Recorded 28 February 2024. Andrea Montanari of Stanford University presents "Solving overparametrized systems of nonlinear equations" at IPAM's EnCORE Workshop on Computational vs Statistical Gaps in Learning and Optimization. Abstract: I will discuss the problem of solving a system of equations F(x)=0, for x a d-dimensional unit vectors and D a non-linear map from R^d to R^n whose components are independent, rotationally invariant Gaussian processes. We studied this problem under the proportional asymptotics in which n and d goes to diverge, with their ratio converging to alpha 0. I will present upper and lower bounds, as well as conjectures about the existence of solutions and the existence of polynomial-time algorithms to find them. Finally, I will discuss generalizations of this model, and how these insights shed light on the optimization landscape of overparametrized neural nets. Based on joint work with Eliran Subag. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/encore-workshop-on-computational-vs-statistical-gaps-in-learning-and-optimization/?tab=overview