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.
Domains
Physics [physics]
Origin : Files produced by the author(s)
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