The deep linear network (DLN) is a phenomenological matrix model of deep learning that was introduced by Arora, Cohen and Hazan in 2018. This talk is a description of the mathematical structure of the DLN, especially the surprising role of minimal cones. The talk will also include some speculation on what the DLN has to tell us about training dynamics in deep learning and a description of some common ties, through Riemannian geometry, between conic programs and deep learning. The talk includes joint work with Nadav Cohen (Tel Aviv) and several students at Brown University (Lulabel Seitz, Zsolt Veraszto and Tianmin Yu).
Bio: Govind Menon is a Professor of Applied Mathematics at Brown University. His current research is on the mathematical foundations for artificial intelligence. This includes the dynamics of optimization, geometric deep learning, embedding theorems, and philosophies of mathematics.