Upper bounds for integrated information

Integrated information theory (IIT) offers a mathematical framework for measuring the causal irreducibility of systems and their subsets. The mechanism integrated information quantifies how much of a mechanism's causal power cannot be explained by its parts; if fully explainable, integrated information is zero. This work investigates the upper bound of this measure and how it is attained, studying isolated mechanisms, groups of mechanisms, and groups of causal relations. New theoretical results show that mechanisms sharing parts cannot all simultaneously reach their maximum. Techniques are introduced for designing systems that maximize integrated information for subsets of mechanisms or relations, potentially reducing computations and comparing connectivity profiles.

Study at a glance

Abstract

Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated information quantifies how much of the causal powers of a subset of units in a state, also referred to as a mechanism, cannot be accounted for by its parts. If the causal powers of the mechanism can be fully explained by its parts, it is reducible and its integrated information is zero. Here, we study the upper bound of this measure and how it is achieved. We study mechanisms in isolation, groups of mechanisms, and groups of causal relations among mechanisms. We put forward new theoretical results that show mechanisms that share parts with each other cannot all achieve their maximum. We also introduce techniques to design systems that can maximize the integrated information of a subset of their mechanisms or relations. Our results can potentially be used to exploit the symmetries and constraints to reduce the computations significantly and to compare different connectivity profiles in terms of their maximal achievable integrated information.