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Entropy and mutual information in models of deep neural networks
Marylou Gabrié · Andre Manoel · Clément Luneau · jean barbier · Nicolas Macris · Florent Krzakala · Lenka Zdeborová

Thu Dec 06 07:45 AM -- 09:45 AM (PST) @ Room 517 AB #110

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 information throughout learning and conclude that, in the proposed setting, the relationship between compression and generalization remains elusive.

Author Information

Marylou Gabrié (École Normale Supérieure)
Andre Manoel (OWKIN)
Clément Luneau (École Polytechnique de Lausanne)
jean barbier (EPFL)
Nicolas Macris (EPFL)
Florent Krzakala (École Normale Supérieure)
Lenka Zdeborová (CEA Saclay)

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