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.