Professor Leon Bungert, leader of working group 1, visited the IDea_Lab at the University of Graz and gave an inspiring presentation on "Robustness on the interface of geometry and probability". Further, Professor Bungert and Hendrik Kleikamp, leader of working group 2, used the chance to exchange some of the latest ideas related to their research.
In this talk I will present the latest developments in the analysis of adversarial machine learning. For this I will build on the geometric interpretation of adversarial training as regularization problem for a nonlocal perimeter of the decision boundary. This perspective allows one to use tools from calculus of variations to derive the asymptotics of adversarial training for small adversarial budgets as well as to rigorously connect it to a mean curvature flow of the decision boundary. We also show that adversarial training is embedded in a larger family of probabilistically robust problems. This is joint work with N. García Trillos, R. Murray, K. Stinson, and T. Laux, and others.
The slides of the talk are available here.
University of Graz, Leechgasse 34, 8010 Graz, Austria