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

Authors

  • Hadrien Montanelli Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique, Palaiseau, France
  • Haizhao Yang Department of Mathematics, Purdue University, Indiana, United States
  • Qiang Du Department of Applied Physics and Applied Mathematics, Columbia University, New York 10027, USA.

DOI:

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

Keywords:

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

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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Published

2021-11-19

Issue

Vol. 39 No. 6 (2021)

Section

Articles