Searching for structure in collective systems

Collective systems such as fish schools, bird flocks, and neural networks are comprised of many mutually-influencing individuals, often without long-term leaders, well-defined hierarchies, or persistent relationships. The remarkably organized group-level behaviors readily observable in these systems contrast with the ad hoc, often difficult to observe, and complex interactions among their constituents. While these complex individual-level dynamics are ultimately the drivers of group-level coordination, they do not necessarily offer the most parsimonious description of a group’s macroscopic properties. Rather, the factors underlying group organization may be better described at some intermediate, mesoscopic scale. We introduce a novel method from information-theoretic first principles to find a compressed description of a system based on the actions and mutual dependencies of its constituents, thus revealing the natural structure of the collective. We emphasize that this method is computationally tractable and requires neither pairwise nor Gaussian assumptions about individual interactions.