Special major 1, 3 satisfiability logic in discrete Hopfield neural networks
Currently, the discrete Hopfield neural network deals with challenges related to searching space and limited memory capacity. To address this issue, we propose integrating logical rules into the neural network to regulate neuron connections. This approach requires adopting a specific logic framework...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024591?viewType=HTML |
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| author | Gaeithry Manoharam Azleena Mohd Kassim Suad Abdeen Mohd Shareduwan Mohd Kasihmuddin Nur 'Afifah Rusdi Nurul Atiqah Romli Nur Ezlin Zamri Mohd. Asyraf Mansor |
| author_facet | Gaeithry Manoharam Azleena Mohd Kassim Suad Abdeen Mohd Shareduwan Mohd Kasihmuddin Nur 'Afifah Rusdi Nurul Atiqah Romli Nur Ezlin Zamri Mohd. Asyraf Mansor |
| author_sort | Gaeithry Manoharam |
| collection | DOAJ |
| description | Currently, the discrete Hopfield neural network deals with challenges related to searching space and limited memory capacity. To address this issue, we propose integrating logical rules into the neural network to regulate neuron connections. This approach requires adopting a specific logic framework that ensures the network consistently reaches the lowest global energy state. In this context, a novel logic called major 1,3 satisfiability was introduced. This logic places a higher emphasis on third-order clauses compared to first-order clauses. The proposed logic is trained by the exhaustive search algorithm, aiming to minimize the cost function toward zero. To evaluate the proposed model effectiveness, we compare the model's learning and retrieval errors with those of the existing non-systematic logical structure, which primarily relies on first-order clauses. The similarity index measures the similarity benchmark neuron state with the existing and proposed model through extensive simulation studies. Certainly, the major random 1,3 satisfiability model exhibited a more extensive solution space when the ratio of third-order clauses exceeds 0.7% compared to first-order clauses. As we compared the experimental results with other state-of-the-art models, it became evident that the proposed model achieved significant results in capturing the overall neuron state. These findings emphasize the notable enhancements in the performance and capabilities of the discrete Hopfield neural network. |
| first_indexed | 2024-04-24T11:41:13Z |
| format | Article |
| id | doaj.art-05c48455aa084713811f3a30d4fa5ed5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T11:41:13Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-05c48455aa084713811f3a30d4fa5ed52024-04-10T01:24:06ZengAIMS PressAIMS Mathematics2473-69882024-03-0195120901212710.3934/math.2024591Special major 1, 3 satisfiability logic in discrete Hopfield neural networksGaeithry Manoharam0Azleena Mohd Kassim 1Suad Abdeen2Mohd Shareduwan Mohd Kasihmuddin3Nur 'Afifah Rusdi 4Nurul Atiqah Romli5Nur Ezlin Zamri 6Mohd. Asyraf Mansor71. School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia2. School of Computer Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia3. Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Malaysia1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia4. School of Distance Education, Universiti Sains Malaysia, Penang 11800, Malaysia4. School of Distance Education, Universiti Sains Malaysia, Penang 11800, MalaysiaCurrently, the discrete Hopfield neural network deals with challenges related to searching space and limited memory capacity. To address this issue, we propose integrating logical rules into the neural network to regulate neuron connections. This approach requires adopting a specific logic framework that ensures the network consistently reaches the lowest global energy state. In this context, a novel logic called major 1,3 satisfiability was introduced. This logic places a higher emphasis on third-order clauses compared to first-order clauses. The proposed logic is trained by the exhaustive search algorithm, aiming to minimize the cost function toward zero. To evaluate the proposed model effectiveness, we compare the model's learning and retrieval errors with those of the existing non-systematic logical structure, which primarily relies on first-order clauses. The similarity index measures the similarity benchmark neuron state with the existing and proposed model through extensive simulation studies. Certainly, the major random 1,3 satisfiability model exhibited a more extensive solution space when the ratio of third-order clauses exceeds 0.7% compared to first-order clauses. As we compared the experimental results with other state-of-the-art models, it became evident that the proposed model achieved significant results in capturing the overall neuron state. These findings emphasize the notable enhancements in the performance and capabilities of the discrete Hopfield neural network.https://www.aimspress.com/article/doi/10.3934/math.2024591?viewType=HTMLdiscrete hopfield neural networkmajor random 13 satisfiabilityexhaustive searchthird-orderfirst-orderbenchmark neuron state |
| spellingShingle | Gaeithry Manoharam Azleena Mohd Kassim Suad Abdeen Mohd Shareduwan Mohd Kasihmuddin Nur 'Afifah Rusdi Nurul Atiqah Romli Nur Ezlin Zamri Mohd. Asyraf Mansor Special major 1, 3 satisfiability logic in discrete Hopfield neural networks AIMS Mathematics discrete hopfield neural network major random 1 3 satisfiability exhaustive search third-order first-order benchmark neuron state |
| title | Special major 1, 3 satisfiability logic in discrete Hopfield neural networks |
| title_full | Special major 1, 3 satisfiability logic in discrete Hopfield neural networks |
| title_fullStr | Special major 1, 3 satisfiability logic in discrete Hopfield neural networks |
| title_full_unstemmed | Special major 1, 3 satisfiability logic in discrete Hopfield neural networks |
| title_short | Special major 1, 3 satisfiability logic in discrete Hopfield neural networks |
| title_sort | special major 1 3 satisfiability logic in discrete hopfield neural networks |
| topic | discrete hopfield neural network major random 1 3 satisfiability exhaustive search third-order first-order benchmark neuron state |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024591?viewType=HTML |
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