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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
85/2020

Complexity as Causal Information Integration

Carlotta Langer and Nihat Ay

Abstract

Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system and one without causal connections. Various measures have been proposed and compared in this setting. We will discuss a class of information geometric measures that aim at assessing the intrinsic causal influences in a system. One promising candidate of these measures, denoted by $\Phi_{CIS}$ , is based on conditional independence statements and does satisfy all of the properties that have been postulated as desirable. Unfortunately it does not have a graphical representation which makes it less intuitive and difficult to analyze. We propose an alternative approach using a latent variable which models a common exterior influence. This leads to a measure $\Phi_{CII}$ , Causal Information Integration, that satisfies all of the required conditions. Our measure can be calculated using an iterative information geometric algorithm, the em-algorithm. Therefore we are able to compare its behavior to existing integrated information measures.

Received:
Aug 24, 2020
Published:
Aug 24, 2020
Keywords:
complexity, Integrated Information, causality, Conditional Independence, em-Algorithm

Related publications

inJournal
2020 Journal Open Access
Carlotta Langer and Nihat Ay

Complexity as causal information integration

In: Entropy, 22 (2020) 10, p. 1107