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Synergistic Motifs in Gaussian Systems

Enrico Caprioglio1,*, Pedro A. M. Mediano2,3, and Luc Berthouze1

  • *Contact author: e.caprioglio@sussex.ac.uk
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Phys. Rev. Lett. 136, 127401 – Published 25 March, 2026

DOI: https://doi.org/10.1103/179y-qp6j

Abstract

High-order interdependencies are central features of complex systems, yet a mechanistic explanation for their emergence remains elusive. Currently, it is unknown under what conditions high-order interdependencies, quantified by the information-theoretic construct of synergy, arise in systems governed by pairwise interactions. We solve this problem by providing precise sufficient and necessary conditions for when synergy prevails over low-order interdependencies in the weak interaction regime; namely, we prove that antibalanced (highly frustrated) correlational structures in Gaussian systems are sufficient for synergy dominance and that antibalanced interaction motifs in Ornstein-Uhlenbeck processes are necessary for synergy dominance. We validate the applicability of these analytical insights beyond the weak interaction regime, as well as in Ising, oscillatory, and empirical networks from multiple domains. Our results demonstrate that pairwise interactions can give rise to synergistic information in the absence of explicit high-order mechanisms, and highlight structural balance theory as an instrumental conceptual framework to study high-order interdependencies.

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Phys. Rev. Lett. 136, 127401– Published 25 March, 2026
  • Received 15 September 2025
  • Accepted 26 February 2026
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