Assessing the relative importance of high-order versus dyadic interactions in information transfer

Determine the relative importance of high-order (polyadic) interactions among processes compared to dyadic (pairwise) relations when quantifying directed information flow in complex systems, particularly within transfer entropy and related Granger-causality frameworks.

Background

The paper discusses how transfer entropy (TE) and Granger causality (GC) are widely used to infer directed information flow, but standard dyadic analyses may miss polyadic dependencies such as redundancy and synergy. Prior critiques argue that relying on dyadic models implicitly downplays the role of polyadic relationships.

Within this context, the authors explicitly note that determining how much high-order interactions contribute relative to dyadic relations remains unresolved. Their contribution proposes a decomposition of TE into unique, redundant, and synergistic components to start addressing this challenge.

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 (paragraph discussing critique of transfer entropy by [cruc])

While this approach seems very promising, it is unclear how the initial candidate set to start their algorithm with can be chosen efficiently for high-dimensional systems.

— Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems  (2608.17452 - Braun et al., 18 Aug 2026) in Introduction