Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation

TL;DR

This study compares six different measures of integrated information in simulated network models to evaluate their behavior and relevance to dynamical complexity, aiding the operationalization of IIT.

Contribution

It provides a systematic comparison of candidate measures of integrated information using simulations, highlighting their differences and relevance to dynamical complexity.

Findings

Measures show diverse behaviors with no consistent agreement.

Only some measures reflect dynamical complexity involving segregation and integration.

Results guide the development and application of integrated information measures.

Abstract

Integrated Information Theory (IIT) is a prominent theory of consciousness that has at its centre measures that quantify the extent to which a system generates more information than the sum of its parts. While several candidate measures of integrated information (`$\Phi$') now exist, little is known about how they compare, especially in terms of their behaviour on non-trivial network models. In this article we provide clear and intuitive descriptions of six distinct candidate measures. We then explore the properties of each of these measures in simulation on networks consisting of eight interacting nodes, animated with Gaussian linear autoregressive dynamics. We find a striking diversity in the behaviour of these measures -- no two measures show consistent agreement across all analyses. Further, only a subset of the measures appear to genuinely reflect some form of dynamical complexity, in the sense of simultaneous segregation and integration between system components. Our results help guide the operationalisation of IIT and advance the development of measures of integrated information that may have more general applicability.