Prizma

Two small-scale research threads built the same way: a pre-registered falsifiable bar, a parameter/FLOP-matched baseline, an adversarial referee audit, and honest, binding limits. No faked metrics — every number is produced by a reproducible script and the raw result JSONs are committed under results/.

Thread	Question	Verdict (in the tested regime)
Prizma-Seq	Can a parameter-free quadratic delta-state sequence mixer stand in for attention at small scale?	Candidate — clears the §4 diagnostic bar param-matched vs a tuned Transformer; constant-memory + long-context O(1)-latency edge; honest losses disclosed.
Prizma	Can a backprop-free, fully-local learner do task-boundary-free continual learning?	Zero forgetting in the input-distinguishable regime, beating backprop & EWC — no replay, no boundaries, no weight transport.

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Prizma-Seq — efficient-attention-replacement candidate

Prizma-Seq is a Gated-DeltaNet-family sequence mixer whose novel lever is a parameter-free quadratic feature map (quad2) that makes the per-head carried associative state rectangular (d_h × d_φ, with the monomials as fixed seeded buffers → 0 added parameters). At small scale, parameter-matched against a tuned decoder-only Transformer (RMSNorm + SwiGLU + RoPE), it clears the project's pre-registered §4 bar:

Leg	Verdict	Headline
MQAR (D=128)	PASS	parity @860K params; solves @130K where the matched TF needs ≥461K → ≥3.5× param-efficiency (coarse grid)
Induction	PASS	quad2 0.9995 (3/3) vs TF 0.996
Selective-copy	PASS	selective 0.9991; a fixed-position control isolates content-selectivity
Char-LM (text8)	PARTIAL — deviated from pre-registration	Prizma 1.7496 vs TF 1.7254 BPC clears the +0.05 margin, but the pre-registered bar demanded both corpora with ≥3 seeds (≥5 for the closest leg). Delivered: text8 only, n=2 — and the other corpus, tiny-shakespeare, FAILED (−0.09) with its raw data not retained. See below.
Inference	PASS (memory)	constant 17.9 MB state ∀n (28–455× less); measured O(1)-latency crossover at n≥32k (2.4–2.8× faster @65k)
Causal ablation	PASS	quad2 ≫ rand_linear ≈ none ≫ TF — the gain is the quadratic monomials, not "a bigger RNN"
Length-extrapolation	WIN (relative)	10× better retention than a RoPE Transformer at 8× train length (absolute accuracy still only ~0.40)

Honest scope — a candidate, not a proven alternative. Char-LM is a loss-within-margin; the latency win is long-context-only (Prizma is ~1.3–1.5× slower below n≈16k) and Prizma trains ~5× slower per step (sequential delta); the FLOP-matched TF arms were optimization-confounded so no per-FLOP claim is made; n=2–3 seeds are descriptive (not powered equivalence); large-scale LM parity and backprop-free parity are NOT claimed (open frontiers).

Corrections and quarantined results (read this before citing anything)

B4 char-LM is a PARTIAL, not a PASS. Spec §B4 pre-registered: test BPC ≤ T+0.05 on BOTH corpora, ≥3 seeds (≥5 for the closest leg). What was delivered is one corpus (text8) at n=2, after the other corpus (tiny-shakespeare) had failed by −0.09 under an overfitting recipe — and that failing run's raw data was not retained on disk, so it cannot be re-examined. A later text8 run reached n=7 vs TF n=10 (Δ = +0.021, still within the margin, and the gap is statistically real: Welch t≈6.7). Calling this leg PASS took credit for a bar that was not met. The result is real and the margin is genuinely cleared on the corpus that was run — it is the pre-registration that was not honoured, and the deviation now sits in the verdict rather than in the fine print.

The powered n=10 recall gate is QUARANTINED — do not cite it. results/campaign_2026-06-08/recall_gate.json is not the n=10 run it describes. A resume-cache bug in seq/recall_gate.py skipped seeds it had already seen keyed on the seed number alone, with no record of the configuration, so an earlier tiny --smoke run supplied seeds 0–1 in all ten cells — at a 4× smaller scale, and for the candidate arm with its key lever (quad2) switched off. It also supplied the stage-1 LR sweep in all ten cells, meaning every arm's learning rate was chosen on the wrong model over the wrong grid. Consequently the reported params, the standard deviations, the CIs, and the published reading that "the Transformer baseline is high-variance… on induction TF is bimodal: ~half its seeds collapse to ~0.06" are all untrustworthy — that last one is a caching bug partly misdiagnosed as a property of the baseline (among the 8 uncontaminated seeds, 3 collapse, not 5 of 10). The error direction was conservative: it widened the CIs and handicapped the candidate, so it produced an under-claim, not an over-claim. The artifact has not been re-run and no replacement numbers have been invented — a clean campaign needs ~28 A100-hours. Full disclosure: results/campaign_2026-06-08/CONTAMINATION.md. The bug is fixed (resume is now keyed on (seed, config-fingerprint)) with regression tests.

Baselines that were built and never run. seq/gla.py (GLA), seq/mamba2.py (Mamba-2) and the 4-arm head-to-head harness seq/landscape.py are faithful, fully-tested implementations that have produced zero results. No GLA or Mamba-2 number appears anywhere in this repo, and none is claimed. The harness exists and has not been run at scale.

• Full writeup + adversarial referee trail → docs/PRIZMA_SEQ_REPORT.md
• Raw A100 results (auditable) → results/gpu_{bench,diag,lengen,latency,charlm2}.json + results/v3_campaign_results.md
• Code → seq/ (mixer, tasks, transformer baseline), gpu_*.py (GPU runners), PRIZMA_run_*.ipynb (Colab bootstrap)

# local kernel self-tests / smoke (CPU/MPS), then the GPU runners on an A100:
PRIZMA_RESULTS=results python gpu_diag.py induction selcopy   # B2/B3
PRIZMA_RESULTS=results python gpu_charlm2.py --skip_none      # B4 (text8)
PRIZMA_RESULTS=results python gpu_latency.py                  # B5 latency/memory
PRIZMA_RESULTS=results python gpu_lengen.py                   # length-extrapolation

Apparatus built beyond the tested regime — what has and has not been run

Read this heading literally. The three subsections below are apparatus and arithmetic, not results. No model above ~1.4M parameters has been trained. No downstream benchmark has been run. The only measured numbers here are the throughput timings in §3, and they are laptop timings.

1. Parameter-count scaling at 50M & 100M — NO TRAINING RUN

These models were instantiated on CPU purely to count parameters and to evaluate a closed-form memory formula. They were never trained, never evaluated, and produced no accuracy or loss number of any kind. What follows is a parameter count and an analytical memory identity:

• 50M Scale: Prizma-Seq (47,964,832 params; $d_{model}=512, L=10, H=8, d_{phi}=320, \text{window}=16$) vs. Transformer (48,015,872 params; $d_{ff}=1376, \text{rope}=\text{True}$).
• 100M Scale: Prizma-Seq (102,602,760 params; $d_{model}=768, L=11, H=12, d_{phi}=320, \text{window}=16$) vs. Transformer (102,653,184 params; $d_{ff}=2056, \text{rope}=\text{True}$).

Analytical (closed-form, NOT measured) memory comparison ($B=1$, FP16): The memory ratio of Transformer KV-cache to Prizma-Seq state size ($\frac{2 \cdot T}{d_{phi} + 2 \cdot W}$) is independent of depth and width. This is an algebraic property of the two state definitions, evaluated on paper — it is not an allocation measurement, and it says nothing about whether either model at this scale would learn anything:

Sequence Length ($T$)	Transformer KV-Cache (50M)	Transformer KV-Cache (100M)	Prizma State (50M / 100M)	Ratio
1,024 Tokens	20.00 MB	33.00 MB	3.44 MB / 5.67 MB	5.82x
8,192 Tokens	160.00 MB	264.00 MB	3.44 MB / 5.67 MB	46.55x
65,536 Tokens	1.25 GB	2.06 GB	3.44 MB / 5.67 MB	372.36x

Details: seq/scaling_analysis.py | JSON: results/scaling_analysis.json | Report: results/scaling_analysis.md

2. Downstream evaluation (MMLU & GSM8k) — PLANNED, NOT RUN

seq/downstream.py is a harness with no committed results. Nothing in this repo has been pre-trained on OpenWebText/The Pile, and neither MMLU nor GSM8k has ever been scored. The code exists; the evaluation does not:

• Pre-Training: A StreamingTextDataset for token packing standard corpus streams (OpenWebText/The Pile) and a PyTorch pre-training loop.
• Downstream Tasks: Few-shot/zero-shot evaluations for MMLU multiple-choice question-answering (via token log-probabilities) and GSM8k math word problems (via autoregressive causal/recurrent decoding).

3. Training throughput (Eager vs. Compiled) — measured on a laptop

Wall-clock timings of the Prizma-Seq delta update, forward and backward. Every row is measured on the device it names. There are no CUDA or Triton rows because this benchmark has not been run on a CUDA box, and nothing is extrapolated to stand in for one.

Execution Path	Pass	Device	Time (ms)	Throughput (tokens/s)	Speedup vs Eager CPU
Eager	Forward	CPU	41.18	198,934.1	1.00x
Eager	Backward	CPU	104.85	78,132.7	1.00x
Compiled	Forward	CPU	26.57	308,341.2	1.55x
Compiled	Backward	CPU	43.17	189,757.1	2.43x
Eager	Forward	MPS	42.72	191,738.2	0.96x
Eager	Backward	MPS	88.60	92,455.3	1.18x
Compiled	Forward	MPS	42.00	195,061.5	0.98x
Compiled	Backward	MPS	84.71	96,705.4	1.24x

B=8, H=4, T=1024, d=64, chunk=64 (8,192 tokens/pass); 5 warmup + 20 timed runs, mean; Apple M4, torch 2.12. Forward and backward are timed in separate loops with synchronisation barriers, not by subtracting one from a combined loop. Absolute times move by up to ~2x with machine load — read the ordering and the ratios, not the milliseconds. On MPS the "Compiled" path falls back to eager (see seq/benchmark_results.md).

Correction (superseded numbers). An earlier version of this table carried six CUDA (Simulated) rows computed as t_cpu / {120, 180, 210} from hardcoded constants and printed to one decimal place next to the measured rows — they were arithmetic on a CPU timing, not measurements of any GPU, and they have been deleted. It also carried a row reading Compiled | Backward | CPU | 0.6660 ms | 235.67x | Measured — a backward pass ~70x faster than its own forward, which is not physically possible. That was a timing-method artifact (t_bwd = t_combined - t_fwd collapsing); the method has been fixed and the whole table re-measured.

Details: seq/throughput_benchmark.py | Report: seq/benchmark_results.md

4. Gradient Stability & Theoretical Convergence

A mathematical analysis in docs/quad2_theoretical_convergence.md proves:

• Jacobian Contractiveness: The recurrent delta state transition Jacobian spectral norm is strictly bounded by the decay gate: $| J_t |_2 \le \alpha_t \le 1.0$, preventing exploding gradients during BPTT.
• Gershgorin Capacity Bounds: Using the Gershgorin Circle Theorem, we derive the capacity limit $N < 1 + 1/\text{cross}(\phi)$, showing that quadratic keys (quad2, crosstalk ~0.076) push capacity bounds to $N < 14$ compared to $N < 8$ for linear keys (none), resolving the capacity block on MQAR $D=128$.

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Prizma — backprop-free, fully-local continual learning

A backprop-free, fully-local, predictive-coding learning architecture targeting neuromorphic/analog hardware.

Prizma demonstrates task-boundary-free, task-label-free continual learning: in an input-distinguishable (domain-incremental) stream it reaches zero forgetting while beating naive backprop and (boundary-using) EWC — using only local learning rules (no backprop, no weight transport; works with random-feedback DFA). Its limits are characterized honestly: it provides no benefit in the fully-ambiguous regime (proven impossible for any single-head learner) and degrades gracefully as domains overlap.

Headline result (E1, structured-permuted, 10 seeds, ±95% CI)

Learner	ACC	FGT (forgetting↓)	boundaries?	buffer?	W^T?
backprop MLP	0.445	0.553	—	—	—
EWC	0.456	0.411	yes	—	—
replay (buffer 1000)	0.737	0.156	yes	yes	—
oracle_multihead (upper bound)	0.879	0.000	task-id given	—	—
Prizma (DFA, no W^T)	0.834	0.000	none	none	none
Prizma (exact W^T)	0.708	0.000	none	none	yes
PRIZMA_noRoute (ablation)	0.446	0.489	—	—	—

Prizma sits between replay and the task-id-oracle, matching the oracle's zero forgetting without being told the task id, no replay, no boundaries, no weight transport (the W^T-free DFA variant is the best). The ablation shows recognition-routing is the causal mechanism. Adversarially audited by a 4-referee panel (no leakage, fair, reproduces, honest).

• Full writeup — the most self-critical document in this repo — → docs/Prizma.md (equations, borrowed-vs-new ledger, neuromorphic mapping, iteration log of what failed, limits). It is worth reading for §8 alone, where the author explains why the headline number above is nearly free: "FGT=0 is an architectural quasi-tautology; the real achievement is the routing." Written in Turkish; now translated in full, with the original preserved verbatim at docs/Prizma.tr.md.
• Code → src/ (prizma + baselines + data + metrics), experiments/ (E1–E5 suite + figure)

python3.13 -m venv .venv && ./.venv/bin/pip install numpy matplotlib
./.venv/bin/python experiments/run_continual.py   # ~2.5 min → results/results.json
./.venv/bin/python experiments/make_figure.py      # → results/figure.png

Status: research prototypes. Neither thread claims large-scale parity; each is a falsifiability gate passed (or honestly refused) in a precisely-characterized small-scale regime.

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Reproducing the falsifiability harness

The invariant test suite (kernel guards, lever off == identical checks, O(1) step == forward equivalence, and the anti-conservative statistics gate) runs on every push via CI:

pip install torch --index-url https://download.pytorch.org/whl/cpu
pip install -r requirements.txt pytest
pytest -q          # CPU-only (what CI runs): 211 collected -> 201 passed, 10 skipped, ~3 min.
                   # 225 collected where MPS is available (216 passed, 9 skipped): several
                   # kernel-equivalence tests are parametrised over devices.

The "94 tests" figure this README used to quote was long out of date — CI was already collecting over 200. The badge above was also green over a red run: CI had been failing since 2026-06-20 on a missing shakespeare.txt fixture. That is fixed, and the counts above are from the passing run.

License

Prizma is released under the Apache License 2.0. © 2026 The Prizma Authors.