We prove a theorem concerning the approximation of 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.
@article{arxiv.1903.00735,
title = {Deep ReLU networks overcome the curse of dimensionality for bandlimited functions},
author = {Hadrien Montanelli and Haizhao Yang and Qiang Du},
journal= {arXiv preprint arXiv:1903.00735},
year = {2020}
}