Geometry of information integration

Shun-ichi Amari, Naotsugu Tsuchiya, Masafumi Oizumi

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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 these measures and elucidate their relations from the 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.

Original languageEnglish
Title of host publicationInformation Geometry and Its Applications
Subtitle of host publicationOn the Occasion of Shun-ichi Amari's 80th Birthday
EditorsNihat Ay, Paolo Gibilisco, Frantisek Matus
Place of PublicationSwitzerland
PublisherSpringer
Pages3-17
Number of pages15
Volume252
ISBN (Electronic)9783319977980
ISBN (Print)9783319977973
DOIs
Publication statusPublished - 1 Jan 2018
EventInformation Geometry and its Applications 2016 - Liblice Castle, Liblice, Czech Republic
Duration: 12 Jun 201617 Jun 2016
Conference number: 4th
http://igaia.utia.cz/

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume252
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInformation Geometry and its Applications 2016
Abbreviated titleIGAIA IV
CountryCzech Republic
CityLiblice
Period12/06/1617/06/16
Internet address

Keywords

  • Consciousness
  • Information geometry
  • Integrated information theory
  • Kullback-Leibler divergence
  • Mismatched decoding

Cite this

Amari, S., Tsuchiya, N., & Oizumi, M. (2018). Geometry of information integration. In N. Ay, P. Gibilisco, & F. Matus (Eds.), Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday (Vol. 252, pp. 3-17). (Springer Proceedings in Mathematics & Statistics; Vol. 252). Switzerland: Springer. https://doi.org/10.1007/978-3-319-97798-0_1
Amari, Shun-ichi ; Tsuchiya, Naotsugu ; Oizumi, Masafumi. / Geometry of information integration. Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday. editor / Nihat Ay ; Paolo Gibilisco ; Frantisek Matus. Vol. 252 Switzerland : Springer, 2018. pp. 3-17 (Springer Proceedings in Mathematics & Statistics).
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Amari, S, Tsuchiya, N & Oizumi, M 2018, Geometry of information integration. in N Ay, P Gibilisco & F Matus (eds), Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday. vol. 252, Springer Proceedings in Mathematics & Statistics, vol. 252, Springer, Switzerland, pp. 3-17, Information Geometry and its Applications 2016, Liblice, Czech Republic, 12/06/16. https://doi.org/10.1007/978-3-319-97798-0_1

Geometry of information integration. / Amari, Shun-ichi; Tsuchiya, Naotsugu; Oizumi, Masafumi.

Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday. ed. / Nihat Ay; Paolo Gibilisco; Frantisek Matus. Vol. 252 Switzerland : Springer, 2018. p. 3-17 (Springer Proceedings in Mathematics & Statistics; Vol. 252).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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AB - 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 these measures and elucidate their relations from the 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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Amari S, Tsuchiya N, Oizumi M. Geometry of information integration. In Ay N, Gibilisco P, Matus F, editors, Information Geometry and Its Applications: On the Occasion of Shun-ichi Amari's 80th Birthday. Vol. 252. Switzerland: Springer. 2018. p. 3-17. (Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-3-319-97798-0_1