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  4. Weighted random 3-satisfiability in discrete Hopfield neural network

Weighted random 3-satisfiability in discrete Hopfield neural network

MMC.
2025;
Volume 12, Number 2
: pp. 468–480
https://doi.org/10.23939/mmc2025.02.468
Received: December 18, 2024
Revised: May 13, 2025
Accepted: May 19, 2025

Liu X., Chang Y., Jiang X.  Weighted random 3-satisfiability in discrete Hopfield neural network.  Mathematical Modeling and Computing. Vol. 12, No. 2, pp. 468–480 (2025) 

Authors:
  1. X. Liu
  2. Y. Chang
  3. X. Jiang
1
School of General Education, Guangzhou College of Technology and Business; School of Mathematical Sciences, Universiti Sains Malaysia
2
School of Mathematical Sciences, Universiti Sains Malaysia; School of Computer Science and Engineering, Hunan Institute of Technology
3
School of Mathematical Sciences, Universiti Sains Malaysia

Satisfiability (SAT) is remarkable in the field of computational mathematics because it can be utilized to represent the information of any categories of any datasets.  Recent research about this paradigm has tended to model Discrete Hopfield Neural Network (DHNN) via SAT.  Despite the widespread implementations of SAT in DHNN, there are limitations to the control of the distribution of negative and positive literals in the logical rule and this aspect has been rarely discussed.  In this paper, a novel logic rule named weighted 3 satisfiability is proposed by implementing ratio to the negative literals in the satisfiability clauses.  The proposed weighted 3 satisfiability was implemented into DHNN where the cost function was derived by minimizing the inconsistency of the logic.  The effectiveness of the novel weighted 3 satisfiability was analyzed by various metrics which was settled before.  Errors in each phase reduced when the ratio is higher than $0.2$.  When the ratio within a low value $r=0.1$, the similarity index shows a high level nearly with RAN3SAT.  Based on the results of the metrics, the proposed logic has outperformed most of the existing logic models and it also has a more positive impact ability to gain the global minimum solutions with special ratio of negative literals.

weighted
satisfiability
discrete Hopfield neural network
systematic error
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