Limitations on approximation by deep and shallow neural networks

Guergana Petrova, Przemyslaw Wojtaszczyk; 24(353):1−38, 2023.

Abstract

We prove Carl’s type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives estimates from below on how well we can approximate the functions in K when requiring the approximants to come from outputs of such networks. Our results are obtained as a byproduct of the study of the recently introduced Lipschitz widths.