Extent and detectability of the correspondence between higher-order interactions and synergistic behaviors

Determine the quantitative extent of the correspondence between genuine higher-order interactions encoded as 2-simplices in simplicial complexes and synergistic higher-order behaviors measured via total dynamical O-information, and ascertain whether low-order observables—specifically pairwise metrics such as the sum of transfer entropies—can detect the presence of these higher-order interactions and to what degree, in the context of the simplicial Ising model and the simplicial social contagion model.

Background

The paper investigates how higher-order mechanisms (group interactions represented by simplices) relate to higher-order behavioral observables, using two canonical models: a simplicial Ising model and a simplicial social contagion model. Higher-order behavior is quantified using total dynamical O-information, a multivariate, time-lagged extension of O-information designed to capture redundancy versus synergy in information-sharing across groups of variables.

Initial results reveal emergent synergistic signatures associated with genuine higher-order interactions (2-simplices), which are not captured by lower-order observables. This motivates the explicit uncertainty about the breadth and conditions under which synergistic behaviors correspond to the presence of higher-order mechanisms, and whether such mechanisms can be detected using low-order metrics such as pairwise transfer entropy.