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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: theactivity patterns of some circuits are nearly completely captured by pairwiseinteractions among neurons. Why are such pairwise models so successful in someinstances, but insufficient in others? Here, we study the emergence ofhigher-order interactions in simple circuits with different architectures andinputs. We quantify the impact of higher-order interactions by comparing theresponses of mechanistic circuit models vs. "null" descriptions in which allhigher-than-pairwise correlations have been accounted for by lower orderstatistics, known as pairwise maximum entropy models.  We find that bimodal input signals produce larger deviations from pairwisepredictions than unimodal inputs for circuits with local and globalconnectivity. Moreover, recurrent coupling can accentuate these deviations, ifcoupling strengths are neither too weak nor too strong. A circuit model basedon intracellular recordings from ON parasol retinal ganglion cells shows that abroad range of light signals induce unimodal inputs to spike generators, andthat coupling strengths produce weak effects on higher-order interactions. Thisprovides a novel explanation for the success of pairwise models in this system.Overall, our findings identify circuit-level mechanisms that produce and failto produce higher-order spiking statistics in neural ensembles.

When are microcircuits well-modeled by maximum entropy methods?