Non-asymptotic approximations of neural networks by Gaussian processes

Abstract

We study the extent to which wide neural networks may be approximated by Gaussian processes when initialized with random weights. It is a well-established fact that as the width of a network goes to infinity, its law converges to that of a Gaussian process. We make this quantitative by establishing explicit convergence rates for the central limit theorem in an infinite-dimensional functional space, metrized with a natural transportation distance. We identify two regimes of interest; when the activation function is polynomial, its degree determines the rate of convergence, while for non-polynomial activations, the rate is governed by the smoothness of the function.

18 pages

References in corpus (2)

• Asymptotics of Wide Convolutional Neural Networks
• On the asymptotics of wide networks with polynomial activations

Cited by in corpus (1)

• A single gradient step finds adversarial examples on random two-layers neural networks