Deep Layers as Stochastic Solvers

Adel Bibi, Bernard Ghanem, Vladlen Koltun, Rene Ranftl

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We provide a novel perspective on the forward pass through a block of layers in a deep network. In particular, we show that a forward pass through a standard dropout layer followed by a linear layer and a non-linear activation is equivalent to optimizing a convex objective with a single iteration of a τ-nice Proximal Stochastic Gradient method. We further show that replacing standard Bernoulli dropout with additive dropout is equivalent to optimizing the same convex objective with a variance-reduced proximal method. By expressing both fully-connected and convolutional layers as special cases of a high-order tensor product, we unify the underlying convex optimization problem in the tensor setting and derive a formula for the Lipschitz constant L used to determine the optimal step size of the above proximal methods. We conduct experiments with standard convolutional networks applied to the CIFAR-10 and CIFAR-100 datasets and show that replacing a block of layers with multiple iterations of the corresponding solver, with step size set via L, consistently improves classification accuracy.
Original languageEnglish (US)
Title of host publicationInternational Conference on Learning Representations
PublisherOpenReview.net
StatePublished - Feb 23 2019

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