Scaling Behaviour and Critical Phase Transitions in Integrated Information Theory

I just published a new paper exploring some of the ideas we initiated in our Integrated information in the thermodynamic limit (Aguilera & Di Paolo, 2019) paper. Here, I  explore in detail many of the assumptions of Integrated Information Theory (specifically IIT 3.0) by computing integration in large kinetic Ising networks presenting a critical point. By combining a simple model with tractable statistical properties that can be analytically characterized with architectures, I show that some assumptions in the theory are problematic for capturing some of the properties associated with critical phase transitions. This example compels researchers interested in IIT and related indices of complexity to apply such measures under careful examination of their design assumptions. Rather than applying the measure off-the-shelf, this work offers some methods to explore in more depth the assumptions behind the measure and how it applies to each situation

Aguilera, M & Di Paolo, EA (2019). Scaling Behaviour and Critical Phase Transitions in Integrated Information TheoryEntropy 2019, 21(12), 1198; https://doi.org/10.3390/e21121198

Abstract: Integrated Information Theory proposes a measure of conscious activity (Φ), characterised as the irreducibility of a dynamical system to the sum of its components. Due to its computational cost, current versions of the theory (IIT 3.0) are difficult to apply to systems larger than a dozen units, and, in general, it is not well known how integrated information scales as systems grow larger in size. In this article, we propose to study the scaling behaviour of integrated information in a simple model of a critical phase transition: an infinite-range kinetic Ising model. In this model, we assume a homogeneous distribution of couplings to simplify the computation of integrated information. This simplified model allows us to critically review some of the design assumptions behind the measure and connect its properties with well-known phenomena in phase transitions in statistical mechanics. As a result, we point to some aspects of the mathematical definitions of IIT 3.0 that fail to capture critical phase transitions and propose a reformulation of the assumptions made by integrated information measures.

About maguilera0

Miguel Aguilera is a Postdoctoral Research Fellow at the IAS Research Center for Life, Mind and Society at the University of the Basque Country. He has been a visiting researcher at the Cognitive Science Program at Indiana University and the Ikegami Lab in the Department of General Systems Studies at the University of Tokyo, and a postdoctoral fellow at the University of the University of Zaragoza and the University of the Balearic Islands. His research focuses on autonomy in biological and social systems from an interdisciplinary perspective, integrating insights from cognitive science, theoretical neuroscience, computational modeling, adaptive behaviour, and complex systems. It combines nonlinear and dynamical models, evolutionary algorithms, and mathematical analysis from dynamical systems, network and information theory, to generate and understand situated and embodied models of agency in the realms of artificial life and evolutionary robotics, computational neuroscience, collective intelligence practices and socio-technical systems.
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