A Simple Mechanism for Beyond-Pairwise Correlations in Integrate-and-Fire Neurons

The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. We have developed an understanding of the circuit mechanisms that lead to correlations among cell pairs, but little is known about what determines the population firing statistics among larger groups of cells. Here, we examine this question for a simple, but ubiquitous, circuit feature: common fluctuating input arriving to spiking neurons of integrate-and-fire type. We show that this leads to strong beyond-pairwise correlations—that is, correlations that cannot be captured by maximum entropy models that extrapolate from pairwise statistics—as for earlier work with discrete threshold crossing (dichotomous Gaussian) models. Moreover, we find that the same is true for another widely used, doubly stochastic model of neural spiking, the linear–nonlinear cascade. We demonstrate the strong connection between the collective dynamics produced by integrate-and-fire and dichotomous Gaussian models, and show that the latter is a surprisingly accurate model of the former. Our conclusion is that beyond-pairwise correlations can be both broadly expected and possible to describe by simplified (and tractable) statistical models.