Kolloquium: Cornelia Schneider (FAU): A Multivariate Riesz Basis of ReLU Neural Networks

A Multivariate Riesz Basis of ReLU Neural Networks - Vortragende: Cornelia Schneider, FAU Erlangen-Nürnberg – Einladender: K.-H. Neeb

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 $L_2([0,1])$ based on the Gershgorin theorem. We also generalize
this system to higher dimensions $d>1$ by a construction, which avoids using
(tensor) products. As a consequence, the functions from the new Riesz basis of
$L_2([0,1]^d)$ can be easily represented by neural networks. Moreover, the
Riesz constants of this system are independent of $d$, making it an attractive
building block regarding future multivariate analysis of neural networks.