Senior Honors Thesis Presentation: "Implicit Regularization and Gradient Descent in Matrix Sensing"

Abstract: Matrix Sensing is the problem of recovering a low-rank matrix based on partial information. This information may not be enough to fully determine the matrix, so there could be many possible solutions. In this talk, we will investigate the properties of a certain gradient descent-based algorithm for picking one such solution. We study this problem primarily in the case of 2x2 matrices and extend the results of Gunasekar et. al, who in 2017 gave sufficient conditions for the matrix to converge to the minimal nuclear norm solution. This talk will be accessible to students with a background in Matrix algebra and will be family-friendly.

Host: Xiang Tang and Ari Stern