Applied math. talk: Adversarially robust classification via geometric flows, by Ryan Murray, North Caroline State University

Abstract: Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be “fooled” using specially constructed adversarial examples. In turn, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will describe a recently proposed framework for optimal adversarial robustness which is related to optimal transportation. I will then discuss some recent work, with Nicolas Garcia Trillos, which characterizes solutions of the optimal adversarial robust classification problem by using a geometric evolution equation. Surprisingly, this geometric evolution equation asymptotically takes the form of a weighted mean curvature flow, which suggests new analytical and computational approaches to the problem. I will also discuss a number of related open questions.