Marvels and Pitfalls of the Langevin in Noisy High-Dimensional Inference

This lecture explores the concept of metastability in physical systems, discussing the equilibrium between different phases and the phase transition. It delves into the approximate message passing algorithm and its limitations in noisy systems, highlighting the challenges of accurately following physical dynamics. The instructor also presents the motivation behind using Langevin dynamics for inference in high-dimensional spaces, emphasizing its efficiency compared to traditional methods.