Triplet correlations among similarly tuned cells impact population coding

Which statistical features of spiking activity matter for how stimuli are encoded in neural populations? A vast body of work has explored how firing rates in individual cells and correlations in the spikes of cell pairs impact coding. Recent experiments have shown evidence for the existence of higher-order spiking correlations, which describe simultaneous firing in triplets and larger ensembles of cells; however, little is known about their impact on encoded stimulus information. Here, we take a first step toward closing this gap. We vary triplet correlations in small (approximately 10 cell) neural populations while keeping single cell and pairwise statistics fixed at typically reported values. This connection with empirically observed lower-order statistics is important, as it places strong constraints on the level of triplet correlations that can occur. For each value of triplet correlations, we estimate the performance of the neural population on a two-stimulus discrimination task. We find that the allowed changes in the level of triplet correlations can significantly enhance coding, in particular if triplet correlations differ for the two stimuli. In this scenario, triplet correlations must be included in order to accurately quantify the functionality of neural populations. When both stimuli elicit similar triplet correlations, however, pairwise models provide relatively accurate descriptions of coding accuracy. We explain our findings geometrically via the skew that triplet correlations induce in population-wide distributions of neural responses. Finally, we calculate how many samples are necessary to accurately measure spiking correlations of this type, providing an estimate of the necessary recording times in future experiments.