Abstract

Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (Φ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating Φ itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the Φ values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system’s state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated Φ, approximations to Φ, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95) but without major reductions in computational demands. Furthermore, the maximum value of Φ across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, rs = 0.722), decoder-based integrated information (Φ*, rs = 0.816), and state differentiation (D1, rs = 0.827). These measures could allow for the efficient estimation of a system’s capacity for high Φ or function as accurate predictors of low- (but not high-)Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established.

Highlights

  • The nature of consciousness, defined as a subjective experience, has been a philosophical topic for centuries but has only recently become incorporated into mainstream neuroscience [1]

  • Across states correlated strongly with measures of signal complexity (LZ, rs = 0.722), decoder-based integrated information (Φ*, rs = 0.816), and state differentiation (D1, rs = 0.827). These measures could allow for the efficient estimation of a system’s capacity for high Φ or function as accurate predictors of low-Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established

  • We randomly generated a population of small networks with linear threshold logic and both excitatory and inhibitory connections

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Summary

Introduction

The nature of consciousness, defined as a subjective experience, has been a philosophical topic for centuries but has only recently become incorporated into mainstream neuroscience [1]. As consciousness is a subjective phenomenon, and not directly measurable, it must be operationalized to allow for empirical investigation of its nature and underlying mechanisms [2]. Entropy 2019, 21, 525 the scientific study of consciousness requires an objective measure. One such measure has been developed within the framework of the integrated information theory (IIT), introduced and elaborated by Giulio Tononi and colleagues [3,4,5]. The theory proposes that consciousness is identical to a particular type of integrated information (Phi; Φ) which is defined and quantified within the theory as a measure of a system’s informational irreducibility, or how much information a system in a definite state specifies about its own past and future above and beyond how much such information is specified by its parts

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