# Deep ReLU networks overcome the curse of dimensionality for bandlimited functions

## TL;DR

This paper proves that deep ReLU networks can efficiently approximate bandlimited multivariate functions, overcoming the curse of dimensionality, by leveraging their ability to approximate Chebyshev polynomials and analytic functions.

## Contribution

The paper establishes a theoretical result showing deep ReLU networks overcome the curse of dimensionality for bandlimited functions, based on approximation of Chebyshev polynomials.

## Key findings

- Deep ReLU networks can approximate bandlimited functions efficiently.
- The curse of dimensionality is overcome in this approximation.
- The proof relies on Maurey's theorem and approximation of Chebyshev polynomials.

## Abstract

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.