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.