Entropy and mutual information in models of deep neural networks

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. We study the behavior of entropies and mutual information throughout learning and conclude that, in the proposed setting, the relationship between compression and generalization remains elusive. Papers published at the Neural Information Processing Systems Conference.