Prizma

⚠️ Research artifact / method — not a plug-and-play model. There are no task weights to load; this repository presents two small-scale research threads, their code, and their auditable results.

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)	PASS	Prizma 1.7496 vs TF 1.7254 BPC — within the pre-registered +0.05 bar (does not beat TF)
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 ~1.3–1.6× 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). The quad2 kernel belongs to the Based/Hedgehog feature-map family — the novelty is the rectangular-delta-state framing, not the kernel.

• 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

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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 (equations, borrowed-vs-new ledger, neuromorphic mapping, limits) → docs/Prizma_EN.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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Citation

@misc{prizma2026,
  author       = {Aylin},
  title        = {Prizma: A Parameter-Free Quadratic Delta-State Sequence Mixer and a Backprop-Free Local Continual Learner},
  year         = {2026},
  note         = {Research artifact}
  % eprint = {XXXX.XXXXX}, archivePrefix={arXiv}, primaryClass={cs.LG}
}

License

Released under the Apache-2.0 license.

Author

Aylin — Independent Researcher