Phase 2 technical write-up for the algorithmic-contribution prize. It corresponds to submission #337578 (v117_kd; graded adjusted score 4.00e-9). That entry is v112_sb (#337384; 4.01e-9) with two constants changed, chosen on a 3-net local meter; §7B discloses the selection bias this introduces. The PDF is attached; the code-and-evidence release is at https://github.com/manderson240/arc-whitebox-phase2.
PHASE2_WRITEUP_V31.pdf (1.2 MB)
What it is. A cumulant-propagation estimator (K = 3 with a free-transport κ4 closure and a learned corrector) for the per-neuron output mean of the Phase 2 1024 × 16 ReLU MLPs, together with the pre-registered gates that decided every lever we tried (about 160 gates; of the 153 ledger records through G-RB147, 73 are KILL, 40 PASS and 12 MISS; pre-registered except where §8 says otherwise).
What we claim, narrowly:
- Oracle injection against a Monte-Carlo-sampled truth is biased. The correction is not ours: it is the standard noise-ceiling / nested-Monte-Carlo correction (Sahani & Linden, Pospisil & Bair, Rainforth et al.), and Artyom_Mazur (forum 18249) already measured and subtracted his oracles’ noise with two independent seeds. Ours, narrowly: a known-answer control (0.305 → 0.002), a 5× dose check, and the measured size of the misreading (an exact per-neuron σ², injected as an oracle, reads 0.776 of baseline MSE uncorrected, 0.511 corrected).
- Upstream changes must be judged with the learned corrector in place. With the corrector in place, 4 of 4 accuracy gains shrank to 3 % or less, and 3 of them reversed with the head frozen (§4).
- Final-layer hypersensitivity. Scaling σ²_z at layers 11–15 by (1 ± 10⁻³) multiplies raw MSE by about 4, a parabola whose fitted optimum is worth about 0.14 %, so cost-neutral constant tuning has reached our instruments’ resolution. Artyom_Mazur (forum 18249, p.18) reported an analogous parabola for a coherent scale of all layers’ variances, with a similar coherent/incoherent reading.
- A measured truncation ceiling. Removing every truncation knob in our chain at unlimited cost reaches only 0.815 of raw MSE (0.807 with the head refit): a KILL for those knobs, not a bound on the method family.
- Engineering.
- A calibrated local wall clock turns the 120 s cap into a knapsack.
- Two transported old-tier bases shared across sources, in place of nine per-source bases, cut util (FLOPs / 2⁴¹) by 6 % and took the graded score 4.21e-9 → 4.01e-9 (v112_sb #337384, the parent of #337578).
- Against the organizers’ reference code. We ran one configuration of it (simple factorized K = 3, MIT-licensed, run unmodified, commit 93d091a). On held-out nets our shipped chain has 0.53× its final-layer MSE (95 % CI 0.49–0.59, lower on 8/8 nets) at 388 vs 3040 n³ FLOPs (ours counts every op, theirs only matmuls, so the count understates the reference’s total). The scope and the history of that net set are in the PDF’s claims box (row 9).
Reproduce. The repo holds the same files as arcwb_phase2_release_v31.zip (sha256 8d75f5852ee9899d2f667fb9634ba0989aebc09ff5a16e02d31d9e44253e9a73, also in RELEASE_ZIP.sha256 at the repo root); the zip is available on request. Appendix E lists 11 steps that run from the unzipped release (numpy, plus mpmath for step 11; minutes in total). Each prints the number the write-up quotes (from a fresh unzip, step 11’s check4 covers Parts A and B only; see the step-11 caveat). Every gate is in research/R2_GO_NOGO.md, queryable through research/rebuild/gates.jsonl.
Credits.
- The organizers’ paper (arXiv 2605.05179) and reference code, for the factorized K = 3 skeleton we build on.
- James Henry (topic 18097, #314695) and Keenan Pepper (#327838), whose Phase 1 write-ups stated the internal-cancellation principle that our §3-§4 measurements instantiate at 1024 × 16.
- Artyom_Mazur (18249): the closest public work to our noise handling (two-seed oracle noise subtraction), the compensation principle in Phase 2 and the p.18 variance-scale parabola.
- kai_leal_gonzalez (18246) and hyojun_kwon (18255): noise estimates for the truth and split-half-corrected Monte-Carlo references.
- Forum write-ups by Nurlanggs (18252) and Susupro (18254), and the prose write-ups of marius_binner, mliston and AndreasHad04, cited where we tested their ideas.
- Team Puffi (#327725, posted by Cipo1): the response-closure form, its ridge-fitted Λ and mode set; earlier Puffi and mliston write-ups are the source of our learned corrector.
LLM use is disclosed in §10. Thanks to ARC and AIcrowd for running the challenge.
— michael_anderson7