Integrated Information in Discrete Dynamical Systems: Motivation and Theoretical Framework

Abstract

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.

Author Summary

We have suggested that consciousness has to do with a system's capacity to generate  integrated information. This suggestion stems from considering two basic properties of consciousness: (i) each conscious experience generates a large amount of information, by ruling out alternative experiences; and (ii) the information is integrated, meaning that it cannot be decomposed into independent parts. We introduce a measure that quantifies how much integrated information is generated by a discrete dynamical system in the process of transitioning from one state to the next. The measure captures the information generated by the causal interactions among the elements of the system, above and beyond the information generated independently by its parts. We present numerical analyses of basic examples, which match well against neurobiological evidence concerning the neural substrates of consciousness. The framework establishes an observer-independent view of information by taking an intrinsic perspective on interactions.