Mean-field theory of a plastic network of integrate-and-fire neurons

TL;DR

This paper develops a mean-field theoretical framework for a noise-driven, plastic integrate-and-fire neural network, predicting phase transitions, synaptic weight distributions, and the effects of fluctuations on network dynamics.

Contribution

It introduces a self-consistent mean-field approach to analyze neural activity and synaptic plasticity, revealing a first-order transition and detailed synaptic weight distribution predictions.

Findings

Predicts a first-order transition with hysteresis in neural activity.

Derives a narrow synaptic weight distribution scaling with plasticity rate.

Shows fluctuations smooth the transition and broaden weight distribution.

Abstract

We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environment can be mapped to the dynamics of an asymmetric random walk in synaptic-weight space. Using a master-equation for small steps, we predict a narrow distribution of synaptic weights that scales with the square root of the plasticity rate for the stationary state of the system given plausible physiological parameter values describing neural transmission and plasticity. The dependence of the distribution on the synaptic weight of the mean-field environment allows us to determine the mean synaptic weight self-consistently. The effect of fluctuations in the total synaptic conductance and plasticity step sizes are also considered. Such fluctuations result in a smoothing of the first-order transition for low number of afferent synapses per neuron and a broadening of the synaptic weight distribution, respectively.