Information Plane Analysis for Dropout Neural Networks

TL;DR

This paper demonstrates that using dropout with continuous noise allows for meaningful information plane analysis of neural networks, overcoming previous issues with infinite mutual information in deterministic models.

Contribution

The authors show that dropout with continuous noise makes mutual information finite, enabling effective information plane analysis for neural networks.

Findings

Dropout with continuous noise ensures finite mutual information.

Enables meaningful information plane analysis in practice.

Applicable to widely used dropout neural networks.

Abstract

The information-theoretic framework promises to explain the predictive power of neural networks. In particular, the information plane analysis, which measures mutual information (MI) between input and representation as well as representation and output, should give rich insights into the training process. This approach, however, was shown to strongly depend on the choice of estimator of the MI. The problem is amplified for deterministic networks if the MI between input and representation is infinite. Thus, the estimated values are defined by the different approaches for estimation, but do not adequately represent the training process from an information-theoretic perspective. In this work, we show that dropout with continuously distributed noise ensures that MI is finite. We demonstrate in a range of experiments that this enables a meaningful information plane analysis for a class of dropout neural networks that is widely used in practice.