callensxavier/cy-sieve-attention-benchmark

CY-Sieve Attention — GPU benchmark results (NVIDIA L4, 2026-06-22)

Benchmark artifacts for the CY-Sieve positional-attention kernel, a falsifiable engineering experiment from the Mirror-Map-Sieve project. The bias derives from the weight-5 Apéry-like sequence $S_{20}(n)=\sum_k \binom{n}{k}^4\binom{n+k}{k}$ (a Calabi–Yau 3-fold period; the geometry fixes the long-range decay slope $\log\lambda=3.762$ and curvature $\beta=2$).

⚠️ Headline: this is a documented NEGATIVE result

On real WikiText-2, trained from scratch, the positional scheme failed its quality gate (KILL, +10.15%) — a plain sliding window beat every CY-Sieve variant. The kernel is numerically correct and has a real memory advantage, but a fast kernel that hurts model quality is a failed kernel. We publish the negative result deliberately; it is the science working as intended.

Files

file	contents
quality_perplexity.csv	§5 quality gate — val perplexity per positional scheme × context (the decisive result)
perf_hbm.csv	§6 — kernel latency + bias-path HBM bytes per sequence length
run3_20260622_l4_quality.json	raw §5 output (corpus, config, verdict)
run3_20260622_l4_perf.json	raw §6 output
run3_20260622_l4_gpu_phase.json	orchestrator summary (§4/§5/§6 headline)
run3_20260622_l4.log	full run log
PHASE3_CYSIEVE_GPU_FINDINGS.md	the complete findings writeup + redesign directions

§5 — Quality gate (the decisive result)

Methodology: train small GPTs from scratch, identical arch/data/compute, one per positional scheme, on real WikiText-2 (Salesforce/wikitext), byte-level. (Zero-shot-swapping the scheme on a frozen model was tried and rejected as invalid — it collapses every scheme equally.) Validation perplexity:

scheme	@512 (train)	@1024 (2×)	@2048 (4×)
learned-absolute	4.22	12.10	20.82
ALiBi	10.74	11.73	11.35
sliding-window	4.99	5.07	5.03
CY-Sieve τ-ladder	11.33	12.31	12.05
CY-Sieve τ=20	16.02	16.81	16.49
CY-Sieve τ=128	6.80	7.12	7.00
CY-Sieve τ=512	4.65	6.08	10.62

Verdict: KILL. Best baseline 4.22 (learned-absolute); best CY-Sieve 4.65 (τ=512) → +10.15%, past the >5% kill threshold. The geometry-fixed slope is too steep for a drop-in scheme: no single τ balances absolute quality against extrapolation, and the τ-ladder lands at ~11–12.

§6 — Performance + memory (NVIDIA L4, D=64, fp16, causal)

L	CY-Sieve (ms)	dense SDPA (ms)	bias-HBM reduction
4096	0.26	0.06	2048×
8192	1.08	0.29	4096×
16384	4.16	1.02	8192×
32768	15.28	2.51	16384×

The bias-path HBM claim is confirmed — O(L) bytes (recurrence-generated) vs O(L²) for a materialized table. But the unfused kernel is ~4–6× slower than fused dense SDPA: a memory-traffic win, not a latency win. Per the project's honesty rule, with §5 failing these numbers are not presented as a contribution.

Autoresearch follow-up (2026-06-22): can a learnable slope beat the baselines?

A propose→screen→select sweep of 10 hypotheses (autoresearch_results.csv, raw/autoresearch_*) testing two fixes to the KILL: learnable per-head γ "Holonomic-ALiBi" ($\text{bias}h(d)=-\gamma_h\log S{20}(d)$, γ learnable, O(L) kept) and a "Comet" hybrid (local window + CY tail).

• Screen (1200 steps): learnable-γ Holonomic-ALiBi BEAT every baseline — holo_ladder 5.89 vs ALiBi 6.15. The mechanism works.
• Full (6000 steps): the ranking INVERTED — best CY 12.7 vs best baseline 4.3. The setup over-trained (~37 epochs over a 2 MB corpus); the expressive learnable bias overfit hardest (train loss 3× lower, val 3× worse) and γ drifted steeper, not flatter. Still KILL — but UNCONFIRMED, not refuted.
• One survivor: the holonomic schemes extrapolate flat (12.7→13.3 over 512→2048) where learned-absolute collapses (4.3→20.6).

A v2 run (γ-regularization toward flat + validation early-stopping + larger corpus) is testing whether the screen-scale +4% margin survives. Lesson: a short screen preferentially crowns the highest-capacity hypothesis — exactly the one that overfits at scale; validate the winner at the target budget.

Hardware / reproducibility

NVIDIA L4 (24 GB), PyTorch 2.9.1+cu129, Triton 3.5.1. §4 Triton↔reference parity: PASS (4/4). Full method: PHASE3_CYSIEVE_GPU_FINDINGS.md and the repo.

Citation

@misc{callens2026cysieve,
  author = {Callens, Xavier},
  title  = {CY-Sieve Attention: a Calabi--Yau positional bias and its negative quality result},
  year   = {2026},
  url    = {https://github.com/xaviercallens/Mirror-Map-Sieve},
  doi    = {10.5281/zenodo.20747943}
}