This is a technical write-up for the Algorithmic Contribution Prize, corresponding to submission #314331 (Phase 1, graded successfully, adjusted score 2.45e-6).
Approach. The submission is a scalar-corrected second-order Gaussian-closure (“k=2”) estimator. Covariance propagation overestimates the final-layer post-ReLU mean by a stable multiplicative factor (~0.992), validated on the official benchmark and cross-validated across networks. A single scalar multiply — zero added FLOPs — reduces final-layer MSE by ~3x.
What the write-up adds (negative results + ablations). Most of the document is an audited falsification map: we test whether any cheap correction beats the scalar — third-cumulant propagation (against the organizers’ own mlp_kprop), low-rank subspace corrections, temporal recurrence of the error, exact-moment Edgeworth corrections (using publicly-available ground-truth higher moments), and learned nonlinear correctors. None improves the final-layer estimator at depth 32. We show the exploitable predictive signal in the residual decays exponentially with depth (tau ~ 5.1 layers, per-network) and is statistically indistinguishable from zero at the scored final layer, connecting this to the challenge’s matching-sampling question.
Full write-up (PDF, 12 pages, 5 figures) attached. Feedback welcome — negative results and methodology critiques especially.
whitebox_algorithmic_writeup.pdf (139.5 KB)