Dynamics of a recurrent network of spiking neurons before and following learning

Abstract

Extensive simulations of large recurrent networks of integrate-and-fire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics and, in particular, coexistence between two types of stable states: spontaneous activity upon stimulation by an unlearned stimulus, and ‘working memory’ states strongly correlated with learned stimuli. Firing rates have very wide distributions, due to the variability in the connectivity from neuron to neuron. ISI histograms are exponential, except for small intervals. Thus the spike emission processes are well approximated by a Poisson process. The variability of the spike emission process is effectively controlled by the magnitude of the post-spike reset potential relative to the mean depolarization of the cell. Cross-correlations (CC) exhibit a central peak near zero delay, flanked by damped oscillations. The magnitude of the central peak in the CCs depends both on the probability that a spike emitted by a neuron affects another randomly chosen neuron and on firing rates. It increases when average rates decrease. Individual CCs depend very weakly on the synaptic interactions between the pairs of neurons. The dependence of individual CCs on the rates of the pair of neurons is in agreement with experimental data. The distribution of firing rates among neurons is in very good agreement with a simple theory, indicating that correlations between spike emission processes in the network are effectively small.