The high-d landscapes paradigm: spin-glasses, and beyond

TL;DR

This paper reviews recent advances in understanding high-dimensional random landscapes, focusing on topology, geometry, and connections to statistical physics and random matrix theory.

Contribution

It introduces new techniques for classifying stationary points and explores their implications in disordered systems and high-dimensional analysis.

Findings

Techniques for counting and classifying stationary points

Connections between landscape topology and statistical physics

Insights into the geometry of high-dimensional random landscapes

Abstract

We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its stationary points and stressing connections with the statistical physics of disordered systems and with random matrix theory.