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

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_{\infty} $ sense. The...

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Bibliographic Details
Published in:AIMS mathematics Vol. 7; no. 10; pp. 19018 - 19025
Main Authors: Chen, Liang, Liu, Wenjun
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2022
Subjects:
approximation complexity
bandlimited functions
deep relu networks
fat-shattering dimension
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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Summary: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_{\infty} $ sense. The key to the proof is to establish a frequency decomposition lemma which may be of independent interest.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20221045