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Category Theoretic Analysis of Photon-Based Decision Making

Author

Listed:
  • Makoto Naruse

    (Network System Research Institute, National Institute of Information and Communications Technology, 4-2-1 Nukui-Kita, Koganei, Tokyo 184-8795, Japan2Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France)

  • Song-Ju Kim

    (Graduate School of Media and Governance Keio University, 5322 Endo, Fujisawa, Kanagawa 252-0882, Japan)

  • Masashi Aono

    (Faculty of Environment and Information Studies, Keio University, 5322 Endo, Fujisawa, Kanagawa 252-0882, Japan)

  • Martin Berthel

    (Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France)

  • Aurélien Drezet

    (Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France)

  • Serge Huant

    (Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France)

  • Hirokazu Hori

    (Interdisciplinary Graduate School, University of Yamanashi, Takeda, Kofu, Yamanashi 400-8511, Japan)

Abstract

Decision making is a vital function in the age of machine learning and artificial intelligence; however, its physical realization and theoretical fundamentals are not yet well understood. In our former study, we demonstrated that single photons can be used to make decisions in uncertain, dynamically changing environments. The two-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. In this study, we present a category theoretic modeling and analysis of single-photon-based decision making, including a quantitative analysis that agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure and the braid structure in triangulated categories provide better understandings and quantitative metrics of the underlying mechanisms for the single-photon decision maker. This study provides insight and a foundation for analyzing more complex and uncertain problems for machine learning and artificial intelligence.

Suggested Citation

  • Makoto Naruse & Song-Ju Kim & Masashi Aono & Martin Berthel & Aurélien Drezet & Serge Huant & Hirokazu Hori, 2018. "Category Theoretic Analysis of Photon-Based Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1305-1333, September.
    • Handle: RePEc:wsi:ijitdm:v:17:y:2018:i:05:n:s0219622018500268
    DOI: 10.1142/S0219622018500268
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    References listed on IDEAS

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    1. Nathaniel D. Daw & John P. O'Doherty & Peter Dayan & Ben Seymour & Raymond J. Dolan, 2006. "Cortical substrates for exploratory decisions in humans," Nature, Nature, vol. 441(7095), pages 876-879, June.
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    Cited by:

    1. Hayato Saigo & Makoto Naruse & Kazuya Okamura & Hirokazu Hori & Izumi Ojima, 2019. "Analysis of Soft Robotics Based on the Concept of Category of Mobility," Complexity, Hindawi, vol. 2019, pages 1-12, March.

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