Surprising properties of dropout in deep networks

TL;DR

This paper uncovers unexpected behaviors of dropout in deep networks with ReLUs, revealing properties that differ from traditional regularizers and explaining some of dropout's effectiveness.

Contribution

It provides new insights into dropout's properties, including its behavior with negative weights, exponential growth of penalty with depth, and insensitivity to re-scaling.

Findings

Dropout can produce negative weights despite the output being a sum of inputs.

Dropout penalty can grow exponentially with network depth.

Dropout is insensitive to input, output, and weight re-scaling.

Abstract

We analyze dropout in deep networks with rectified linear units and the quadratic loss. Our results expose surprising differences between the behavior of dropout and more traditional regularizers like weight decay. For example, on some simple data sets dropout training produces negative weights even though the output is the sum of the inputs. This provides a counterpoint to the suggestion that dropout discourages co-adaptation of weights. We also show that the dropout penalty can grow exponentially in the depth of the network while the weight-decay penalty remains essentially linear, and that dropout is insensitive to various re-scalings of the input features, outputs, and network weights. This last insensitivity implies that there are no isolated local minima of the dropout training criterion. Our work uncovers new properties of dropout, extends our understanding of why dropout succeeds, and lays the foundation for further progress.