Correlated firing and oscillations in spiking networks with global delayed inhibition

In feed-forward networks, output pairwise correlations can increase with firing rate. Here, we study correlations between sensory neurons with global inhibitory feedback and cross-correlated external inputs. The average pairwise correlation coefficient is computed from simulations of a network of noisy leaky integrate-and-fire neurons with delayed spike-driven feedback. We focus on the relation between the correlation and the feedback strength. This relation is monotonically increasing when the common noise is frozen, and non-monotonic when it varies across trials. In both cases, beyond a certain feedback strength, the increase in correlation mirrors the emergence of asynchronous network oscillations quantified by the sharpness (“coherence”) of the peak in the spike train power spectral density. Our results suggest that pairwise correlations are strongly controlled by feedback via the interplay of mean firing rate and oscillatory activity. For frozen common noise, correlations in fact remain near zero up until oscillatory activity is sufficiently coherent. These results are found in both sub- and supra-threshold dynamic regimes, for low and moderate internal noise levels, as well as for a heterogeneous distribution of feedback gains or firing thresholds.