Toward a unified taxonomy of information dynamics via Integrated Information Decomposition

Our ability to understand and control complex systems of many interacting partsremains limited. A key challenge is that we still do not know how best to describe — and quantify — the many-to-many dynamical interactions that characterize their complexity. To address this limitation, we introduce the mathematical framework of Integrated Information Decomposition, or PhiID. PhiID provides a comprehensive frameworkto disentangle and characterize the information dynamics of complex multivariatesystems. On the theoretical side, PhiID reveals the existence of previously unreportedmodes of collective information flow, providing tools to express well-known measuresof information transfer, information storage, and dynamical complexity as aggregatesof these modes, thereby overcoming some of their known theoretical shortcomings. Onthe empirical side, we validate our theoretical results with computational models andexamples from over 1000 biological, social, physical, and synthetic dynamical systems.Altogether, PhiID improves our understanding of the behavior of widely used measuresfor characterizing complex systems across disciplines and leads to new more refinedanalyses of dynamical complexity.