Dynamics of Structured Complex-Valued Hopfield Neural Networks
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916743555842048 |
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| author | Garimella, Rama Murthy Valle, Marcos Eduardo Vieira, Guilherme Rayala, Anil Munugoti, Dileep |
| author_facet | Garimella, Rama Murthy Valle, Marcos Eduardo Vieira, Guilherme Rayala, Anil Munugoti, Dileep |
| contents | In this paper, we explore the dynamics of structured complex-valued Hopfield neural networks (CvHNNs), which arise when the synaptic weight matrix possesses specific structural properties. We begin by analyzing CvHNNs with a Hermitian synaptic weight matrix and establish the existence of four-cycle dynamics in CvHNNs with skew-Hermitian weight matrices operating synchronously. Furthermore, we introduce two new classes of complex-valued matrices: braided Hermitian and braided skew-Hermitian matrices. We demonstrate that CvHNNs utilizing these matrix types exhibit cycles of length eight when operating in full parallel update mode. Finally, we conduct extensive computational experiments on synchronous CvHNNs, exploring other synaptic weight matrix structures. The findings provide a comprehensive overview of the dynamics of structured CvHNNs, offering insights that may contribute to developing improved associative memory models when integrated with suitable learning rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of Structured Complex-Valued Hopfield Neural Networks Garimella, Rama Murthy Valle, Marcos Eduardo Vieira, Guilherme Rayala, Anil Munugoti, Dileep Neural and Evolutionary Computing Artificial Intelligence In this paper, we explore the dynamics of structured complex-valued Hopfield neural networks (CvHNNs), which arise when the synaptic weight matrix possesses specific structural properties. We begin by analyzing CvHNNs with a Hermitian synaptic weight matrix and establish the existence of four-cycle dynamics in CvHNNs with skew-Hermitian weight matrices operating synchronously. Furthermore, we introduce two new classes of complex-valued matrices: braided Hermitian and braided skew-Hermitian matrices. We demonstrate that CvHNNs utilizing these matrix types exhibit cycles of length eight when operating in full parallel update mode. Finally, we conduct extensive computational experiments on synchronous CvHNNs, exploring other synaptic weight matrix structures. The findings provide a comprehensive overview of the dynamics of structured CvHNNs, offering insights that may contribute to developing improved associative memory models when integrated with suitable learning rules. |
| title | Dynamics of Structured Complex-Valued Hopfield Neural Networks |
| topic | Neural and Evolutionary Computing Artificial Intelligence |
| url | https://arxiv.org/abs/2503.19885 |