  This paper analyzes the convergence and generalization of training a
one-hidden-layer neural network when the input features follow the Gaussian
mixture model consisting of a finite number of Gaussian distributions. Assuming
the labels are generated from a teacher model with an unknown ground truth
weight, the learning problem is to estimate the underlying teacher model by
minimizing a non-convex risk function over a student neural network. With a
finite number of training samples, referred to the sample complexity, the
iterations are proved to converge linearly to a critical point with guaranteed
generalization error. In addition, for the first time, this paper characterizes
the impact of the input distributions on the sample complexity and the learning
rate.
