Learning One-hidden-layer ReLU Networks via Gradient Descent

We study the problem of learning one-hidden-layer neural networks with Recti-fied 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 char-acterizing the recovery guarantee for practi-cal learning of one-hidden-layer ReLU net-works with multiple neurons. Numerical ex-periments verify our theoretical findings.