1302.6951 (Tanguy Cabana et al.)

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

Tanguy Cabana, Jonathan Touboul

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.

View original: http://arxiv.org/abs/1302.6951