DEEP RELU NETWORKS OVERCOME the CURSE of DIMENSIONALITY for GENERALIZED BANDLIMITED FUNCTIONS*

Hadrien Montanelli; Haizhao Yang; Qiang Du

doi:10.4208/jcm.2007-m2019-0239

DEEP RELU NETWORKS OVERCOME the CURSE of DIMENSIONALITY for GENERALIZED BANDLIMITED FUNCTIONS^*

Hadrien Montanelli
, Haizhao Yang
, Qiang Du

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	801-815
Number of pages	15
Journal	Journal of Computational Mathematics
Volume	39
Issue number	6
DOIs	https://doi.org/10.4208/jcm.2007-m2019-0239
Publication status	Published - 1 Jan 2021

Keywords

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

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10.4208/jcm.2007-m2019-0239

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title = "DEEP RELU NETWORKS OVERCOME the CURSE of DIMENSIONALITY for GENERALIZED BANDLIMITED FUNCTIONS*",

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.",

keywords = "Approximation theory, Bandlimited functions, Chebyshev polynomials, Curse of dimensionality, Deep ReLU networks, Machine learning",

author = "Hadrien Montanelli and Haizhao Yang and Qiang Du",

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AU - Yang, Haizhao

AU - Du, Qiang

PY - 2021/1/1

Y1 - 2021/1/1

N2 - 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.

AB - 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.

KW - Approximation theory

KW - Bandlimited functions

KW - Chebyshev polynomials

KW - Curse of dimensionality

KW - Deep ReLU networks

KW - Machine learning

UR - https://www.scopus.com/pages/publications/85122052349

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DO - 10.4208/jcm.2007-m2019-0239

M3 - Article

AN - SCOPUS:85122052349

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JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

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ER -

DEEP RELU NETWORKS OVERCOME the CURSE of DIMENSIONALITY for GENERALIZED BANDLIMITED FUNCTIONS^*

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Keywords

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