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Stochastic firing rate models

Jonathan Touboul 1, 2 Bard Ermentrout 3 Olivier Faugeras 4 Bruno Cessac 4, 5 
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS-PSL - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis (1965 - 2019), 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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Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Tuesday, November 9, 2010 - 1:15:25 PM
Last modification on : Friday, November 18, 2022 - 9:28:17 AM

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


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



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