Label-Based Diversity Measure Among Hidden Units of Deep Neural Networks: A Regularization Method

TL;DR

This paper introduces an information-theoretic measure of diversity among hidden units in deep neural networks, linking it to generalization capacity and proposing a regularization method to reduce overfitting.

Contribution

It formalizes a new redundancy-based diversity measure rooted in mutual information and demonstrates its effectiveness as a regularizer for improving generalization.

Findings

Redundancy reduction improves generalization capacity.

Regularization with the redundancy measure reduces overfitting.

Theoretical proof links lower redundancy to better generalization.

Abstract

Although the deep structure guarantees the powerful expressivity of deep networks (DNNs), it also triggers serious overfitting problem. To improve the generalization capacity of DNNs, many strategies were developed to improve the diversity among hidden units. However, most of these strategies are empirical and heuristic in absence of either a theoretical derivation of the diversity measure or a clear connection from the diversity to the generalization capacity. In this paper, from an information theoretic perspective, we introduce a new definition of redundancy to describe the diversity of hidden units under supervised learning settings by formalizing the effect of hidden layers on the generalization capacity as the mutual information. We prove an opposite relationship existing between the defined redundancy and the generalization capacity, i.e., the decrease of redundancy generally improving the generalization capacity. The experiments show that the DNNs using the redundancy as the regularizer can effectively reduce the overfitting and decrease the generalization error, which well supports above points.