AUTHOR=Marshall William , Gomez-Ramirez Jaime , Tononi Giulio 

TITLE=Integrated Information and State Differentiation

JOURNAL=Frontiers in Psychology

VOLUME=7

YEAR=2016

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2016.00926

DOI=10.3389/fpsyg.2016.00926

ISSN=1664-1078

ABSTRACT=<p>Integrated information (Φ) is a measure of the cause-effect power of a physical system. This paper investigates the relationship between Φ as defined in Integrated Information Theory and state differentiation (<inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">D</mml:mi></mml:mrow></mml:math></inline-formula>), the number of, and difference between potential system states. Here we provide theoretical justification of the relationship between Φ and <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">D</mml:mi></mml:mrow></mml:math></inline-formula>, then validate the results using a simulation study. First, we show that a physical system in a state with high Φ necessarily has many elements and specifies many causal relationships. Furthermore, if the average value of integrated information across all states is high, the system must also have high differentiation. Next, we explore the use of <inline-formula><mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">D</mml:mi></mml:mrow></mml:math></inline-formula> as a proxy for Φ using artificial networks, evolved to have integrated structures. The results show a positive linear relationship between Φ and <inline-formula><mml:math id="M4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="-tex-caligraphic">D</mml:mi></mml:mrow></mml:math></inline-formula> for multiple network sizes and connectivity patterns. Finally we investigate the differentiation evoked by sensory inputs and show that, under certain conditions, it is possible to estimate integrated information without a direct perturbation of its internal elements. In concluding, we discuss the need for further validation on larger networks and explore the potential applications of this work to the empirical study of consciousness, especially concerning the practical estimation of Φ from neuroimaging data.</p>