Thesis defense: Khashayar Gatmiry

Thesis Defense:  New Techniques in Non-convex and Non-smooth Machine Learning

Speaker: Khashayar Gatmiry
Speaker Affiliation: MIT CSAIL
Host: Stefanie Jegelka
Host Affiliation: MIT CSAIL

Date: Thursday, July 10, 2025
Time: 2:00 PM – 3:00 PM
Location: 32-G575

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 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 and global convergence 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.
Co-advisors: Stefanie Jegelka, Jonathan A. Kelner Thesis Committee: Constantinus Daskalakis, Stefanie Jegelka, and Jonathan A.
Kelner

Details

• Date: Thursday, July 10
• Time: 2:00 pm - 3:00 pm
• Location: 32-G575