Entropy and mutual information in models of deep neural networks

26Citations
Citations of this article
140Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) we show how entropies and mutual informations can be derived from heuristic statistical physics methods, under the assumption that weight matrices are independent and orthogonally-invariant. (ii) We extend particular cases in which this result is known to be rigorously exact by providing a proof for two-layers networks with Gaussian random weights, using the recently introduced adaptive interpolation method. (iii) We propose an experiment framework with generative models of synthetic datasets, on which we train deep neural networks with a weight constraint designed so that the assumption in (i) is verified during learning. We study the behavior of entropies and mutual informations throughout learning and conclude that, in the proposed setting, the relationship between compression and generalization remains elusive.

Author supplied keywords

Cite

CITATION STYLE

APA

Gabrié, M., Manoel, A., Luneau, C., Barbier, J., Macris, N., Krzakala, F., & Zdeborová, L. (2019). Entropy and mutual information in models of deep neural networks. Journal of Statistical Mechanics: Theory and Experiment, 2019(12). https://doi.org/10.1088/1742-5468/ab3430

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free