Upper bounds for integrated information
Alireza Zaeemzadeh, Giulio Tononi
arXiv Preprint Archive May 16, 2023 preprint
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or mathematical paper |
|---|---|
| Keywords | Q-bio.nc Math.ds Math.pr |
| Key points | Proposes that mechanisms sharing parts cannot all achieve their maximum integrated information, and introduces techniques to design systems that maximize integrated information for subsets of mechanisms or relations. |
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.