Abstract
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 (), the number of, and difference between potential system states. Here we provide theoretical justification of the relationship between Φ and , 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 as a proxy for Φ using artificial networks, evolved to have integrated structures. The results show a positive linear relationship between Φ and 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.
Highlights
Integrated information ( ) is a quantity that describes the intrinsic causal properties of a physical system in a state (Oizumi et al, 2014)
A natural follow-up question is whether the reverse is true, do high levels of differentiation imply high integrated information? or are there any other relationships between integrated information and differentiation? These questions are further explored in two different settings, using artificially evolved networks called animats
Animats are artificial entities consisting of several elements, connections between them, and a logic governing the interaction of the elements
Summary
Integrated information ( ) is a quantity that describes the intrinsic causal properties of a physical system in a state (Oizumi et al, 2014). Information emphasizes that the causal power of a system in a state must be specific, implying that it should be different in different states, a property referred to as differentiation (Tononi and Edelman, 1998; Tononi, 2004). Despite this intuitive connection, a formal examination of the relationship between integrated information and differentiation has not yet been performed. The connection between consciousness and integrated information proposed by IIT has motivated neuroimaging studies which employ simple perturbational approaches aimed at estimating the brain’s capacity to integrate information (Massimini et al, 2005; Casali et al, 2013)
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