The Geometry of Adversarial Training
Leon Bungert  1@  , Nicolás García Trillos  2  , Ryan Murray  3  
1 : Hausdorff Center for Mathematics
2 : Department of Statistics, University of Wisconsin Madison
3 : Mathematics of Mathematics, North Carolina State University

In this talk I will show that ``Adversarial Training''---a methodology designed for the training of adversarially robust classifiers---is equivalent to a variational regularization problem involving a nonlocal perimeter term. Using this structure one can show that adversarial training admits a convex relaxation which is reminiscent of the Chan-Esedoglu model from image denoising. Furthermore, this allows to prove existence of solutions and study finer properties and regularity. Finally, I hint at how to modify adversarial training to an Almgren-Taylor-Wang like scheme for mean curvature flow.

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