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

TL;DR

This paper investigates how Hebbian learning reshapes the structure and dynamics of random neural networks with excitatory and inhibitory neurons, leading to more organized, small-world structures and a critical state near chaos.

Contribution

It demonstrates that Hebbian learning causes significant structural and dynamical changes in biologically plausible neural networks, including small-world organization and proximity to the edge of chaos.

Findings

Hebbian learning contracts the weight matrix norm and reduces network complexity.

Emerging synaptic structures form small-world networks.

Spectral radius contraction drives the system to the edge of chaos.

Abstract

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the ``edge of chaos'' where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.