Garimella Rama Murthy, Valle Marcos Eduardo, Vieira Guilherme, Rayala Anil, Munugoti Dileep
Ecole Centrale School of Engineering, Mahindra University, Hyderabad, India.
Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil.
Cogn Neurodyn. 2025 Dec;19(1):74. doi: 10.1007/s11571-025-10257-7. Epub 2025 May 19.
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.
在本文中，我们探讨了结构化复值霍普菲尔德神经网络（CvHNNs）的动力学特性，当突触权重矩阵具有特定结构特性时就会出现这种网络。我们首先分析具有埃尔米特突触权重矩阵的CvHNNs，并确定在同步运行的具有斜埃尔米特权重矩阵的CvHNNs中存在四周期动力学。此外，我们引入了两类新的复值矩阵：辫状埃尔米特矩阵和辫状斜埃尔米特矩阵。我们证明，在全并行更新模式下运行时，使用这些矩阵类型的CvHNNs会表现出长度为八的周期。最后，我们对同步CvHNNs进行了广泛的计算实验，探索其他突触权重矩阵结构。这些发现全面概述了结构化CvHNNs的动力学特性，当与合适的学习规则相结合时，可能为开发改进的联想记忆模型提供见解。
