小型 packed-validity mask 才有两个 physical slots。 + +5. **交接不变量(handoff invariant)。** 在这个 specialization 中,ready/done barriers 转移每个可复用 segment 的 ownership,proxy fences 则对 generic 与 asynchronous SMEM access 排序。唯一 issuer 保证 QK($k$) 先于 PV($k-1$) 发射,而 threshold 为 6 的优化保证上报 maximum 的语义不变,并保持 online LSE 的递推关系。 + +前两条不变量定义 FlashMLA sparse-prefill operator semantics,后三条定义 regular head-128 specialization 的 schedule contract。另一条由 dispatch 选中的 specialization 可以修改 tile sizes、register budgets、ownership 或 barrier topology,但必须显式给出替代 contract,而不能悄悄改变 operator 所计算的结果。 ## 接下来应该测试什么? -Regular head-128 specialization 只是 dispatch space 中的一个点。源码树还包含 -head-64 phase-1 specialization,以及 head-128 `d_qk=512` small-top-k -specialization。它们使用不同 schedule,这说明 sparse attention 应根据 tile -economics 做 dispatch,而不应被强行塞进一个 universal template。 - -1. **复现 weight absorption。** 给可执行的 absorption proof 加入 causal mask。 - 确认 MHA mode 与 MQA mode 仍然一致,再故意把 absorbed path 的 scale 改为 - $1/\sqrt{D_{latent}}$,测量产生的误差。 - -2. **压力测试 sparse validity。** 在 `sparse_prefill_reference` 中加入全 invalid - query、重复 indices、`topk_length=0`,以及正负无穷的 sink values。分别写出 - 预期的 `(out, max_logits, lse)`。 - -3. **追踪 ownership。** 对一个 top-k tile,给 Q、K、$L$、$W$、V 和 O 的每个 - dimension 标注 `(CTA, local row, local column)`,找出一个 logical row 在哪些 - 位置需要另一个 CTA 拥有的信息。 - -4. **审计 residency。** 从 `SMEMPool` allocation 开始画出每个 alias interval。 - 验证为什么 $d_{sq}$ Q prefix 必须保持 live,而 384-column suffix 可以移到 - TMEM,并找出结束每个 reuse hazard 的 barrier。 - -5. **测量 threshold。** 对 random 和 adversarial logits 加入 instrumentation, - 统计 `should_scale_o` 取 true 的频率。比较 threshold 6、always-rebase 和 - never-rebase 三种策略的 numerical error 与 TMEM O traffic。 - -6. **比较 dispatch。** 对 head count 64/128、`d_qk` 512/576,以及 1280 附近的 - top-k values 调用 `select_kernel`。运行前先预测选择的 specialization,再检查哪些 - constraint 属于 front door,哪些由单个 specialization 强制执行。 - -7. **阅读 generated program。** 编译 smoke shape,在生成的 PTX 中找到 - `tcgen05` MMA、TMA gather、mbarrier 和 proxy-fence instructions,再把它们 - 映射回对应 TIRx line。最后重新运行 numerical check:source、generated - code 和实际观察值是三类互补的证据。 - -本章的核心结论并不局限于 FlashMLA。高性能 irregular operator 往往会分阶段 -把工作规则化:indexer 生成 sparse addresses,TMA 把这些 addresses gather 成 -dense tiles,tensor cores 消费 tiles,显式 barrier 则保护激进的 storage -reuse。只有同时理解 algorithm、dispatch contract、ownership map 和 memory -protocol,才能把高速 kernel 从难以理解的产物变成可以解释的程序。 +Regular head-128 specialization 只是 dispatch space 中的一个点。源码树还包含 head-64 phase-1 specialization,以及 head-128 `d_qk=512` small-top-k specialization。它们使用不同 schedule,这说明 sparse attention 应根据 tile economics 做 dispatch,而不应被强行塞进一个 universal template。 + +1. **复现 weight absorption。** 给可执行的 absorption proof 加入 causal mask。确认 MHA mode 与 MQA mode 仍然一致,再故意把 absorbed path 的 scale 改为 $1/\sqrt{D_{latent}}$,测量产生的误差。 + +2. **压力测试 sparse validity。** 在 `sparse_prefill_reference` 中加入全 invalid query、重复 indices、`topk_length=0`,以及正负无穷的 sink values。分别写出预期的 `(out, max_logits, lse)`。 + +3. **追踪 ownership。** 对一个 top-k tile,给 Q、K、$L$、$W$、V 和 O 的每个 dimension 标注 `(CTA, local row, local column)`,找出一个 logical row 在哪些位置需要另一个 CTA 拥有的信息。 + +4. **审计 residency。** 从 `SMEMPool` allocation 开始画出每个 alias interval。验证为什么 $d_{sq}$ Q prefix 必须保持 live,而 384-column suffix 可以移到 TMEM,并找出结束每个 reuse hazard 的 barrier。 + +5. **测量 threshold。** 对 random 和 adversarial logits 加入 instrumentation,统计 `should_scale_o` 取 true 的频率。比较 threshold 6、always-rebase 和 never-rebase 三种策略的 numerical error 与 TMEM O traffic。 + +6. **比较 dispatch。** 对 head count 64/128、`d_qk` 512/576,以及 1280 附近的 top-k values 调用 `select_kernel`。运行前先预测选择的 specialization,再检查哪些 constraint 属于 front door,哪些由单个 specialization 强制执行。 + +7. **阅读 generated program。** 编译 smoke shape,在生成的 PTX 中找到 `tcgen05` MMA、TMA gather、mbarrier 和 proxy-fence instructions,再把它们映射回对应 TIRx line。最后重新运行 numerical check:source、generated code 和实际观察值是三类互补的证据。 + +本章的核心结论并不局限于 FlashMLA。高性能 irregular operator 往往会分阶段把工作规则化:indexer 生成 sparse addresses,TMA 把这些 addresses gather 成 dense tiles,tensor cores 消费 tiles,显式 barrier 则保护激进的 storage reuse。只有同时理解 algorithm、dispatch contract、ownership map 和 memory protocol,才能把高速 kernel 从难以理解的产物变成可以解释的程序。 From 75c4607aed3bf1a002ddc34718d1912a3999006c Mon Sep 17 00:00:00 2001 From: tlopex <820958424@qq.com> Date: Fri, 14 Aug 2026 02:17:02 -0400 Subject: [PATCH 4/5] Refine FlashMLA tutorial flow --- chapter_flashmla/index.md | 767 +++++++++++++++++------------------ zh/chapter_flashmla/index.md | 410 +++++++++---------- 2 files changed, 566 insertions(+), 611 deletions(-) diff --git a/chapter_flashmla/index.md b/chapter_flashmla/index.md index 5d361614..4f749c5c 100644 --- a/chapter_flashmla/index.md +++ b/chapter_flashmla/index.md @@ -7,264 +7,199 @@ - Start from an ordinary MHA KV cache and derive why MLA stores one shared compressed state per token, including where the head-specific K/V transformations move. -- Define the FlashMLA sparse-prefill operator: an external indexer selects KV - rows, then FlashMLA attends over those rows. An executable reference fixes its - numerical behavior and edge cases. +- Define FlashMLA sparse attention: an external indexer selects KV rows, then + the kernel performs QK, softmax, and PV over those rows. An executable + reference fixes its numerical behavior and edge cases. - Use a concrete implementation to understand how sparse attention maps to Blackwell, then compile and verify it on B200. ::: -Before introducing MLA, recall why ordinary attention needs a **KV cache**. To -compute a new query, attention must read the keys and values of earlier tokens. -Recomputing them every time would repeat a large amount of work, so the system -caches the K/V states and lets later queries read them directly. - -Those states remain reusable because generative models normally use causal -attention: the K/V at position $s$ depend only on tokens up to position $s$. -Appending later tokens cannot change them. Prefill computes the prompt tokens -in parallel and fills the cache; decode then reads that cache step by step and -appends the new token's K/V. A KV cache therefore trades storage capacity and -read bandwidth for avoiding repeated computation over the whole prefix. +A language model normally predicts one new token at a time. At every step, +attention compares the query at the current position with the keys and values +of all earlier tokens, then uses the attention weights to gather information +from that history. Without saving the historical K/V states, the model would +recompute K/V for the entire prefix at every step. A **KV cache** avoids that +repeated work by storing those states once and letting later attention steps +read them directly. Generative models normally use causal attention, so the K/V +at position $s$ depend only on tokens up to position $s$ and remain unchanged +when later tokens are appended. Prefill computes the prompt tokens in parallel +and fills the cache; decode then reads that cache step by step and appends the +new token's K/V. In ordinary multi-head attention (MHA), every attention head has its own K and -V. The KV cache must therefore store every head's K/V for every processed token. -As the context grows, the amount of state that must be stored and read grows -with it. The next problem is how to reduce this cache. - -**Multi-head Latent Attention (MLA)** uses a different cache representation. -Instead of storing expanded K/V for every head, it stores one compressed state -per token and shares that state across all heads. This does not merge all heads -into one. Each head still has its own transformations; the cache simply no -longer stores the K/V produced by those transformations as long-lived state. We -will derive how one shared state can preserve head-specific behavior. - -MLA specifies what the cache stores and how attention is computed; FlashMLA -addresses how to perform those computations efficiently on a GPU. **FlashMLA** -is DeepSeek's library of optimized GPU kernels for MLA, with operators for -different attention stages and cache formats. - -This chapter focuses on sparse attention during prefill. Unlike dense attention, -which visits the whole history, an external indexer first selects the relevant -KV rows and FlashMLA attends only to those rows. We will first establish the -shared operator semantics and postpone implementation choices until the -algorithm is clear. - -This raises the central MLA question: if multiple query heads read one shared -cached state, how can they still produce different results? The key is that only -the compressed source state is shared. Head-specific transformations do not -disappear; they move to the two sides of the core attention computation. The -next figure uses 128 heads to make the question concrete, while the derivation -that follows keeps the head count general. - -```{figure} ../img/flashmla_cache_story.png -:width: 100% -:alt: Ordinary MHA caches separate key and value data for every head; MLA stores one shared compressed state and keeps head-specific work around attention - -Ordinary MHA stores a separate key/value slice per head. MLA stores one shared -compressed content state plus shared position information per token; -head-specific query and output transformations happen before and after -attention. -``` - -Why is the transformation in the figure valid? Start with the ordinary MHA KV -cache. - -## Start with the ordinary MHA KV cache - -The intuition above does not yet tell us how large the cache is. Let -$h_t\in\mathbb{R}^{d_{model}}$ be the hidden state of token $t$. Write $n_h$ -for the number of heads and $d_h$ for the width of one head; $i$ selects a head, -while $s$ will select a cached key-token position. Ordinary MHA produces a -separate query, key, and value for every head $i$: +V, so the KV cache must store every head's K/V for every processed token. As the +context grows, the cache consumes more GPU memory, and attention must read an +ever-longer K/V history for every newly generated token. It can therefore +become both a capacity and a memory-bandwidth bottleneck. **Multi-head Latent +Attention (MLA)** reduces these costs by changing the cache representation: it +compresses the K/V-related information for each token into one state shared by +all heads. During attention, every head still applies its own transformations +and therefore retains distinct attention behavior. + +FlashMLA is DeepSeek's library of optimized GPU kernels for MLA. This chapter +studies one sparse-attention forward kernel for Blackwell that is used during +prefill. While the prompt tokens are processed in parallel, an external indexer +first selects the history positions that each query token should attend to. The +kernel loads the corresponding KV rows, then performs QK, softmax, and PV. Compared with +dense attention, it reduces only the history positions that participate in the +calculation; the main attention chain remains unchanged. + +In the kernel studied here, each query token corresponds to 128 query heads, +while every selected history token has one KV-cache row shared by those heads. +But if 128 heads read the same row, how can they still produce different +results? The cached compressed state is shared, but every head retains its own +transformations on the query and output paths. To see how those transformations +move, start with the KV cache of ordinary MHA. + +## Ordinary MHA KV-cache cost + +Ordinary MHA has $n_h$ heads of width $d_h$, each with its own query, key, and +value projections. Fix one head and write its projection matrices as $W^Q$, +$W^K$, and $W^V$. Within one layer, write the current token vector entering the +attention projections as $h_t$ and the input vector for the earlier token at +position $s$ as $h_s$. Then $$ -q_{t,i}=W_i^Q h_t,\qquad -k_{t,i}=W_i^K h_t,\qquad -v_{t,i}=W_i^V h_t. +q=W^Q h_t,\qquad +k_s=W^K h_s,\qquad +v_s=W^V h_s. $$ -For a query at position $t$, head $i$ computes +This head computes $$ -p_{t,s,i}=\operatorname{softmax}_s -\left(\frac{q_{t,i}^{\mathsf T}k_{s,i}}{\sqrt{d_h}}\right), +p_s=\operatorname{softmax}_s +\left(\frac{q^{\mathsf T}k_s}{\sqrt{d_h}}\right), \qquad -o_{t,i}=\sum_s p_{t,s,i}v_{s,i}. +o=\sum_s p_s v_s. $$ -The output projection mixes the per-head results. During autoregressive -generation, however, every earlier $k_{s,i}$ and $v_{s,i}$ must remain available. -The cache therefore stores $2n_h d_h$ elements per token per layer: one K slice -and one V slice for every head. +During autoregressive generation, the current query can be discarded after use, +but later queries repeatedly read the historical $k_s$ and $v_s$. +Each layer therefore caches $2n_hd_h$ elements per token: one K and one V for +every head. -Batch size, sequence length, layer count, and dtype quickly amplify that number. -For a batch of $B$ equal-length sequences of length $S$, a model with -$N_{layer}$ layers, and $b_{elem}$ bytes per element, an ordinary MHA KV cache -occupies +The total grows linearly with batch size, context length, and layer count. For +example, 32 layers, context length 4096, 32 heads of width 128, batch size 1, +and BF16 require about 2 GB of KV cache. Generating every new token +also rereads this growing history, so KV cache creates both memory-capacity and +bandwidth pressure. -$$ -M_{MHA}=2N_{layer}BSn_hd_hb_{elem}\quad\text{bytes}. -$$ - -For a variable-length batch, replace $BS$ with $\sum_{j=1}^{B}S_j$, where $S_j$ -is the length of sequence $j$. As a concrete example, 32 layers, batch size 1, -context length 4096, 32 heads of width 128, and BF16 require 2 GiB for the KV -cache alone. This estimate excludes allocator metadata, model weights, and -other intermediate state. - -For a fixed $d_{model}=n_h d_h$, changing only the head count need not change -that total width. The structural cost is that the cache still materializes -separate per-head state. - -During dense decode, each new query reads the growing K/V history, so those -reads often become a bottleneck. A smaller representation not only permits a -longer context or larger batch; it also reduces HBM traffic on every decode -step. - -Multi-query attention (MQA) reduces the cache by sharing one K/V head across all -query heads. Grouped-query attention shares within groups. Those are useful model -architectures, but MLA takes a different route: retain the expressive per-head -projections while caching a shared low-dimensional source from which they can be -recovered. +One direct way to reduce this cost is to share more state across query heads. +Multi-query attention (MQA) shares one K/V pair across all query heads, while +grouped-query attention (GQA) shares within groups. MLA uses a different form of +sharing: every head retains its own projection, but the cache stores only one +shared low-dimensional state. -### What if we cache one shared state first? +### From a shared state to a low-dimensional latent cache -Temporarily ignore RoPE and low-rank compression. Let $h_s$ denote the hidden -state fed to the attention projections at position $s$ in one layer. It is not -a token embedding from the vocabulary. The superscript $C$ denotes the -non-positional content channel; ordinary MHA content keys and values are +Start with the non-positional content path and write the current query content +as $q^C$. Ordinary MHA first forms $k_s^C=W^Kh_s$, then computes the content +score in QK. Associativity lets us rewrite that step as $$ -k_{s,i}^{C}=W_i^Kh_s,\qquad v_{s,i}^{C}=W_i^Vh_s. +\mathrm{QK}_s +=(q^{C})^{\mathsf T}k_s^C +=(q^{C})^{\mathsf T}W^Kh_s +=\left((W^K)^{\mathsf T}q^{C}\right)^{\mathsf T}h_s. $$ -If we cache one shared $h_s$, associativity and the distributivity of a linear -map over a sum let us change the evaluation order: +PV likewise forms $v_s=W^Vh_s$ before taking the attention-weighted sum with +weights $p_s$. Linearity gives $$ -(q_{t,i}^{C})^{\mathsf T}W_i^Kh_s -=\left((W_i^K)^{\mathsf T}q_{t,i}^{C}\right)^{\mathsf T}h_s, -\qquad -\sum_s p_{t,s,i}W_i^Vh_s -=W_i^V\left(\sum_s p_{t,s,i}h_s\right). +\mathrm{PV} +=\sum_s p_s v_s +=\sum_s p_s W^Vh_s +=W^V\left(\sum_s p_s h_s\right). $$ -The left side expands K/V for every key and every head. The right side moves -the key projection to the current query and the value projection after the -weighted sum. The values are identical, yet only one $h_s$ must persist. Think -of this as an uncompressed latent-cache thought experiment. - -The problem is that $h_s$ is still $d_{model}$ coordinates wide. The cache is -shared across heads, but QK (the query--key dot product) and PV (the -probability--value weighted sum) now operate in that wide space, so this is -usually not a practical design. MLA adds a learned low-rank bottleneck that -shrinks the shared state to $d_c$ coordinates. The original -[DeepSeek-V2 MLA derivation](https://arxiv.org/abs/2405.04434) defines +The first identity moves the key projection to the current query; the second +moves the value projection after the weighted sum. The numerical results stay +the same, while the cache only needs to retain one $h_s$. Think of this as an +uncompressed latent-cache thought experiment. -$$ -c_t^{KV}=W^{DKV}h_t, -$$ +$h_s$ is still $d_{model}$ coordinates wide. Caching it shares state across +heads, but QK scoring and PV aggregation still operate in that wide space. +Actual MLA uses two steps. -followed by separate up-projections +First, every head shares a matrix $D$ that compresses $h_s$ into a +$d_c$-dimensional vector $c_s$. For the content path, the KV cache stores only +this $c_s$: $$ -k_{t,i}^{C}=W_i^{UK}c_t^{KV},\qquad -v_{t,i}^{C}=W_i^{UV}c_t^{KV}. +c_s=Dh_s,\qquad c_s\in\mathbb{R}^{d_c}. $$ -Here $c^{KV}\in\mathbb{R}^{d_c}$ is the shared latent state. The thought -experiment above corresponds to $d_c=d_{model}$, $W^{DKV}=I$, $c^{KV}=h$, -$W_i^{UK}=W_i^K$, and $W_i^{UV}=W_i^V$; MLA learns a much narrower $c^{KV}$. - -This low-rank step is not a lossless compression of an arbitrary pretrained -MHA. It is a joint low-rank structure imposed during training. If we write the -MLA content path as an equivalent projection from $h_t$, its effective K/V -projection matrices factor as +Second, each head uses its own matrices $U_K$ and $U_V$ to obtain that head's +content key and value from $c_s$: $$ -W_i^K=W_i^{UK}W^{DKV},\qquad -W_i^V=W_i^{UV}W^{DKV}. +k_s^C=U_Kc_s,\qquad +v_s=U_Vc_s. $$ -Thus every head's content K/V projections share the right factor $W^{DKV}$. -These $W_i^K$ and $W_i^V$ denote the effective MLA projections defined by this -factorization; the equations do not claim that arbitrary MHA projection -matrices can always be factored this way. Under the MLA training constraint, -the model learns what information to preserve in $c^{KV}$. - -The construction therefore has two steps: use associativity and linearity to -move per-head projections to the query and output paths so that one shared state -can participate directly in core attention, then use a learned bottleneck to -make that state narrow. The cache stores one $c^{KV}$ per token instead of -expanded $k^C$ and $v^C$ for every head. +$D$, $U_K$, and $U_V$ are learned together during model training. Because $d_c$ +is much smaller than $d_{model}$, the content state cached for each token is +correspondingly smaller. -### Why does RoPE need a separate positional channel? +### RoPE and the separate positional channel -Rotary positional embedding (RoPE) rotates a position-carrying subspace of Q -and K. Let $R_u$ denote the RoPE rotation at position $u$. Suppose we applied -RoPE directly to the content query and key. Their dot product would become +The preceding content-only QK path has no position-dependent transform on the +query side, so one transformed query can be reused for every cached row. RoPE +rotates Q/K according to token position; let $R_t$ and $R_s$ be the rotations +at positions $t$ and $s$. Applying it directly to the content query and content +key would give $$ -\left(R_tq_{t,i}^{C}\right)^{\mathsf T} -\left(R_sW_i^{UK}c_s^{KV}\right) +\left(R_tq^{C}\right)^{\mathsf T} +\left(R_sU_Kc_s\right) = -(q_{t,i}^{C})^{\mathsf T}R_t^{\mathsf T}R_sW_i^{UK}c_s^{KV}. +\left(U_K^{\mathsf T}R_s^{\mathsf T}R_tq^{C}\right)^{\mathsf T}c_s. $$ -The factor $R_t^{\mathsf T}R_s$ changes with the relative query/key position. -Matrix multiplication can still be reassociated, of course, but $W_i^{UK}$ can -no longer be folded into one projection that the current query can reuse for -every key position. MLA therefore uses a decoupled positional channel: each query head has -$q_{t,i}^{R}$, while all heads share a cached $k_t^R$. The actual MHA-form query -and key are +The query position $t$ is fixed, but the historical position $s$ changes from +one cached row to another. The transformed query in parentheses therefore also +changes with $s$ and cannot be computed once and reused across the history. -$$ -q_{t,i}=[q_{t,i}^{C};q_{t,i}^{R}],\qquad -k_{s,i}=[k_{s,i}^{C};k_s^R]. -$$ +MLA instead separates content and position into two paths. The content path +does not apply RoPE and continues to compute $(q^C)^{\mathsf T}U_Kc_s$. The +positional channel is a small extra block of Q/K coordinates, not another +attention head. Let $q_t^R$ and $k_s^R$ denote the positional query and key +after RoPE has been applied at positions $t$ and $s$. $q_t^R$ belongs to the +current head, whereas $k_s^R$ is shared by all heads and cached. -The unscaled score therefore separates into +The two paths produce $$ -\operatorname{score}_{t,s,i} -=(q_{t,i}^{C})^{\mathsf T}W_i^{UK}c_s^{KV} -+(q_{t,i}^{R})^{\mathsf T}k_s^R. +\mathrm{content}_s=(q^{C})^{\mathsf T}U_Kc_s, +\qquad +\mathrm{position}_s=(q_t^{R})^{\mathsf T}k_s^R, $$ -The cache is now $[c_s^{KV};k_s^R]$, still shared across heads. The positional -channel remains explicit; weight absorption applies to the content channel. +and the final score is -This lets us compare MLA with ordinary MQA precisely. The table counts cached -elements per token per layer; it does not compare model quality or include dtype -and allocator metadata. - -| Mechanism | Cached elements per token per layer | Cached state | -| --- | ---: | --- | -| MHA | $2n_hd_h$ | $n_h$ expanded K/V heads | -| GQA | $2n_{kv}d_h$ | $n_{kv}$ expanded K/V heads, $1

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