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The aim of the present paper is to study the effects of Hebbian learning inrandom recurrent neural networks with biological connectivity, i.e. sparseconnections and separate populations of excitatory and inhibitory neurons. Wefurthermore consider that the neuron dynamics may occur at a (shorter) timescale than synaptic plasticity and consider the possibility of learning ruleswith passive forgetting. We show that the application of such Hebbian learningleads to drastic changes in the network dynamics and structure. In particular,the learning rule contracts the norm of the weight matrix and yields a rapiddecay of the dynamics complexity and entropy. In other words, the network isrewired by Hebbian learning into a new synaptic structure that emerges withlearning on the basis of the correlations that progressively build up betweenneurons. We also observe that, within this emerging structure, the strongestsynapses organize as a small-world network. The second effect of the decay ofthe weight matrix spectral radius consists in a rapid contraction of thespectral radius of the Jacobian matrix. This drives the system through the``edge of chaos'' where sensitivity to the input pattern is maximal. Takentogether, this scenario is remarkably predicted by theoretical argumentsderived from dynamical systems and graph theory.

Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons