The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 in lecture room K3. The talk will be given by Jan Vybíral. Please see the details below.

Speaker: **Jan Vybíral**

Title: **A multivariate Riesz basis of ReLU neural networks**

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 L2([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 L2([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.