Deep Information Propagation

TL;DR

This paper analyzes the propagation of information in untrained neural networks using mean field theory, identifying depth limits for trainability and effects of dropout and criticality on gradients.

Contribution

It introduces a theoretical framework for understanding depth scales in random networks and links them to trainability, criticality, and gradient behavior.

Findings

Depth scales limit maximum trainable depth.

Networks at the edge of chaos can be trained if sufficiently deep.

Dropout destroys criticality, reducing trainable depth.

Abstract

We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these random networks. Our main practical result is to show that random networks may be trained precisely when information can travel through them. Thus, the depth scales that we identify provide bounds on how deep a network may be trained for a specific choice of hyperparameters. As a corollary to this, we argue that in networks at the edge of chaos, one of these depth scales diverges. Thus arbitrarily deep networks may be trained only sufficiently close to criticality. We show that the presence of dropout destroys the order-to-chaos critical point and therefore strongly limits the maximum trainable depth for random networks. Finally, we develop a mean field theory for backpropagation and we show that the ordered and chaotic phases correspond to regions of vanishing and exploding gradient respectively.