Our Phase 2 submission combines two verified fixes to the starter kit’s covariance_propagation.
First, an exact closed form for the nonzero-mean bivariate ReLU covariance: Price’s theorem plus Plackett’s identity, reduced to a 1-D Gauss-Legendre integral, verified to 1.665e-16 against scipy and against 20M-sample Monte Carlo across 720 parameter combinations. It costs 0.18 points of FLOP budget but cuts final-layer MSE only 7.4% on its own, because Gaussian closure, not any one pairwise moment, dominates the remaining error.
Second, a per-layer ridge calibration fitted on held-out local MLPs and applied only to each layer’s recorded output row, never fed back into propagation. An early version that fed it back made things 69x worse.
Together they score 1.32e-7 adjusted on the live public leaderboard (submission 329951) versus 3.93e-7 for the kit baseline submitted verbatim as a control (submission 329916), and 1.3697e-07 versus 3.670e-07 on a grader-faithful 4-MLP public-shard check with baked N=1e9 truth.
We also report four negative results with numbers, to save others the time: plain and antithetic Monte Carlo, randomised QMC, a coupled control variate, and a naive Kerdock MUB construction that collapses to a spherical 3-design. And one robustness finding: the grader’s smoke test runs a shape other than 16 x 1024, so anything indexed by layer must be guarded. A shape probe script that would have saved us seven failed uploads is included.
Code, results logs, scripts and the full write-up (MIT): GitHub - agentaiventure-dot/arc-whest-estimator · GitHub
Full write-up: arc-whest-estimator/docs/ALGORITHMIC_CONTRIBUTION.md at main · agentaiventure-dot/arc-whest-estimator · GitHub
Disclosure: developed with substantial assistance from AI coding agents directed and reviewed by the participant; every number comes from the unmodified whestbench/flopscope pipeline or the referenced scripts.