Itay Safran

We study the dynamics and implicit bias of gradient flow (GF) on univariate ReLU neural networks with a single hidden layer in a binary classification setting. We show that when the labels are determined by the sign of a target network with r neurons, with high probability over the initialization of the network and the sampling of the dataset, GF converges in direction (suitably defined) to a network achieving perfect training accuracy and having at most O(r) linear regions, implying a generalization bound. Unlike many other results in the literature, under an additional assumption on the distribution of the data, our result holds even for mild over-parameterization, where the width is Õ(r) and independent of the sample size.