Evaluating Approximations and Heuristic Measures of Integrated Information.

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 (