When are microcircuits well-modeled by maximum entropy methods?
Describing the collective activity of neural populations is a daunting task: the number of possible patterns grows exponentially with the number of cells, resulting in practically unlimited complexity. Recent empirical studies, however, suggest a vast simplification in how multi-neuron spiking occurs: the activity patterns of some circuits are nearly completely captured by pairwise interactions among neurons. Why are such pairwise models so successful in some instances, but insufficient in others? Here, we study the emergence of higher-order interactions in simple circuits with different architectures and inputs. We quantify the impact of higher-order interactions by comparing the responses of mechanistic circuit models vs. "null" descriptions in which all higher-than-pairwise correlations have been accounted for by lower order statistics, known as pairwise maximum entropy models. We find that bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs for circuits with local and global connectivity. Moreover, recurrent coupling can accentuate these deviations, if coupling strengths are neither too weak nor too strong. A circuit model based on intracellular recordings from ON parasol retinal ganglion cells shows that a broad range of light signals induce unimodal inputs to spike generators, and that coupling strengths produce weak effects on higher-order interactions. This provides a novel explanation for the success of pairwise models in this system. Overall, our findings identify circuit-level mechanisms that produce and fail to produce higher-order spiking statistics in neural ensembles.