A scalable, synergy-first backbone decomposition of higher-order structures in complex systems
<|reference_start|>A scalable, synergy-first backbone decomposition of higher-order structures in complex systems: Since its introduction in 2011, the partial information decomposition (PID) has triggered an explosion of interest in the field of multivariate information theory and the study of emergent, higher-order ("synergistic") interactions in complex systems. Despite its power, however, the PID has a number of limitations that restrict its general applicability: it scales poorly with system size and the standard approach to decomposition hinges on a definition of "redundancy", leaving synergy only vaguely defined as "that information not redundant." Other heuristic measures, such as the O-information, have been introduced, although these measures typically only provided a summary statistic of redundancy/synergy dominance, rather than direct insight into the synergy itself. To address this issue, we present an alternative decomposition that is synergy-first, scales much more gracefully than the PID, and has a straightforward interpretation. Our approach defines synergy as that information in a set that would be lost following the minimally invasive perturbation on any single element. By generalizing this idea to sets of elements, we construct a totally ordered "backbone" of partial synergy atoms that sweeps systems scales. Our approach starts with entropy, but can be generalized to the Kullback-Leibler divergence, and by extension, to the total correlation and the single-target mutual information. Finally, we show that this approach can be used to decompose higher-order interactions beyond just information theory: we demonstrate this by showing how synergistic combinations of pairwise edges in a complex network supports signal communicability and global integration. We conclude by discussing how this perspective on synergistic structure (information-based or otherwise) can deepen our understanding of part-whole relationships in complex systems.<|reference_end|>
@article{varley2024a,
    title={A scalable, synergy-first backbone decomposition of higher-order
  structures in complex systems},
    author={Thomas F. Varley},
    journal={arXiv preprint arXiv:2402.08135},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08135},
    primaryClass={cs.IT math.IT stat.OT}
}