Our current approach: Korobov hybrid trunk (E) + offline ridge residual corrector (G) — ~16% graded gain, what we learned

ARC White-Box Estimation Challenge 2026
1

Hi everyone!

TL;DR We have a Trunk with the following:

\* **Analytic** full-cov ReLU propagation for all layer rows (diagnostic).
  • Final layer: blend 0.3 · oval + 0.7 · y_cv, where y_cv is a vector L1 ridge CV from layer-1 activations, anchored to the exact L1 mean.
  • Sampling: Korobov lattice → Gaussian, n capped at 8000, seeded from mlp.seed + 17.
  • Under this trunk, Korobov beat Roberts/Kronecker swaps locally.

The G add-on

From the same Korobov batch, build 12 per-neuron predict-time features (α through α⁴, CV/MC gaps vs oval, κ₃/κ₄, global layer-gap, relative variance).

Fit offline on held-out MLPs (64 networks, heavy MC truth, seeds disjoint from public mini):

target = (truth − y_base) / σ
ŷ = y_base + σ · (f @ θ) — ridge, λ=1e-2.

Important: fit on noisy predict-time features, not clean analytic moments — same recipe as public Korobov hybrids that reported ~18–23% beyond sampling alone.

What helped vs what didn’t

Helped: trunk blend + L1 CV + small linear θ (~16% graded).

Didn’t: richer θ / more training MLPs (~+2%), early-layer κ₃ features, GNN/MoE correctors, terminal-shrink MC, cloud-transport glue, cubature rollouts, Sobol swaps — all flat or worse on this trunk.

For the a longer write-up find it here: WhestBench.pdf (497.4 KB)

2 Likes