Exact Asymptotics and Universality for Gradient Flows and Empirical Risk Minimizers

          @misc{ scivideos_18847,
            doi = {},
            url = {https://simons.berkeley.edu/talks/tba-152},
            author = {},
            keywords = {},
            language = {en},
            title = {Exact Asymptotics and Universality for Gradient Flows and Empirical Risk Minimizers},
            publisher = {The Simons Institute for the Theory of Computing},
            year = {2021},
            month = {dec},
            note = {18847 see, \url{https://scivideos.org/Simons-Institute/18847}}
          }
          

Abstract

We consider a class of supervised learning problems whereby we are given n data points (y_i,x_i), with x_i a d-dimensional dfeature factor, y_i a response, and the model is parametrized by a vector of dimension kd. We consider the high-dimensional asymptotics in which n,d diverge, with n/d and k of order one. As a special case, this class of models includes neural networks with k hidden neurons. I will present two sets of results: 1. Universality of certain properties of empirical risk minimizers with respect to the distribution of the feature vectors x_i. 2. A sharp asymptotic characterization of gradient flow in terms of a one-dimensional stochastic process. [Based on joint work with Michael Celentano, Chen Cheng, Basil Saeed]