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...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:AIMS mathematics Ročník 7; číslo 10; s. 19018 - 19025
Hlavní autori: Chen, Liang, Liu, Wenjun
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: AIMS Press 01.01.2022
Predmet:
approximation complexity
bandlimited functions
deep relu networks
fat-shattering dimension
ISSN:2473-6988, 2473-6988
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí: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