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Solving Overparametrized Systems of Nonlinear Equations

Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube

Tags

Mathematics Courses Neural Networks Courses Computational Complexity Courses Nonlinear Equations Courses Gaussian Processes Courses

Course Description

Overview

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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.

Syllabus

Andrea Montanari - Solving overparametrized systems of nonlinear equations - IPAM at UCLA


Taught by

Institute for Pure & Applied Mathematics (IPAM)

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