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) confirmed the margin survives: +8.1% PASS at GPU scale. A controlled
attribution experiment then showed the gain is learnability, not the Calabi–Yau
shape (PHASE4_HC_ATTRIBUTION.md). Lesson: a short screen preferentially crowns
the highest-capacity hypothesis — exactly the one that overfits at scale; validate
the winner at the target budget.
Final selection (Phases 5–6): plain learnable-ALiBi
Two further GPU bake-offs settled the shipped form (hetero_pos_extrapolation.csv,
raw/hetero_pos_gpu_20260623.*):
Bias-family bake-off (PHASE5_FINAL_BAKEOFF.md): of six learnable families,
learnable-ALiBi wins; log-curvature, Fourier, the fixed CY shape, and a
local+tail hybrid all lose at scale.
Hetero-positional (PHASE6_HETERO_POS.md, NVIDIA L4, 2026-06-23, from
scratch, ctx 512, 4000 steps): the last orthogonal axis — per-head
content↔position balance — only ties the learnable-ALiBi control
(+0.35% @4×, +0.17% @8×), and adding a per-head softmax temperature
regresses:
| mode |
1× |
2× |
4× |
8× |
| alibi_fixed |
3.705 |
3.623 |
3.577 |
3.513 |
| alibi_learn (control) |
3.651 |
3.559 |
3.500 |
3.429 |
| nope |
10.290 |
10.845 |
11.571 |
12.311 |
| content_balance |
3.642 |
3.548 |
3.488 |
3.428 |
| cb_softmax_temp |
3.732 |
3.659 |
3.599 |
3.548 |
Selected hypothesis: ship learnable-ALiBi — one learnable linear slope per
head, no log term, no $S_{20}$ sequence, no content scale, no temperature. Every
extra knob ties within noise or hurts at scale.
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}
}
