The correlated state in balanced neuronal networks
Understanding the magnitude and structure of inter-neuronal correlations and their relationship to synaptic connectivity structure is an important and difficult problem in computational neuroscience. Early studies show that neuronal network models with excitatory-inhibitory balance naturally create very weak spike train correlations. Later work showed that, under some connectivity structures, balanced networks can produce larger correlations between some neuron pairs, even when the average correlation is very small. All of these previous studies assume that the local neuronal network receives feedforward synaptic input from a population of uncorrelated spike trains. We show that when spike trains providing feedforward input are correlated, the downstream recurrent neuronal network produces much larger correlations. We provide an in-depth analysis of the resulting \"correlated state\" in balanced networks and show that, unlike the asynchronous state of previous work, it produces a tight excitatory-inhibitory balance consistent with in vivo cortical recordings.