DEEP RELU NETWORKS OVERCOME THE CURSE OF DIMENSIONALITY FOR GENERALIZED BANDLIMITED FUNCTIONS

被引：17

作者：

Montanelli, Hadrien ^{[1
]}

Yang, Haizhao ^{[2
]}

Du, Qiang ^{[3
]}

机构：

[1] Ecole Polytech, Ctr Math Appl, Palaiseau, France

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

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

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2021年 / 39卷 / 06期

关键词：

Machine learning; Deep ReLU networks; Curse of dimensionality; Approxima-tion theory; Bandlimited functions; Chebyshev polynomials; ERROR-BOUNDS; OPTIMAL APPROXIMATION; SUPERPOSITION; SMOOTH;

D O I：

10.4208/jcm.2007-m2019-0239

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a theorem concerning the approximation of generalized bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is based on a result by Maurey and on the ability of deep ReLU networks to approximate Chebyshev polynomials and analytic functions efficiently.

引用

页码：801 / 815

页数：15

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