Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks
Mathematical Physics
2015-06-15 v1 math.MP
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.
Cite
@article{arxiv.1302.6951,
title = {Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks},
author = {Tanguy Cabana and Jonathan Touboul},
journal= {arXiv preprint arXiv:1302.6951},
year = {2015}
}