Lecture 1: Introduction
Lecture 1: Introduction to spectral methods
Lectures 2-3: Spectral methods: L2 perturbation theory
Lecture 4: Matrix concentration inequalities
Lectures 5-6: Applications of spectral methods: L2 theory
Lectures 7-9: Spectral methods: Linf perturbation theory
Lectures 10-12: Introduction to nonconvex optimization
Lectures 13: Generic analysis of local convergence
Lectures 14: Implicit regularization in nonconvex optimization
Lectures 15: Global convergence in nonconvex optimization
Lecture 16: ScaledGD: Global convergence from small initialization