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

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.
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https://hal.inria.fr/hal-00942206
Contributor : Jonathan Touboul <>
Submitted on : Tuesday, February 4, 2014 - 6:24:29 PM
Last modification on : Thursday, April 4, 2019 - 1:20:54 AM

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  • HAL Id : hal-00942206, version 1
  • ARXIV : 1302.6951

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Tanguy Cabana, Jonathan Touboul. Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks. Journal of Statistical Physics, Springer Verlag, 2013, 153 (2), pp.211-269. ⟨hal-00942206⟩

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