This talks consists of two parts, one rigorous and one speculative. The rigorous part is a description of the geometric structure of the deep linear network (DLN): a phenomenological model of deep learning. We illustrate several surprising connections between the DLN and other areas of mathematics (geometric invariant theory, minimal surfaces and random matrix theory) and use this as a basis for a thermodynamic description of the learning process.

This rich structure is then used as a basis for some speculation on the geometry of training dynamics for deep learning.

The talk is based on joint work with several co-authors (especially Nadav Cohen, Kathryn Lindsey, Zsolt Veraszto and Tianmin Yu).

Bio: Govind Menon is a mathematician at Brown University. He has worked in the past on dynamical systems, kinetic theory, random matrix theory, synthetic biology and turbulence. His current interests lie in the Nash embedding theorems and the mathematical foundations of AI.