ResNets of All Shapes and Sizes: Convergence of Training Dynamics in the Large-scale Limit
We establish convergence of the training dynamics of residual neural networks (ResNets) to their joint infinite depth L, hidden width M, and embedding dimension D limit. Specifically, we consider ResNets with two-layer perceptron blocks in the maximal local feature update (MLU) regime and prove that, after a bounded number of training steps, the error between the ResNet and its large-scale limit is O(1/L + sqrt(D/(L M)) + 1/sqrt(D)). This error rate is empirically tight when measured in embedding space. For a budget of P = Theta(L M D) parameters, this yields a convergence rate O(P^(-1/6)) for the scalings of (L, M, D) that minimize the bound. Our analysis exploits in an essential way the...
| Authors | Louis-Pierre Chaintron, Lénaïc Chizat, Javier Maass |
|---|---|
| Primary category | stat.ML |
| Published | 18 March 2026 |
| Last updated at source | 18 March 2026 |
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