A scalable estimator of higher-order information in complex dynamical systems
File(s)
Accepted version
Supporting information
Author(s)
Liardi, Alberto
Blackburne, George
Rajpal, Hardik
Rosas, Fernando
Mediano, Pedro
Type
Journal Article
Abstract
Understanding complex systems requires characterising how they perform distributed computation and integrate information. Information theory offers several quantities for describing complex information structures,
where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies.
However, applying these approaches to large systems is severely hindered by their poor scalability, and
few measures are specifically designed for multivariate time series data. Here we introduce M-information,
a novel measure that quantifies the higher-order information integration in complex dynamical systems.
We show that M-information can be calculated via a convex optimisation problem, and derive a robust,
efficient algorithm that scales gracefully with system size. M-information is resilient to noise, indexes critical
behaviour in artificial neuronal populations, and tracks consciousness and task performance in macaque and
mouse neuroimaging data. Finally, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics, helping unravel collective
computation in large complex systems.
where collective patterns of coordination emerge from higher-order (i.e. beyond-pairwise) interdependencies.
However, applying these approaches to large systems is severely hindered by their poor scalability, and
few measures are specifically designed for multivariate time series data. Here we introduce M-information,
a novel measure that quantifies the higher-order information integration in complex dynamical systems.
We show that M-information can be calculated via a convex optimisation problem, and derive a robust,
efficient algorithm that scales gracefully with system size. M-information is resilient to noise, indexes critical
behaviour in artificial neuronal populations, and tracks consciousness and task performance in macaque and
mouse neuroimaging data. Finally, M-information can be incorporated into existing information decomposition frameworks to reveal a comprehensive taxonomy of information dynamics, helping unravel collective
computation in large complex systems.
Date Acceptance
2026-08-25
Citation
Cell Reports Physical Science
ISSN
2666-3864
Publisher
Elsevier
Journal / Book Title
Cell Reports Physical Science
Copyright Statement
Copyright This paper is embargoed until publication. Once published the Version of Record (VoR) will be available on immediate open access.
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Publication Status
Accepted