Gradient-Based Algorithms in High-Dimensional Learning

This lecture by the instructor provides insights on gradient-based algorithms in high-dimensional non-convex learning, focusing on supervised learning, neural networks, and stochastic gradient descent. It discusses the challenges of non-convex problems, the core of machine learning, and the mysteries of deep learning theory. The lecture explores the concepts of overfitting, underfitting, and the double-descent phenomenon, shedding light on the generalization capabilities of modern neural networks. It also delves into the understanding of gradient descent and the importance of assumption-free models in data analysis. The talk presents toy models like the spiked matrix-tensor model and discusses the dynamics of deep learning, emphasizing the need to rethink generalization and the role of gradient descent.