2007/05/25 by Benoît Siri, Hugues Berry, Siri, Benoit +7
Computer Science · Neuroscience · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Biological sciences #FOS: Physical sciences #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0705.3690
openalex publication_date 2007/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.