Integrated Information, a Complexity Measure for optimal partitions
arXiv Preprint Archive April 27, 2023 via arXiv
Summary
AI-generated from the abstractUsing Tononi's integrated information theory, a complexity index for consciousness is calculated analytically for two systems of Ising spins with parallel update dynamics: a homogeneous model and a modular infinite-range model. The geometric integrated information index is computed for fixed partitions with two or three components. In the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest component is above its critical temperature while the largest component is below. Partitioning effects are accounted for by introducing site dilution.
Study at a glance
| Characteristics | Theoretical or mathematical analysis Peer reviewed |
|---|---|
| Keywords | Cond-mat.stat-mech |
| Key finding | Proposes that for systems in the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest component is above its critical temperature and the largest component is below its critical temperature. |
Abstract
Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi's idea and calculate analytically a complexity index for two systems of Ising spins with parallel update dynamics, the homogeneous and a modular infinite range models. Using the information geometry formulation of integrated information theory, we calculate the geometric integrated information index, $φ_G(Π)$ for a fixed partition $Π$ with $K$ components and $Φ=$max$_Πφ_G(Π)$ for $K=2$ or $3$. For systems in the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest (largest) component is above (resp. below) its critical temperature. The effects of partitioning are taken into account by introducing site dilution.