Width and Depth Limits Commute in Residual Networks

Published: 24 Apr 2023, Last Modified: 15 Jun 2023ICML 2023 PosterEveryoneRevisions
Abstract: We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by $1/\sqrt{depth}$, result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.
Submission Number: 3667