Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Entropy and mutual information in models of deep neural networks

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.
Complete list of metadatas

Cited literature [89 references]  Display  Hide  Download
Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, November 21, 2018 - 4:50:52 PM
Last modification on : Friday, April 10, 2020 - 5:20:37 PM
Document(s) archivé(s) le : Friday, February 22, 2019 - 3:47:49 PM


Files produced by the author(s)


  • HAL Id : cea-01930228, version 1


Marylou Gabrié, Andre Manoel, Clément Luneau, Jean Barbier, Nicolas Macris, et al.. Entropy and mutual information in models of deep neural networks. 2018. ⟨cea-01930228⟩



Record views


Files downloads