Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions

Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions

Year:    2021

Author:    Hadrien Montanelli, Haizhao Yang, Qiang Du

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 801–815

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2007-m2019-0239

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 801–815

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Machine learning Deep ReLU networks Curse of dimensionality Approximation theory Bandlimited functions Chebyshev polynomials.

Author Details

Hadrien Montanelli

Haizhao Yang

Qiang Du