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How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation

Bruno Cessac 1, 2 Horacio Rostro 1 Juan Carlos Vasquez 1 Thierry Viéville 3 
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
3 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks? and; (ii) what are the effects of synaptic plasticity on these statistics? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.
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Contributor : Thierry Viéville Connect in order to contact the contributor
Submitted on : Monday, July 27, 2009 - 7:21:15 PM
Last modification on : Thursday, August 4, 2022 - 5:05:30 PM

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Bruno Cessac, Horacio Rostro, Juan Carlos Vasquez, Thierry Viéville. How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation. Journal of Statistical Physics, 2009, Journal of Statistical Physics, 136 (3), pp.565-602. ⟨10.1007/s10955-009-9786-1⟩. ⟨inria-00407905⟩



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