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

Yuan Gao, Yueling Guo, Nurul Atiqah Romli, Mohd Shareduwan Mohd Kasihmuddin, Weixiang Chen, Mohd. Asyraf Mansor and Ju Chen
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Yuan Gao: School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
Yueling Guo: School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
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

Mathematics, 2022, vol. 10, issue 11, 1-28

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.

Keywords: G-Type Random k Satisfiability; artificial neural network; Hopfield Neural Network; flexibility; random dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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