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J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network

The Discrete Hopfield Neural Network has been widely used for solving combinatorial optimization problems. DHNN is a simple structure with no hidden layer and binary input/output which leads to lower complexity compared to other networks. Satisfiability as a neuron representation is considered a sui...

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Main Authors: Jiang, Xiaofeng, Kasihmuddin, Mohd Shareduwan Mohd, Guo, Yueling, Gao, Yuan, Mansor, Mohd. Asyraf, Zamri, Nur Ezlin, Marsani, Muhammad Fadhil
Format: Article
Published: Springer Science and Business Media LLC 2024
Online Access:http://psasir.upm.edu.my/id/eprint/115114/
https://link.springer.com/article/10.1007/s12065-024-00936-5?error=cookies_not_supported&code=87996f48-6e9f-425d-b60d-1244b11a8acc
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spelling my.upm.eprints.1151142025-02-20T07:12:45Z http://psasir.upm.edu.my/id/eprint/115114/ J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network Jiang, Xiaofeng Kasihmuddin, Mohd Shareduwan Mohd Guo, Yueling Gao, Yuan Mansor, Mohd. Asyraf Zamri, Nur Ezlin Marsani, Muhammad Fadhil The Discrete Hopfield Neural Network has been widely used for solving combinatorial optimization problems. DHNN is a simple structure with no hidden layer and binary input/output which leads to lower complexity compared to other networks. Satisfiability as a neuron representation is considered a suitable logical structure due to its simple construction. DHNN model has the potential for enhancement by incorporating various logical rules. The main problem of existing work is the need for higher-order logical rules combined with systematic, non-systematic logic. This paper proposed a novel satisfiability logical structure named J-Type Random 2,3 Satisfiability by considering both the characteristics of the second and third-order variable per clause. The proposed logical rule randomly assigns values based on the structure of either second-order, third-order, or both orders of the clause. The proposed J Random 2,3 Satisfiability logical rule will store the information externally and only be true if all the clauses are satisfiable. This logic will be implemented into the Discrete Hopfield Neural Network. By utilizing the proposed hybrid logical rule, specifically the J Random 2,3 Satisfiability, the neuron in the Hopfield Neural Network can be effectively modeled. The model will be evaluated using various performance metrics in terms of learning error, retrieval error, energy analysis, and similarity analysis. The proposed logic will undergo a comparison analysis with previously established logical rules. Based on the ratio of global solutions, the proposed model exhibited a slower decline from 1 to 0 as the number of neurons increased which suggests that the proposed model will outperform existing models in retrieving global neuron state. Springer Science and Business Media LLC 2024 Article PeerReviewed Jiang, Xiaofeng and Kasihmuddin, Mohd Shareduwan Mohd and Guo, Yueling and Gao, Yuan and Mansor, Mohd. Asyraf and Zamri, Nur Ezlin and Marsani, Muhammad Fadhil (2024) J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network. Evolutionary Intelligence, 17 (5-6). pp. 3317-3336. ISSN 1864-5909; eISSN: 1864-5917 https://link.springer.com/article/10.1007/s12065-024-00936-5?error=cookies_not_supported&code=87996f48-6e9f-425d-b60d-1244b11a8acc 10.1007/s12065-024-00936-5
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description The Discrete Hopfield Neural Network has been widely used for solving combinatorial optimization problems. DHNN is a simple structure with no hidden layer and binary input/output which leads to lower complexity compared to other networks. Satisfiability as a neuron representation is considered a suitable logical structure due to its simple construction. DHNN model has the potential for enhancement by incorporating various logical rules. The main problem of existing work is the need for higher-order logical rules combined with systematic, non-systematic logic. This paper proposed a novel satisfiability logical structure named J-Type Random 2,3 Satisfiability by considering both the characteristics of the second and third-order variable per clause. The proposed logical rule randomly assigns values based on the structure of either second-order, third-order, or both orders of the clause. The proposed J Random 2,3 Satisfiability logical rule will store the information externally and only be true if all the clauses are satisfiable. This logic will be implemented into the Discrete Hopfield Neural Network. By utilizing the proposed hybrid logical rule, specifically the J Random 2,3 Satisfiability, the neuron in the Hopfield Neural Network can be effectively modeled. The model will be evaluated using various performance metrics in terms of learning error, retrieval error, energy analysis, and similarity analysis. The proposed logic will undergo a comparison analysis with previously established logical rules. Based on the ratio of global solutions, the proposed model exhibited a slower decline from 1 to 0 as the number of neurons increased which suggests that the proposed model will outperform existing models in retrieving global neuron state.
format Article
author Jiang, Xiaofeng
Kasihmuddin, Mohd Shareduwan Mohd
Guo, Yueling
Gao, Yuan
Mansor, Mohd. Asyraf
Zamri, Nur Ezlin
Marsani, Muhammad Fadhil
spellingShingle Jiang, Xiaofeng
Kasihmuddin, Mohd Shareduwan Mohd
Guo, Yueling
Gao, Yuan
Mansor, Mohd. Asyraf
Zamri, Nur Ezlin
Marsani, Muhammad Fadhil
J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
author_facet Jiang, Xiaofeng
Kasihmuddin, Mohd Shareduwan Mohd
Guo, Yueling
Gao, Yuan
Mansor, Mohd. Asyraf
Zamri, Nur Ezlin
Marsani, Muhammad Fadhil
author_sort Jiang, Xiaofeng
title J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
title_short J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
title_full J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
title_fullStr J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
title_full_unstemmed J-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
title_sort j-type random 2, 3 satisfiability a higher-order logical rule in discrete hopfield neural network
publisher Springer Science and Business Media LLC
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/115114/
https://link.springer.com/article/10.1007/s12065-024-00936-5?error=cookies_not_supported&code=87996f48-6e9f-425d-b60d-1244b11a8acc
_version_ 1825162435365961728
score 13.244413

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