Residual Networks Behave Like Ensembles of Relatively Shallow Networks

TL;DR

Residual networks function as ensembles of paths of varying lengths, primarily utilizing short paths during training to effectively mitigate vanishing gradients and enable very deep architectures.

Contribution

This paper introduces a novel path-based interpretation of residual networks, highlighting the importance of short paths in training deep models.

Findings

Most gradient flow comes from short paths of 10-34 layers.

Paths in residual networks vary in length and behave like an ensemble.

Longer paths do not significantly contribute to training gradients.

Abstract

In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short paths during training. To support this observation, we rewrite residual networks as an explicit collection of paths. Unlike traditional models, paths through residual networks vary in length. Further, a lesion study reveals that these paths show ensemble-like behavior in the sense that they do not strongly depend on each other. Finally, and most surprising, most paths are shorter than one might expect, and only the short paths are needed during training, as longer paths do not contribute any gradient. For example, most of the gradient in a residual network with 110 layers comes from paths that are only 10-34 layers deep. Our results reveal one of the key characteristics that seem to enable the training of very deep networks: Residual networks avoid the vanishing gradient problem by introducing short paths which can carry gradient throughout the extent of very deep networks.