New theory shows how to scale residual network updates when layer weights are correlated

burkov · x · 2026-09-06

Andrey Burkov breaks down a recent paper on very deep residual networks: each layer's update must be carefully scaled — too small and the network approaches the identity map, too large and hidden states become unstable. The paper develops scaling theory for initializations with long-range cross-layer correlations, showing the correct scaling depends on how fast correlations decay and how initial weights are generated — making these meaningful initialization hyperparameters. It also characterizes what ultra-deep networks converge to beyond the previously known ODE and SDE regimes.

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