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arXiv · 2002.10553

Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networks

Mert Pilanci·Tolga Ergen
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Abstract

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden neurons. Our theory utilizes semi-infinite duality and minimum norm regularization. We show that ReLU networks trained with standard weight decay are equivalent to block $\ell_1$ penalized convex models. Moreover, we show that certain standard convolutional linear networks are equivalent semi-definite programs which can be simplified to $\ell_1$ regularized linear models in a polynomial sized discrete Fourier feature space.

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Mert Pilanci, Tolga Ergen. 2020-02-24. Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networks. https://arxiv.org/abs/2002.10553

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