High-dimensional Asymptotics of Denoising Autoencoders

Hugo Cui, Lenka Zdeborova

Keywords: statistical physics, replica method, autoencoder, exact asymptotics

TL;DR: We provide sharp asymptotics for the test error of non-linear denoising auto-encoders in high dimensions.

Abstract: We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection. We consider the high-dimensional limit where the number of training samples and the input dimension jointly tend to infinity while the number of hidden units remains bounded. We provide closed-form expressions for the denoising mean-squared test error. Building on this result, we quantitatively characterize the advantage of the considered architecture over the autoencoder without the skip connection that relates closely to principal component analysis. We further show that our results capture accurately the learning curves on a range of real datasets.

Submission Number: 3486