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 language | English (US) |
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Title of host publication | International Conference on Learning Representations |
Publisher | OpenReview.net |
State | Published - Feb 23 2019 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: This work was partially supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research.