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

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.

References in corpus (14)

• Estimating Mutual Information
• Granger causality and transfer entropy are equivalent for Gaussian variables
• Quantifying unique information
• Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems
• Measuring integrated information from the decoding perspective
• Measuring multivariate redundant information with pointwise common change in surprisal
• Improved Measures of Integrated Information
• Higher-order clustering in networks
• Shared Information -- New Insights and Problems in Decomposing Information in Complex Systems
• The signatures of conscious access and phenomenology are consistent with large-scale brain communication at criticality
• Understanding interdependency through complex information sharing
• Fast and exact search for the partition with minimal information loss
• Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
• Exact partial information decompositions for Gaussian systems based on dependency constraints

Cited by in corpus (7)

• Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information
• Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data
• Integrated information as a common signature of dynamical and information-processing complexity
• Falsification and consciousness
• General anesthesia reduces complexity and temporal asymmetry of the informational structures derived from neural recordings in Drosophila
• Integrated Information in the Spiking-Bursting Stochastic Model
• Non-separability of Physical Systems as a Foundation of Consciousness