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 (“”) 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. A subset of the measures appears to 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 and dynamical complexity that may have more general applicability.
Highlights
Measures of integrated information seek to quantify the extent to which a whole system generates more information than the sum of its parts as it transitions between states
We focus on the earlier, dynamical/empirical conceptions of integrated information because (i) they are more readily applicable to empirical time-series; (ii) they remain conceptually powerful in theories of consciousness, and (iii) they promise general applicability to many other questions in neuroscience and beyond, in which part-whole relations are of interest
All of the measures of integrated information that we have described have the potential to behave in ways which are not obvious a priori, and in a manner difficult to express analytically
Summary
Measures of integrated information seek to quantify the extent to which a whole system generates more information than the sum of its parts as it transitions between states. Integrated information measures have the potential to capture the dynamical complexity of any many body system, and to aid with understanding and characterising complex systems [1]. Several of them are beginning to see application to empirical data [6], or to large-scale simulations [7,8], yet a systematic comparison of the behaviour of the various measures on non-trivial network models has not previously been performed. This paper has two goals: first, to provide a unified source of explanation of the principles and practicalities of a class of prominent candidate measures of integrated information; second, to examine the behaviour of candidate measures on non-trivial network models, in order to shed light on their comparative practical utility
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