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arXiv · 1905.11887

On Dropout and Nuclear Norm Regularization

Poorya Mianjy·Raman Arora
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Abstract

We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.

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Poorya Mianjy, Raman Arora. 2019-05-28. On Dropout and Nuclear Norm Regularization. https://arxiv.org/abs/1905.11887

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