On the convergence of gradient descent for two layer neural networks

Abstract

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing works, we investigate the gradient descent method for training two-layer neural networks for approximating some target continuous functions. By making use the generic chaining technique from probability theory, we show that gradient descent can yield an exponential convergence rate, while the width of the neural networks needed is independent of the size of the training data. The result also implies some strong approximation ability of the two-layer neural networks without curse of dimensionality.

arXiv commentThere was some issue in the manuscript

References in corpus (4)

• A Mean Field View of the Landscape of Two-Layers Neural Networks
• Gradient Descent Provably Optimizes Over-parameterized Neural Networks
• Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data
• A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics