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.
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