This is my Phase 2 algorithmic-contribution write-up. It corresponds to submission #333755 only.
Score. 1.91944e-9 adjusted (final-layer MSE 1.571e-8 at a FLOP fraction of 0.122). 100/100 networks graded, residual wall time median 0.311 s, max 0.335 s. Across nine official runs of the same code the slowest network stayed at 0.334–0.348 s in seven runs.
Write-up (PDF, 8 pages):
What it is. Sampling-free moment propagation through all 16 layers. Per layer the estimator carries the mean, a dense covariance on near-kink units, a compressed history of third cumulants in canonical-polyadic form, and an isotropic fourth-order term. The ReLU step uses Gaussian-plus-Edgeworth closures, and small learned heads correct what the closure misses. Gaussian moment propagation alone is about 330× less accurate.
What I claim (each item is measured in the PDF):
- Low-rank third-cumulant history. Every near-kink unit births a rank-one star factor. Factors are transported exactly through the weights, and aged blocks are compressed by weighted SVD (rank 256). Compression costs at most ~4% of the raw error.
- Exact-linear refits and held-out calibration. The returned final layer is exactly linear in the terminal head constants, so the last layers’ heads can be refitted in closed form. Physical closure constants are calibrated by Gauss–Newton on held-out networks. Every step had a pre-registered paired gate, and each one transferred to the official board.
- Computing under per-operation metering. Round trips and new large server-side arrays set the residual-time cost, not FLOPs. The official cost was about 4 µs per removed round trip. Recursion and packing thresholds trace a near-linear frontier of ~2,000 round trips per 1% of FLOPs. Vectorising the per-history-block loops removed ~7,700 round trips at float32 parity, and the freed residual budget bought a deeper Strassen recursion: 1.9665e-9 → 1.9194e-9 with raw MSE unchanged.
- Where the error comes from, and the limits of this family. 81% of the final error is born in layers 10–15. Fed the true pre-activation moments, the Edgeworth closure reproduces the true means to ~1e-10. Injecting true moments at layers 8–15 cuts the error to 0.40×, but the gain disappears at 0.1% noise on the variance. In an in-pipeline oracle ladder, exact third- and fourth-order information is worth 0.44×, yet suppliers built from the model’s own state reach only correlation 0.22–0.33 with the needed correction (~0.59 required). Section 7 lists the negative results, each with its decisive number.
Code (MIT): GitHub - Hero988/arc-whitebox-estimation-2026-phase2: ARC White-Box Estimation Challenge 2026, Phase 2: cumulant-history moment closure estimator (AIcrowd submission #333755) and write-up · GitHub — the exact estimator.py of #333755 (SHA-256 b1f91d17…473ceb, all constants embedded).
Credits. Built from the AIcrowd starter kit and on ARC’s public cumulant-propagation work (Wu et al., arXiv:2605.05179; mlp_cumulant_propagation, MIT). Constants were fitted only on the public WhestBench dataset (CC BY 4.0).
Use of AI tools. Most of the implementation, experiments and drafting were done by AI coding agents (Anthropic’s Claude and OpenAI’s Codex) working under my direction, with pre-registered gates and independent agent audits. I take responsibility for the accuracy of the write-up.
Thanks to ARC and AIcrowd for a well-posed problem, and to everyone who shared their methods on this forum.