A multivariate Riesz basis of ReLU neural networks
Information Theory
2023-03-02 v1 Functional Analysis
math.IT
Abstract
We consider the trigonometric-like system of piecewise linear functions introduced recently by Daubechies, DeVore, Foucart, Hanin, and Petrova. We provide an alternative proof that this system forms a Riesz basis of based on the Gershgorin theorem. We also generalize this system to higher dimensions by a construction, which avoids using (tensor) products. As a consequence, the functions from the new Riesz basis of can be easily represented by neural networks. Moreover, the Riesz constants of this system are independent of , making it an attractive building block regarding future multivariate analysis of neural networks.
Keywords
Cite
@article{arxiv.2303.00076,
title = {A multivariate Riesz basis of ReLU neural networks},
author = {Cornelia Schneider and Jan Vybíral},
journal= {arXiv preprint arXiv:2303.00076},
year = {2023}
}