Synergistic signatures of group mechanisms in higher-order systems

TL;DR

This paper explores how higher-order group interactions in complex systems lead to emergent synergistic behaviors that are not detectable through low-order observables, providing a new framework for understanding causal mechanisms.

Contribution

It introduces a methodological framework to analyze the relationship between higher-order mechanisms and emergent behaviors in networked systems with group interactions.

Findings

Higher-order interactions produce emergent synergy only at the group level.

Synergy depends non-linearly on the balance of low- and higher-order mechanisms.

Emergent behaviors are invisible to low-order observables.

Abstract

The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order mechanisms and higher-order behavioral observables in two representative models with group interactions: a simplicial Ising model and a social contagion model. In both systems, we find that group (higher-order) interactions show emergent synergistic (higher-order) behavior. The emergent synergy appears only at the group level and depends in a complex, non-linear way on the trade-off between the strengths of the low- and higher-order mechanisms and is invisible to low-order behavioral observables. Our work sets the basis for systematically investigating the relation between causal mechanisms and behavioral patterns in complex networked systems with group interactions, offering a robust methodological framework to tackle this challenging task.