Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality
Xerxes D. Arsiwalla, Pedro A.M. Mediano, Paul F.M.J. Verschure

TL;DR
This paper analytically investigates how the informational complexity of network dynamics increases near criticality, revealing that eigenmodes of covariance and adjacency matrices govern this complexity, with implications for brain and communication systems.
Contribution
It introduces an analytic method to compute integrated information based on network weights and spectral decomposition, highlighting increased complexity near criticality across topologies.
Findings
Informational complexity peaks near criticality.
Eigenmodes of covariance dominate information integration.
High integrated information is driven by the leading eigenmode.
Abstract
What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this problem taking a whole-versus-parts perspective, wherein one explicitly computes the amount of information generated by a network as a whole over and above that generated by the sum of its parts during state transitions. While several numerical schemes for estimating network integrated information exist, it is instructive to pursue an analytic approach that computes integrated information as a function of network weights. Our formulation of integrated information uses a Kullback-Leibler divergence between the multi-variate distribution on the set of network states versus the corresponding factorized distribution over its parts. Implementing stochastic…
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