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.
@article{arxiv.2212.02223,
title = {Limitations on approximation by deep and shallow neural networks},
author = {Guergana Petrova and Przemysław Wojtaszczyk},
journal= {arXiv preprint arXiv:2212.02223},
year = {2022}
}