Abstract
Integrated Information Theory proposes a measure of conscious activity (), 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 that 3.0 fail to capture critical phase transitions and propose a reformulation of the assumptions made by integrated information measures.
Highlights
Integrated Information Theory (IIT [1]) was developed to address the problem of consciousness by characterizing its underlying processes in a quantitative manner
Criticisms concerning the definition of integrated information measures have addressed a variety of topics, e.g., the existence of “trivially non-conscious” systems, composed of units distributed in relatively simple arrangements yielding arbitrarily large values of Φ, or the absence of a canonical metric of the probability distribution space [5]
We explore some of these aspects and explore possible reformulations of the measures concerning how current measures behave around critical phase transitions
Summary
For simplicity, in most cases we compute only the integrated information φ of a mechanism comprising the system of interest This homogeneous architecture allows us to assume that under some conditions (systems with possible couplings and near the thermodynamic limit) the MIP is always either a partition that cuts a single node from the mechanism of the system or a cut that separates entire regions in different partitions (see Appendix B.3). This assumption will reduce drastically the computational cost of calculating integrated information.
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