2017/09/07 by Шун-ичи Амари, Naotsugu Tsuchiya, Amari, Shun-ichi +3 · 1 citation
Computer Science · Neuroscience · Physics and Astronomy · #FOS: Computer and information sciences #Information Theory (cs.IT) #Neural dynamics and brain function #Statistical Mechanics and Entropy #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1709.02050
openalex publication_date 2017/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information transmission between the parts is removed. Multiple measures have been proposed as a measure of integrated information. Here, we analyze four of the previously proposed measures and elucidate their relations from a viewpoint of information geometry. Two of them use dually flat manifolds and the other two use curved manifolds to define a split model. We show that there are hierarchical structures among the measures. We provide explicit expressions of these measures.