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This paper introduces a time- and state-dependent measure of integrated information, φ, which captures the repertoire of causal states available to a system as a whole. Specifically, φ quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) φ varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) φ varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) φ varies as a function of network architecture. High φ values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high φ because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high φ but are inefficient. (iv) In Hopfield networks, φ is low for attractor states and neutral states, but increases if the networks are optimized to achieve tension between local and global interactions. These basic examples appear to match well against neurobiological evidence concerning the neural substrates of consciousness. More generally, φ appears to be a useful metric to characterize the capacity of any physical system to integrate information.

The integrated information theory (IIT) starts from phenomenology and makes use of thought experiments to claim that consciousness is integrated information. Specifically: (i) the quantity of consciousness corresponds to the amount of integrated information generated by a complex of elements; (ii) the quality of experience is specified by the set of informational relationships generated within that complex. Integrated information () is defined as the amount of information generated by a complex of elements, above and beyond the information generated by its parts. Qualia space (Q) is a space where each axis represents a possible state of the complex, each point is a probability distribution of its states, and arrows between points represent the informational relationships among its elements generated by causal mechanisms (connections). Together, the set of informational relationships within a complex constitute a shape in Q that completely and univocally specifies a particular experience. Several observations concerning the neural substrate of consciousness fall naturally into place within the IIT framework. Among them are the association of consciousness with certain neural systems rather than with others; the fact that neural processes underlying consciousness can influence or be influenced by neural processes that remain unconscious; the reduction of consciousness during dreamless sleep and generalized seizures; and the distinct role of different cortical architectures in affecting the quality of experience. Equating consciousness with integrated information carries several implications for our view of nature. Abbreviations: , integrated information • IIT, integrated information theory • MIP, minimum information partition

Consciousness poses two main problems. The first is understanding the conditions that determine to what extent a system has conscious experience. For instance, why is our consciousness generated by certain parts of our brain, such as the thalamocortical system, and not by other parts, such as the cerebellum? And why are we conscious during wakefulness and much less so during dreamless sleep? The second problem is understanding the conditions that determine what kind of consciousness a system has. For example, why do specific parts of the brain contribute specific qualities to our conscious experience, such as vision and audition?

This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv) In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks are optimized to achieve tension between local and global interactions. These basic examples appear to match well against neurobiological evidence concerning the neural substrates of consciousness. More generally, phi appears to be a useful metric to characterize the capacity of any physical system to integrate information. Publication Types: Research Support, N.I.H., Extramural Research Support, Non-U.S. Gov't PMID: 18551165 [PubMed - indexed for MEDLINE] PMCID: PMC2386970

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