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Asymmetric Synaptic Connections in Z(2) Gauge Neural Network

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Neural Information Processing (ICONIP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9950))

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Abstract

We consider Z(2) gauge neural network which involves neuron variables \(S_i (=\pm 1)\) and synaptic connection (gauge) variables \(J_{ij} (=\pm 1)\). Its energy consists of the Hopfield term \(-c_1S_iJ_{ij}S_j\) and the reverberation term \(-c_2J_{ij}J_{jk}J_{ki}\) for signal propagation on a closed loop. The model of symmetric couplings \(J_{ij}=J_{ji}\) has been studied; its phase diagram in the \(c_2-c_1\) plane exhibits Higgs, Coulomb and confinement phases, each of which is characterized by the ability of learning and/or recalling patterns. In this paper, we consider the model of asymmetric coupling (\(J_{ij}\) and \(J_{ji}\) are independent), and examine the effect of asymmetry on a partially connected random network.

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Acknowledgment

The authors would like to thank Dr. Y. Nakano for discussion.

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Authors and Affiliations

  1. Department of Physics, Kindai University, Higashi-Osaka, 577-8502, Japan

    Atsutomo Murai & Tetsuo Matsui

Authors
  1. Atsutomo Murai
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  2. Tetsuo Matsui
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Corresponding author

Correspondence to Tetsuo Matsui .

Editor information

Editors and Affiliations

  1. The University of Tokyo , Tokyo, Japan

    Akira Hirose

  2. Kobe University , Kobe, Japan

    Seiichi Ozawa

  3. Okinawa Institute of Science and Technology Graduate University, Onna, Japan

    Kenji Doya

  4. Nara Institute of Science and Technology , Ikoma, Japan

    Kazushi Ikeda

  5. Kyungpook National University , Daegu, Korea (Republic of)

    Minho Lee

  6. Chinese Academy of Sciences , Beijing, China

    Derong Liu

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Murai, A., Matsui, T. (2016). Asymmetric Synaptic Connections in Z(2) Gauge Neural Network. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9950. Springer, Cham. https://doi.org/10.1007/978-3-319-46681-1_62

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  • DOI: https://doi.org/10.1007/978-3-319-46681-1_62

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46680-4

  • Online ISBN: 978-3-319-46681-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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