Alberto Liardi

Alberto Liardi, Keenan J. A. Down, George Blackburne et al.

Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique solution constraining precisely how a PID should be constructed, leading to a multiverse of different formalisms with different mathematical commitments. In this work, we provide a comprehensive overview of the mathematical landscape of PID. By integrating existing PID measures into a common language, we systematically examine all major approaches to the PID framework that have emerged so far, determining for each measure whether or not each known property holds. In addition, we derive a web of all known theorems mapping the relationships and incompatibilities between these properties, before also revealing some novel interdependency results. In doing so, we chart a brief history of the framework, promote a unified perspective for its discussions, and offer a path towards both theoretical refinement and informed empirical applications for the future of this powerful method.

Alberto Liardi, George Blackburne, Hardik Rajpal et al.

Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information structures, where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies. Unfortunately, the use of these approaches to study large complex systems is severely hindered by the poor scalability of existing techniques. Moreover, there are relatively few measures specifically designed for multivariate time series data. Here we introduce a novel measure of information about macroscopic structures, termed M-information, which quantifies the higher-order integration of information in complex dynamical systems. We show that M-information can be calculated via a convex optimisation problem, and we derive a robust and efficient algorithm that scales gracefully with system size. Our analyses show that M-information is resilient to noise, indexes critical behaviour in artificial neuronal populations, and reflects states of consciousness and task performance in real-world macaque and mouse neuroimaging data. Furthermore, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics. Taken together, these results help us unravel collective computation in large complex systems.