Batch Normalization Biases Residual Blocks Towards the Identity Function in Deep Networks

TL;DR

This paper explains how batch normalization enables training very deep residual networks by biasing residual blocks towards the identity function at initialization, and introduces an alternative initialization scheme that removes the need for normalization.

Contribution

The authors reveal the mechanism by which batch normalization facilitates training deep residual networks and propose a simple initialization method to train such networks without normalization.

Findings

Batch normalization biases residual blocks towards the identity function at initialization.

Deep residual networks can be trained without normalization using a new initialization scheme.

Benefits of batch normalization's larger learning rates are limited to specific compute regimes.

Abstract

Batch normalization dramatically increases the largest trainable depth of residual networks, and this benefit has been crucial to the empirical success of deep residual networks on a wide range of benchmarks. We show that this key benefit arises because, at initialization, batch normalization downscales the residual branch relative to the skip connection, by a normalizing factor on the order of the square root of the network depth. This ensures that, early in training, the function computed by normalized residual blocks in deep networks is close to the identity function (on average). We use this insight to develop a simple initialization scheme that can train deep residual networks without normalization. We also provide a detailed empirical study of residual networks, which clarifies that, although batch normalized networks can be trained with larger learning rates, this effect is only beneficial in specific compute regimes, and has minimal benefits when the batch size is small.