Assessing the relative importance of high-order interactions versus dyadic relations

Determine a quantitative framework to assess the relative importance of high-order (polyadic) interactions among components of complex systems compared to dyadic (pairwise) relations, so as to evaluate how multi-variable dependencies contribute to observed information flow relative to two-variable dependencies.

Background

The paper discusses limitations of dyadic analyses such as pairwise Transfer Entropy (TE) and Granger causality (GC) in the presence of high-order dependencies like redundancy and synergy. Within this context, the authors note that existing approaches often neglect polyadic relationships, motivating the need to explicitly compare their contributions against dyadic relations.

To address this need, the paper proposes a decomposition of TE by searching for conditioning sets that minimize or maximize TE, thereby partitioning information flow into unique, redundant, and synergistic components. This is presented as a way to quantify many-body effects, highlighting the underlying open question of how to systematically and quantitatively assess the relative importance of high-order interactions compared to dyadic ones.

References

However, assessing the relative importance of these high-order interactions compared to dyadic relations remains an open problem.

— Disentangling high order effects in the transfer entropy  (2402.03229 - Stramaglia et al., 2024) in Main text, introduction (following citation to [cruc]); page 1

A central open problem is to connect governing mechanisms to the higher-order signatures that can actually be measured. For equilibrium systems, the joint distribution $p_N(\mathbf{s})$ provides a natural probabilistic description; for dynamical systems, the corresponding object is more generally a transition law or probability distribution over trajectories. Developing a framework that connects these descriptions to interaction structure, collective behaviour and the reducibility criterion of Eq.~eq:reducibility would help place the diverse approaches reviewed here on a common footing.

— Higher-Order Interactions in Complex Systems: Mechanisms, Behaviour, Representation and Reducibility  (2609.20142 - Pérez-Reche, 17 Sep 2026) in Section 7, subsection “Open problems”

The Dowker complex records whether a set of entities occurred together; whether it occurred more often than its pairs imply is a separate, statistical question.

— Beyond the Clique: Comparing Clique and Dowker Complexes for Co-occurrence Data in Learning Analytics  (2610.01305 - Yasutake et al., 1 Oct 2026) in Section 6, Outlook, item (2)