Abstract
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. This is joint work with N. García Trillos, R. Murray, K. Stinson, and T. Laux.
Biographical Information
Leon Bungert is Professor of Mathematics of Machine Learning at the University of Würzburg. In 2020 he earned his PhD at the University of Erlangen under supervision of Martin Burger. His thesis was awarded the Biennial French-German Mathematics in Imaging PhD Prize. In 2021 - 2023 he was a postdoctoral researcher at the Hausdorff Center for Mathematics of the University of Bonn, before becoming a junior research group leader at the Technical University of Berlin and successively moving to Würzburg in 2023. His research focuses on applied analysis and numerical methods for problems in machine learning, with a special emphasis on robustness, sparse and non-smooth optimization, as well as partial differential equations on graphs.