Evaluating Approximations and Heuristic Measures of Integrated Information

Abstract

Integrated information theory (IIT) proposes a measure of integrated information (Φ) to capture the level of consciousness for a physical system in a given state. Unfortunately, calculating Φ itself is currently only possible for very small model systems, and far from computable for the kinds of systems typically associated with consciousness (brains). Here, we consider several proposed measures and computational approximations, some of which can be applied to larger systems, and test 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. In this study, we evaluated these approximations and heuristic measures, based not on practical or clinical considerations, but rather based on how well they estimate the Φ values of model systems. 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), as well as its state transition matrix (STM) over time for all possible initial states. From these matrices, we calculated, approximations to Φ, and measures based on state differentiation, state entropy, state uniqueness, and integrated information. All measures were correlated with Φ in a state dependent and state independent manner. 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, Φ 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), on the system level (state independent). These measures could allow for efficient estimation of Φ on a group level, or as accurate predictors of low, but not high, Φ systems. While it’s 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 are at a minimum rigorously tested in an environment where the ground truth can be established.

The Emergence of Integrated Information, Complexity, and ‘Consciousness’ at Criticality

“… is then a function of the total system X , the state of the system x and the partition P . The basic schematic of calculating is outlined below and more detail is available in [ 21 , 23 , 24 , 25 , 26 ]. …”

“…Though other measures exist [ 22 ] which attempt to capture some form of integration or complexity, this paper uses as the metric quantifying conscious experience. For a comprehensive overview of the mathematical taxonomy of the possible variations in defining integrated information, see [ 23 , 24 ].…”

Phi Fluctuates with Surprise: An empirical pre-study for the synthesis of the Free Energy Principle and Integrated Information Theory

“…The cut one assumption assumes that the MIP on the system level is the cut of an elementary mechanism and the bipartition assumption assumes that the MIP on mechanism level is a bipartition. Both assumptions greatly reduce computational load and their resulting Φ measures are strongly correlated with the system's true Φ (Nilsen, Juel & Marshall, 2019). All IIT measures were calculated using the python package pyphi (Mayner et al, 2018).…”