High-dimensional random landscapes: statistics of critical points and dynamical instantons
Valentina Ros (LPTMS)
Online seminar — ZOOM Meeting ID: 919 8494 7729 — Password: Ask L. Mazza and D. Petrov —
High-dimensional random functionals emerge ubiquitously when modeling complex systems: for example as energy landscapes in physics, fitness landscapes in biology, or more recently loss landscapes in machine learning. They are typically very non-convex: their optimization with stochastic dynamics is highly non-trivial due to the abundance of local minima that trap the dynamics for very large times. In this talk, I will focus on random functionals with Gaussian statistics and discuss simple activated processes, in which the system jumps between trapping local minima passing through the saddles (or transition states) connecting them. In particular, I will discuss how to use random matrix theory to gain information on the distribution and reciprocal arrangement of the local minima and saddles in configuration space, and how to exploit this information to build dynamical instantons describing the activated jumps.