Govind Menon (Brown)
Abstract: We will discuss the interplay between some ideas from random matrix theory and deep learning. Specifically, we present a geometric perspective on classical constructions in random matrix theory and then adapt these ideas to training dynamics in deep learning. The talks are aimed at graduate students and young researchers and will include several open problems.
Jake Mundo (Brown)
Abstract: The multivariate Bessel processes are stochastic processes on Weyl chambers which are parametrized by a multiplicity function k on a root system. We will construct these processes from diffusion processes on certain spaces of matrices, making use of the geometry of the orbits of the adjoint action of a Lie group on its Lie algebra. The construction applies for arbitrary positive k, and generalizes to a broader algebraic setting the construction of arbitrary-beta Dyson Brownian motion from a diffusion process in the space of Hermitian matrices.