Analytic function approximation by path norm regularized deep networks

Aleksandr Beknazaryan

doi:10.48550/arXiv.2104.02095

Analytic function approximation by path norm regularized deep networks

Aleksandr Beknazaryan

Mathematics of Operations Research

Research output: Working paper › Preprint › Academic

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Abstract

We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on $1/\varepsilon$ can $\varepsilon$-approximate functions that are analytic on certain regions of $\mathbb{C}^d$.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2104.02095
Publication status	Published - 5 Apr 2021

Keywords

stat.ML
cs.LG

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10.48550/arXiv.2104.02095Licence: CC BY

2104.02095v4Final published version, 166 KBLicence: CC BY

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title = "Analytic function approximation by path norm regularized deep networks",

abstract = " We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on \$1/\textbackslash{}varepsilon\$ can \$\textbackslash{}varepsilon\$-approximate functions that are analytic on certain regions of \$\textbackslash{}mathbb\{C\}\textasciicircum{}d\$. ",

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AB - We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on $1/\varepsilon$ can $\varepsilon$-approximate functions that are analytic on certain regions of $\mathbb{C}^d$.

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KW - cs.LG

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Analytic function approximation by path norm regularized deep networks

Abstract

Keywords

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