Learning One-hidden-layer ReLU Networks via Gradient Descent

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Xiao Zhang, Yaodong Yu, Lingxiao Wang, Quanquan Gu ;
Proceedings of Machine Learning Research, PMLR 89:1524-1534, 2019.

Abstract

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of neural networks based on empirical risk minimization, and provide algorithm-dependent guarantees. In particular, we prove that tensor initialization followed by gradient descent can converge to the ground-truth parameters at a linear rate up to some statistical error. To the best of our knowledge, this is the first work characterizing the recovery guarantee for practical learning of one-hidden-layer ReLU networks with multiple neurons. Numerical experiments verify our theoretical findings.

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