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arXiv · 1709.02050

Geometry of Information Integration

Shun-ichi Amari·Naotsugu Tsuchiya·Masafumi Oizumi
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Abstract

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.

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Shun-ichi Amari, Naotsugu Tsuchiya, Masafumi Oizumi. 2017-09-07. Geometry of Information Integration. https://arxiv.org/abs/1709.02050

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