Random recurrent neural networks dynamics View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2007-03

AUTHORS

M. Samuelides, B. Cessac

ABSTRACT

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are varying according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using an averaging principle. After a first introductory section, the section 2 reviews the various models from the points of view of the single neuron dynamics and of the global network dynamics. A summary of notations is presented, which is quite helpful for the sequel. In section 3, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 4, some applications of mean-field theory to the prediction of chaotic regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The case of AFRRNN with an homogeneous population of neurons is studied in section 4.1. Then, a two-population model is studied in section 4.2. The occurrence of a cyclo-stationary chaos is displayed using the results of [16]. In section 5, an insight of the application of mean-field theory to IF networks is given using the results of [9]. More... »

PAGES

89-122

References to SciGraph publications

  • 2001-10. Mean-field Theory and Synchronization in Random Recurrent Neural Networks in NEURAL PROCESSING LETTERS
  • 2007-03. From neuron to neural networks dynamics in THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
  • 1943-12. A logical calculus of the ideas immanent in nervous activity in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2000-05. Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons in JOURNAL OF COMPUTATIONAL NEUROSCIENCE
  • 2002-05. Large deviations and mean-field theory for asymmetric random recurrent neural networks in PROBABILITY THEORY AND RELATED FIELDS
  • 1995-12. Large deviations for Langevin spin glass dynamics in PROBABILITY THEORY AND RELATED FIELDS
  • 1996-03. Chaos and synchrony in a model of a hypercolumn in visual cortex in JOURNAL OF COMPUTATIONAL NEUROSCIENCE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1140/epjst/e2007-00059-1

    DOI

    http://dx.doi.org/10.1140/epjst/e2007-00059-1

    DIMENSIONS

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