Solving Overparametrized Systems of Nonlinear Equations

Explore a 58-minute lecture on solving overparametrized systems of nonlinear equations presented by Andrea Montanari from Stanford University at IPAM's EnCORE Workshop. Delve into the problem of solving equations F(x)=0, where x represents d-dimensional unit vectors and D is a non-linear map with independent, rotationally invariant Gaussian processes. Examine the study under proportional asymptotics as n and d diverge, with their ratio converging to alpha 0. Discover upper and lower bounds, conjectures about solution existence, and the potential for polynomial-time algorithms. Investigate generalizations of this model and gain insights into the optimization landscape of overparametrized neural networks. Learn about the joint work with Eliran Subag and its implications for computational and statistical gaps in learning and optimization.