A scalable, synergy-first backbone decomposition of higher-order structures in complex systems
CoRR(2024)
摘要
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.
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