The formal write-up submission for #330001 was made by email to arc-whestbench@aicrowd.com on 6 September 2026. This post is a community share of the same document, not a second submission.
Submission #330001 (estimator v6) · adjusted score 1.066e-07 on the public split · participant rank 64 of 877 at the time of posting · 0 fitted constants, 0 sampling. The full PDF write-up is attached; this post is the short version, with every number labelled by the corpus it came from.
What the estimator is. A ReLU-MLP mean propagator in the closure family — propagate the pre-activation mean and covariance layer by layer, close the ReLU moments analytically — with two things removed and one thing added. Removed: the 64 per-layer calibration constants that the fitted version of this family carries (16 layers × 4 coefficients, fitted offline on MLPs from the specified distribution), and every sampling branch. Added: a rank-4,608 CP channel that carries the inherited joint third cumulant of the pre-activations forward through the weights in O(r n), so the ReLU closure at each layer sees a skewed input rather than a Gaussian one. Compute is 9.89% of the budget, under the free floor, with FLOP counts shape-determined (sd 0 across MLPs).
What was measured, and on what. The headline comparison was pre-registered (commit f2445768, branch decision by a frozen GT-noise rule) and run on 32 MLPs, seeds 200–231, with 4 × 10^6-sample ground truth per network. None of those networks was used to design or tune anything; the write-up discloses that 16 of them had been seen once before as a 10^6-sample holdout on which an earlier candidate was chosen.
| estimator (32 MLPs, seeds 200–231, 4M GT) | fitted constants | sampling | final-layer MSE | vs bundled baseline |
|---|---|---|---|---|
bundled 03_covariance_propagation |
— | — | 4.141153e-06 | 1.00x |
| v2: exact ReLU covariance + 64 fitted mean constants | 64 | none | 1.230525e-06 | 3.37x |
| v5: v2’s constants + derived one-step k3 term | 64 | none | 1.091853e-06 | 3.79x |
| v6: inherited-cumulant CP channel (submitted) | 0 | none | 1.134226e-06 | 3.65x |
v6 vs v2: +7.26 pp, 95% CI [+2.59, +11.94], paired t p = 0.003, Wilcoxon p = 0.005, better on 23/32 networks. v6 vs v5: −4.95 pp, CI [−11.09, +1.19], p = 0.11 — not resolved, and the achieved MDE for that comparison was 8.44 pp, so it could not have resolved the difference it observed. “Not distinguished” is not “equal”; v5’s mean is 3.74% lower. On the official public split v6 scored 1.066e-06 final-layer MSE (50 scored MLPs), 6% better than our own holdout number, so the holdout was if anything pessimistic. The fitted comparator v5 was graded too, after a smoke-test failure and a one-line patch (submission #330006: 1.048e-06, 0 failures, 3.83% compute) — 1.7% better than v6 on the public split, the same direction and scale as the unresolved holdout difference.
The result I think is worth reading, which is not the score. The 64 fitted constants in this family are usually described as “calibration”. I asked what they actually absorb. The fitted coefficients are stable across 12 MLPs (seeds 0–11; final-layer scalar 0.998305, sd 1.7e-04) and their basis is exactly the Edgeworth one-step correction {sigma·alpha·phi, sigma·alpha^2·phi, sigma·phi} — the derivation forces that basis, and it is verified by quadrature (identity_check.py, 8.9e-16). But the residual those constants absorb is not the one-step non-Gaussianity: on a split-sample test, the oracle-input one-step residual correlates 0.975 with the Edgeworth prediction, while the propagated residual — the thing the fit sees — correlates −0.05 with it and is 5.2x larger. The constants are absorbing accumulated drift, not local skew. That is why a derived one-step k3 term (v4, zero constants) recovers only 40% of the mean error on the tuning corpus (seeds 100–107) and why an inherited cumulant channel, which addresses accumulation, is the one that reaches the fitted version’s accuracy with zero constants. An earlier draft of the write-up claimed the opposite (“the constants are a low-rank stand-in for k3”); an adversarial review found that the test had measured the wrong residual, and the corrected reading predicted v6 before v6 was built. Sections 4.1–4.2 of the PDF are that story with the numbers.
Relation to the two Phase 2 write-ups already posted. @venture_agent_ai’s (#329951, 1.32e-07) is the same two-part construction as our v2 — exact bivariate ReLU covariance plus per-layer calibration fitted on local MLPs — and reports the same smoke-test shape trap we fell into; @baghyeonsig’s (#328274, 3.04e-07) blends propagation with whitened antithetic MC. Neither asks what the fitted calibration absorbs or whether it can be removed. That is the question here, and the answer scores 1.066e-07 with zero constants.
Where this family stops. Two independent measurements, one mine (single MLP, data/mlp0.npz, 10^6-sample oracle at layer 14: final MSE floors near 3.18e-07 even with the true layer-14 mean injected, of which roughly 1e-07 is GT noise) and one from @thylinao’s Phase 1 thread (perfect marginals at every layer on 256×32: 7.07e-07), agree that closure-family propagation without sampling sits an order of magnitude above the current leaders. I am not claiming a route to the top of the leaderboard; I am claiming a mechanistic account of what one term in this family does, measured properly.
What did not work, reported rather than deleted. A width-transfer experiment whose pre-registered gate turned out to be smaller than the within-width noise (Section 8.2); a “void” homogeneity experiment that could not have moved the quantity it tested (8.1); a v5 submission (#330004) that failed the grader’s smoke test on a depth-indexed constant table after a reviewer had recommended a one-line guard and I had judged it “won’t fire” (8). Two flopscope issues found on the way (an einsum broadcast error and a SymmetryError on finite symmetric results) are filed with cross-platform reproductions as AIcrowd/flopscope#256 and #257.
Reproduction. CANONICAL_NUMBERS.md and make_canonical_numbers.py regenerate every MSE and ratio in the table above with its corpus attached; PHASE_H_FINDINGS.md carries the per-network holdout table from which every statistic recomputes to the printed digit; the bundle validates against flopscope 0.12.1 / whestbench 0.16.1 with 0 failures.
LLM disclosure. This work was done by one human with two LLM systems in a fixed division: the human set direction, scope, go/no-go, and every judgement about what to claim and withdraw; Claude (Anthropic) produced the research direction, the Edgeworth derivation, experiment designs and the prose of the write-up; a Codex (OpenAI) agent wrote the diagnostic programs, the estimators, and ran every comparison. No claim was verified by a human by hand — verification was by running measurements and by handing the draft to independent LLM reviewers with instructions to refute it, which is how the central-claim correction above was found. The PDF’s Section 9 carries the per-item breakdown.
PDF: WRITEUP_FINAL.pdf (attached). Submission: #330001. Happy to answer questions on the propagated-vs-oracle residual test in particular, since it is the part I would most like someone to break.
WRITEUP_FINAL.pdf (152.9 KB)