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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| Vydáno v: | AIMS mathematics Ročník 7; číslo 10; s. 19018 - 19025 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
AIMS Press
01.01.2022
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| Témata: | |
| ISSN: | 2473-6988, 2473-6988 |
| On-line přístup: | Získat plný text |
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| 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. |
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| ISSN: | 2473-6988 2473-6988 |
| DOI: | 10.3934/math.20221045 |