Stochastic firing rate models

Jonathan Touboul 1, 2 Bard Ermentrout 3 Olivier Faugeras 4 Bruno Cessac 4, 5
4 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network equations in a general setting, and we express here the results in a more customary and simpler framework. We propose a heuristic argument to derive these equations providing a more intuitive understanding of their origin. These equations are characterized by a strong coupling between the different moments of the solutions. We analyse the equations, present an algorithm to simulate the solutions of these mean-field equations, and investigate numerically the equations. In particular, we build a bridge between these equations and Sompolinsky and collaborators approach (1988, 1990), and show how the coupling between the mean and the covariance function deviates from customary approaches.
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https://hal.inria.fr/inria-00534332
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : mardi 9 novembre 2010 - 13:15:25
Dernière modification le : vendredi 12 janvier 2018 - 01:51:00

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  • HAL Id : inria-00534332, version 1
  • ARXIV : 1001.3872

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Jonathan Touboul, Bard Ermentrout, Olivier Faugeras, Bruno Cessac. Stochastic firing rate models. 2010. 〈inria-00534332〉

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