Talk: New geometric techniques in non-convex and non-smooth machine learning

Live stream: TBD

Abstract: While the classical theory of convex optimization provides efficient algorithms for optimizing convex functions in Euclidean space given first or second-order information, modern machine learning methods—such as deep learning—often require optimizing or sampling from non-convex objectives or distributions, or handling non-smooth domains, making algorithm design significantly more challenging. In this talk, I will demonstrate how uncovering and leveraging the hidden geometric structure in these problems can lead to new insights for designing efficient algorithms. I will begin by discussing how we can provably learn continuous mixtures of Gaussians using diffusion models by understanding the structure of the score function and effectively learning it. I will then move on to the non-convex landscape of training neural networks and showcase how new geometric tools help us understand the implicit bias of SGD. Finally, I will present a faster algorithm for sampling a point uniformly within a polytope by imposing a carefully constructed geometric structure on its interior.

Bio: Khashayar Gatmiry is a final-year graduate student in the EECS department at MIT, co-advised by Stefanie Jegelka and Jonathan A. Kelner. His research broadly spans machine learning, sampling, and optimization, with a focus on designing reliable and efficient algorithms, and on uncovering the fundamental principles behind the practical success of modern deep learning.