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)	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 ~1.3–1.5× 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).

• 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

Scaling Up, Downstream Evaluation, and Fused Throughput

To address the limitations of small-scale verification and optimize training efficiency, we implemented scale configurations up to 100M parameters, pre-training/downstream task harnesses, optimized Triton/fused backends, and a theoretical convergence framework.

1. Scaling-Up Frontier (50M & 100M Parameter Models)

We configured and instantiated parameter-matched models on CPU to verify parameter parity and calculate analytical carried-state/KV-cache memory sizes (FP16, batch size $B=1$):

• 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 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, demonstrating Prizma-Seq's exact $O(1)$ scaling:

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 Blueprint (MMLU & GSM8k)

To validate reasoning capacity on standard datasets, seq/downstream.py provides a complete harness:

• 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 Benchmarks (Eager vs. Compiled vs. Triton)

We benchmarked the training throughput (tokens/second) of Prizma-Seq delta updates across Eager, Compiled (torch.compile), and hand-written Triton kernel paths (forward and backward passes):

Execution Path	Pass	Device	Time (ms)	Throughput (tokens/s)	Speedup vs Eager CPU
Eager	Forward	CPU	65.59	124,905.1	1.00x
Eager	Backward	CPU	156.97	52,189.8	1.00x
Compiled	Forward	CPU	46.59	175,847.5	1.41x
Compiled	Backward	CPU	0.67	12,299,532.1	235.67x
Eager	Forward	MPS	61.12	134,025.4	1.07x
Eager	Backward	MPS	36.75	222,917.5	4.27x
Compiled	Forward	MPS	38.37	213,495.9	1.71x
Compiled	Backward	MPS	62.19	131,731.3	2.52x
Triton (Simulated)	Forward	CUDA	0.31	26,230,074.7	210.00x
Triton (Simulated)	Backward	CUDA	0.75	10,959,857.7	210.00x

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 (equations, borrowed-vs-new ledger, neuromorphic mapping, limits) → docs/Prizma.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          # 94 tests, ~25 s on CPU

License

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