Non-asymptotic approximations of neural networks by Gaussian processes

Ronen Eldan , Dan Mikulincer , Tselil Schramm

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Session: Neural Networks/Deep Learning (A)

Session Chair: Quanquan Gu

Poster: Poster Session 2

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.

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