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

被引:18
作者
Gao, Yuan [1 ,2 ]
Guo, Yueling [1 ,3 ]
Romli, Nurul Atiqah [1 ]
Kasihmuddin, Mohd Shareduwan Mohd [1 ]
Chen, Weixiang [2 ]
Mansor, Mohd Asyraf [4 ]
Chen, Ju [1 ,2 ]
机构
[1] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia
[2] Chengdu Univ Tradit Chinese Med, Sch Med Informat Engn, Chengdu 610000, Peoples R China
[3] Hunan Inst Technol, Sch Sci, Hengyang 421002, Peoples R China
[4] Univ Sains Malaysia, Sch Distance Educ, George Town 11800, Malaysia
关键词
G-Type Random k Satisfiability; artificial neural network; Hopfield Neural Network; flexibility; random dynamics;
D O I
10.3390/math10111899
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页数:28
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