### 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 language | English |
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Title of host publication | Information Geometry and Its Applications |

Subtitle of host publication | On the Occasion of Shun-ichi Amari's 80th Birthday |

Editors | Nihat Ay, Paolo Gibilisco, Frantisek Matus |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 3-17 |

Number of pages | 15 |

Volume | 252 |

ISBN (Electronic) | 9783319977980 |

ISBN (Print) | 9783319977973 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Event | Information Geometry and its Applications 2016 - Liblice Castle, Liblice, Czech Republic Duration: 12 Jun 2016 → 17 Jun 2016 Conference number: 4th http://igaia.utia.cz/ |

### Publication series

Name | Springer Proceedings in Mathematics & Statistics |
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Publisher | Springer |

Volume | 252 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | Information Geometry and its Applications 2016 |
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Abbreviated title | IGAIA IV |

Country | Czech Republic |

City | Liblice |

Period | 12/06/16 → 17/06/16 |

Internet address |

### Keywords

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

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Geometry of information integration

AU - Amari, Shun-ichi

AU - Tsuchiya, Naotsugu

AU - Oizumi, Masafumi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

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.

KW - Consciousness

KW - Information geometry

KW - Integrated information theory

KW - Kullback-Leibler divergence

KW - Mismatched decoding

UR - http://www.scopus.com/inward/record.url?scp=85056355780&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-97798-0_1

DO - 10.1007/978-3-319-97798-0_1

M3 - Conference Paper

SN - 9783319977973

VL - 252

T3 - Springer Proceedings in Mathematics & Statistics

SP - 3

EP - 17

BT - Information Geometry and Its Applications

A2 - Ay, Nihat

A2 - Gibilisco, Paolo

A2 - Matus, Frantisek

PB - Springer

CY - Switzerland

ER -