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2023 JMLR JMLR 2023

Limitations on approximation by deep and shallow neural networks

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. [abs] [ pdf ][ bib ] © JMLR 2023. (edit, beta)

Authors

Guergana Petrova, Przemyslaw Wojtaszczyk

Topics

Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Optimization & Theory > Theory Deep Learning > Architectures > Neural Networks

Keywords

function approximation deep neural network approximation theory error bound neural network approximation lipchitz width

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