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arXiv · 1806.07863

Learning ReLU Networks via Alternating Minimization

Gauri Jagatap·Chinmay Hegde
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Abstract

We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given samples, interleaved with weight updates via a least-squares step. The main focus of our paper are 1-hidden layer networks with $k$ hidden neurons and ReLU activation. We show that under standard distributional assumptions on the $d-$dimensional input data, our algorithm provably recovers the true `ground truth' parameters in a linearly convergent fashion. This holds as long as the weights are sufficiently well initialized; furthermore, our method requires only $n=\widetilde{O}(dk^2)$ samples. We also analyze the special case of 1-hidden layer networks with skipped connections, commonly used in ResNet-type architectures, and propose a novel initialization strategy for the same. For ReLU based ResNet type networks, we provide the first linear convergence guarantee with an end-to-end algorithm. We also extend this framework to deeper networks and empirically demonstrate its convergence to a global minimum.

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Gauri Jagatap, Chinmay Hegde. 2018-06-20. Learning ReLU Networks via Alternating Minimization. https://arxiv.org/abs/1806.07863

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