A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Other Publications Year : 2008

A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks

Abstract

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning dynamics. Previous numerical works have reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on the neural network evolution. Furthermore, we show that the sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest.
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Dates and versions

inria-00149181 , version 1 (24-05-2007)
inria-00149181 , version 2 (07-04-2008)

Identifiers

  • HAL Id : inria-00149181 , version 2
  • ARXIV : 0705.3690

Cite

Benoit Siri, Hugues Berry, Bruno Cessac, Bruno Delord, Mathias Quoy. A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks. 2008. ⟨inria-00149181v2⟩
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