license: mit
tags:
- attention
- positional-encoding
- benchmark
- negative-result
- calabi-yau
- number-theory
pretty_name: CY-Sieve Attention — GPU Quality/Perf Benchmark (NVIDIA L4)
configs:
- config_name: quality_perplexity
data_files: quality_perplexity.csv
- config_name: perf_hbm
data_files: perf_hbm.csv
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}
}