Wei Hu will present his Pre FPO on Tuesday, April 13, 2021 at 4pm via Zoom. Zoom link: https://princeton.zoom.us/j/2180408086 Committee: Examiners: Sanjeev Arora (advisor), Mark Braverman, Chi Jin (ECE) Readers: Elad Hazan, Jason D. Lee (ECE) All are welcome to attend. Title: Understanding Deep Learning via Analyzing Dynamics of Gradient Descent Abstract: The phenomenal successes of deep learning build upon the mysterious abilities of gradient-based optimization algorithms. Not only can these algorithms often successfully optimize complicated non-convex training objectives, but the solutions found can also generalize remarkably well to unseen test data despite significant over-parameterization of the models. Classical approaches in optimization and learning theory that treat empirical risk minimization as a black box are insufficient to explain these mysteries in modern deep learning. In this talk, I will illustrate how we can make progress towards understanding optimization and generalization in deep learning by a more refined approach that opens the black box and analyzes the dynamics taken by the optimizer. In particular, I will present several results focusing on analyzing the dynamics of the gradient descent algorithm, including: (i) solving low-rank matrix completion via deep linear neural networks, (ii) positive and negative convergence results which reveal the optimal depth-width tradeoff for efficiently training deep linear neural networks, and (iii) the connection between wide neural networks and neural tangent kernels, and its theoretical and practical implications.