Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks

TL;DR

This paper investigates the macroscopic dynamics of large, heterogeneous neural networks with delays, revealing phase transitions and non-equilibrium states through large deviation principles and self-consistent equations.

Contribution

It introduces a novel analysis of neural networks with delays and heterogeneity, establishing large deviation principles and identifying phase transitions in complex systems.

Findings

Existence of phase transitions with changing delays and connectivity

Emergence of synchronized oscillations in non-equilibrium states

Convergence towards a self-consistent non-Markovian process

Abstract

We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation principle, and converge towards a self-consistent non-Markovian process. The proof differs in that we are working in infinite-dimensional spaces (interaction delays), non-centered interactions and multiple cell types. The limit equation is qualitatively analyzed, and we identify a number of phase transitions in such systems upon changes in delays, connectivity patterns and dispersion, particularly focusing on the emergence of non-equilibrium states involving synchronized oscillations.