Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks

TL;DR

This paper reviews recent research on complex systems, including glasses, spin glasses, high-dimensional inference, and neural networks, highlighting models and transitions relevant to physics and machine learning.

Contribution

It introduces the KHGPS model for amorphous solids, reviews rigidity and jamming transitions in high-dimensional systems, and discusses dynamics of learning algorithms in inference and neural networks.

Findings

Progress in modeling low-temperature amorphous solids with KHGPS

Insights into rigidity and jamming transitions in high dimensions

Analysis of learning dynamics in high-dimensional inference

Abstract

The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is the subject of the first chapter where I discuss a new model, the KHGPS model, which allows to make some progress. In the second chapter I review a second research line that concerns the study of the rigidity/jamming transitions in particle system models and their relation to constraint satisfaction and optimization problems in high dimension. Finally in the last chapter I review my activity on the problem of the dynamics of learning algorithms in high-dimensional inference and supervised learning problems.