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Research Article | Open Access

On the uniform approximation estimation of deep ReLU networks via frequency decomposition

Liang Chen( ), Wenjun Liu
Department of Mathematics, Jiujiang University, Jiujiang 332005, China
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Abstract

A recent line of works established the approximation complexity estimation of deep ReLU networks for the bandlimited functions in the MSE (mean square error) sense. In this note, we significantly enhance this result, that is, we estimate the approximation complexity in the L ∞ sense. The key to the proof is to establish a frequency decomposition lemma which may be of independent interest.

Keywords

bandlimited functionsfat-shattering dimensiondeep ReLU networksapproximation complexity
CLC number: 41A30, 41A63

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AIMS Mathematics
Volume 7 Issue 10,
October 2022
Pages 19018-19025
DOI: 10.3934/math.20221045

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Cite this article:
Chen L, Liu W. On the uniform approximation estimation of deep ReLU networks via frequency decomposition. AIMS Mathematics, 2022, 7(10): 19018-19025. https://doi.org/10.3934/math.20221045

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Received: 30 March 2022
Revised: 07 August 2022
Accepted: 08 August 2022
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)