An empirical analysis of dropout in piecewise linear networks

TL;DR

This paper empirically examines dropout in piecewise linear neural networks, focusing on its regularization effectiveness, ensemble interpretation, and inference procedures, especially with ReLU activations.

Contribution

It provides a detailed empirical analysis of dropout's performance, explores the impact of tied weights, and evaluates alternative ensemble gradient criteria.

Findings

Geometric mean inference closely matches exact ensemble performance in small models.

Tied weights influence the ensemble interpretation of dropout.

Alternative biased estimators of the ensemble gradient offer potential improvements.

Abstract

The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.