Upper and lower bounds for the Lipschitz constant of random neural networks

no code implementations • 2 Nov 2023 • Paul Geuchen, Thomas Heindl, Dominik Stöger, Felix Voigtlaender

Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input.

Universal approximation with complex-valued deep narrow neural networks

no code implementations • 26 May 2023 • Paul Geuchen, Thomas Jahn, Hannes Matt

We show that a width of $2n+2m+5$ is always sufficient and that in general a width of $\max\{2n, 2m\}$ is necessary.