The nonlocal geometry of adversarial machine learning

It is well-known that, despite their aptness for complicated tasks like image classification, modern neural networks are prone to insusceptible input perturbations (a.k.a. adversarial attacks) which can lead to severe misclassifications. Adversarial training is a method to obtain classifiers which are robust against such attacks. In this talk I will show that in the binary clas- sification setting the method can be rephrased as geometric regularization problem, involving a nonlocal perimeter of Minkowski type. I will present existence and regularity theorems for minimizers, study local asymptotics of the nonlocal perimeter using Gamma-convergence, and discuss probabilistic relaxations which correspond to more classical notions of nonlocal perimeters.