  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. But little is known about how higher-order correlations, which describe
simultaneous firing in triplets and larger ensembles of cells, impact encoded
stimulus information. Here, we take a first step toward closing this gap. We
vary triplet correlations in small (~10 cell) neural populations while keeping
single cell and pairwise statistics fixed at typically reported values. For
each value of triplet correlations, we estimate the performance of the neural
population on a two-stimulus discrimination task. We identify a predominant way
that such triplet correlations can strongly enhance coding: if triplet
correlations differ for the two stimuli, they skew the response distributions
of the two stimuli apart from each other, separating them and making them
easier to distinguish. This coding benefit does not occur when both stimuli
elicit similar triplet correlations. These results indicate that higher-order
correlations could have a strong effect on population coding. 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 experiments.
