Thresholds of descending algorithms in inference problems

Abstract

We review recent works (Sarao Mannelli et al 2018 arXiv:1812.09066, 2019 Int. Conf. on Machine Learning 4333–42, 2019 Adv. Neural Information Processing Systems 8676–86) on analyzing the dynamics of gradient-based algorithms in a prototypical statistical inference problem. Using methods and insights from the physics of glassy systems, these works showed how to understand quantitatively and qualitatively the performance of gradient-based algorithms. Here we review the key results and their interpretation in non-technical terms accessible to a wide audience of physicists in the context of related works.