Unique Characterization of Spatiotemporal Neural Network Activity

Abstract

We prove that three-spike motifs and phase relationships between frequency bands are essential to characterizing spatiotemporal neural activity and, in fact, sufficient. This follows from applying a theorem from optical science to show that all finite neural data have both unique triple (third-order) correlation and unique bispectrum. We simplify triple correlation by classifying three-spike motifs into motif-classes according to their sequencing, which can embody well-studied neural properties such as synchrony, feedback, feedforward, convergence, and divergence. Summing triple correlations within these classes yields a summary revealing structure underlying the neural network data. This simple approach demonstrates the power of complete statistical representations of neural activity. Since these representations generalize across recording modalities, we present our analysis as a potential avenue for investigation throughout the field.