4 papers
Upper and lower bounds for the Lipschitz constant of random neural networks
Paul Geuchen, Dominik Stöger, Thomas Telaar +1
Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-ca…
On best approximation by multivariate ridge functions with applications to generalized translation networks
Paul Geuchen, Palina Salanevich, Olov Schavemaker +1
In this paper, we prove sharp upper and lower bounds for the approximation of Sobolev functions by sums of multivariate ridge functions, i.e., for approximation by functions of the…
Near-optimal estimates for the -Lipschitz constants of deep random ReLU neural networks
Sjoerd Dirksen, Patrick Finke, Paul Geuchen +2
This paper studies the -Lipschitz constants of ReLU neural networks with random parameters for . The distribution of the…
Universal approximation with complex-valued deep narrow neural networks
Paul Geuchen, Thomas Jahn, Hannes Matt
We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functio…