Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem

被引：50

作者：

Montanelli, Hadrien ^{[1
]}

Yang, Haizhao ^{[2
]}

机构：

[1] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

[2] Natl Univ Singapore, Dept Math, Singapore, Singapore

来源：

NEURAL NETWORKS | 2020年 / 129卷

关键词：

Deep ReLU networks; Curse of dimensionality; Approximation theory; Kolmogorov-Arnold superposition theorem; NUMERICAL IMPLEMENTATION; REPRESENTATION; VARIABLES;

D O I：

10.1016/j.neunet.2019.12.013

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov-Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks. (C) 2019 Published by Elsevier Ltd.

引用

页码：1 / 6

页数：6

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