Vorträge in der Woche 15.07.2024 bis 21.07.2024

Donnerstag, 18.07.2024: TBA

Paul Vögele (Tübingen)

Freitag, 19.07.2024: A Wasserstein perspective of Vanilla GANs

Lea Kunkel (Karlsruhe Institute of Technology )

Generative Adversarial Networks (GANs) have attracted much attention since their introduction by Goodfellow el al. (2014), initially due to impressive results in the creation of photorealistic images. Meanwhile, the areas of application have expanded far beyond this, and GANs serve as a prototypical example of the rapidly developing experimental and theoretical research area of generative models. The statistical literature focuses mainly on Wasserstein GANs and their generalizations, which allow for good dimension reduction properties. Statistical results for vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from vanilla GANs to the Wasserstein distance. In doing so, existing results for Wasserstein GANs can be extended to vanilla GANs. In particular, we obtain an oracle inequality for vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by commonly used network architectures, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded Hölder norm, we conclude a convergence rate for Vanilla GANs.