Limitations on approximation by deep and shallow neural networks

Guergana Petrova, Przemysław Wojtaszczyk

Published 2022-11-30Version 1

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 lower bounds 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.