In this talk I will first review recent results which characterize adversarial training (AT) of binary classifiers as nonlocal perimeter regularization. Then I will speak about a probabilistic generalization of AT which also admits such a geometric interpretation, albeit with a different nonlocal perimeter. Using suitable relaxations one can prove the existence of solutions for a large family of such probabilistically robust training problems. Furthermore, these problems have (mildly surprising) connections to the conditional value at risk (CVaR), a quantity from math finance. I will also discuss local asymptotics of the probabilistic perimeters and mention some open problems. This talk is based on joint work with N. García Trillos, R. Murray, M. Jacobs, D. McKenzie, D. Nikolic, and Q. Wang.

Zoom meeting: Link