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GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network

Author

Listed:
  • Yuan Gao

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
    School of Medical Information Engineering, Chengdu University of Traditional Chinese Medicine, Chengdu 610000, China)

  • Yueling Guo

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
    School of Science, Hunan Institute of Technology, Hengyang 421002, China)

  • Nurul Atiqah Romli

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia)

  • Mohd Shareduwan Mohd Kasihmuddin

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia)

  • Weixiang Chen

    (School of Medical Information Engineering, Chengdu University of Traditional Chinese Medicine, Chengdu 610000, China)

  • Mohd. Asyraf Mansor

    (School of Distance Education, Universiti Sains Malaysia, Penang 11800, Malaysia)

  • Ju Chen

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
    School of Medical Information Engineering, Chengdu University of Traditional Chinese Medicine, Chengdu 610000, China)

Abstract

One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity.

Suggested Citation

  • Yuan Gao & Yueling Guo & Nurul Atiqah Romli & Mohd Shareduwan Mohd Kasihmuddin & Weixiang Chen & Mohd. Asyraf Mansor & Ju Chen, 2022. "GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network," Mathematics, MDPI, vol. 10(11), pages 1-28, June.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1899-:d:829988
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    References listed on IDEAS

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