Abstract
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.
Footnotes
Author contributions: C.R.T. formulated the problem and solution, and wrote the paper; A.T.H. and P.R. assisted with the solution and writing; P.R. contributed simulation model and data; M.M.G. contributed empirical tracking data and writing.
Data and materials availability: Empirical video data for schooling fish provided by Iain D. Couzin, from the work of Katz et al. (2011). I.D.C. contributed directly to the filming and collection of this data.
Funding: P.R. acknowledges support from the German Science Foundation (DFG) grant RO 47766/2-1; M.M.G. was supported by an NSF Graduate Research Fellowship. Funding and support for the empirical data used in this paper was provided by I.D.C. (see Katz et al., 2011, for additional information). Early funding and support for C.R.T.’s work with rate-distortion theory was provided by I.D.C. and an NSF Graduate Research Fellowship; current funding and support is provided by Joshua B. Plotkin and a mindCORE Postdoctoral Research Fellowship.