A scalable synergy-first backbone decomposition of higher-order structures in complex systems

This paper introduces a novel decomposition method for analyzing synergistic information in complex systems. It addresses limitations of existing methods like Partial Information Decomposition (PID) and O-information by offering a synergy-first approach that scales more efficiently and provides a straightforward interpretation. Synergy is defined as information lost upon minimally invasive perturbation of a single element, generalized to sets of elements. This approach builds a totally ordered "backbone" of partial synergy atoms, applicable to entropy, Kullback-Leibler divergence, total correlation, and mutual information. The method's applicability extends beyond information theory; it decomposes higher-order interactions in graphs, assessing how synergistic edge combinations support global integration. The paper demonstrates the method's utility through various examples and discusses its implications for understanding part-whole relationships in complex systems.

Thomas F. Varley