One of the influential models in the artificial neural network (ANN) research field for addressing the issue of knowledge in the non-systematic logical rule is Random k Satisfiability. In this context, knowledge structure representation is also the potential application of Random k Satisfiability. Despite many attempts to represent logical rules in a non-systematic structure, previous studies have failed to consider higher-order logical rules. As the amount of information in the logical rule increases, the proposed network is unable to proceed to the retrieval phase, where the behavior of the Random Satisfiability can be observed. This study approaches these issues by proposing higher-order Random k Satisfiability for k ≤ 3 in the Hopfield Neural Network (HNN). In this regard, introducing the 3 Satisfiability logical rule to the existing network increases the synaptic weight dimensions in Lyapunov’s energy function and local field. In this study, we proposed an Election Algorithm (EA) to optimize the learning phase of HNN to compensate for the high computational complexity during the learning phase. This research extensively evaluates the proposed model using various performance metrics. The main findings of this research indicated the compatibility and performance of Random 3 Satisfiability logical representation during the learning and retrieval phase via EA with HNN in terms of error evaluations, energy analysis, similarity indices, and variability measures. The results also emphasized that the proposed Random 3 Satisfiability representation incorporates with EA in HNN is capable to optimize the learning and retrieval phase as compared to the conventional model, which deployed Exhaustive Search (ES).

中文翻译：

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具有随机 3 可满足性的选举算法的新型 Hopfield 神经网络模型

在人工神经网络 (ANN) 研究领域中，用于解决非系统逻辑规则中的知识问题的有影响的模型之一是随机k 可满足性。在这种情况下，知识结构表示也是随机k 可满足性的潜在应用。尽管许多尝试在非系统结构中表示逻辑规则，但先前的研究未能考虑高阶逻辑规则。随着逻辑规则中信息量的增加，所提出的网络无法进入检索阶段，在该阶段可以观察到随机可满足性的行为。本研究通过提出高阶随机接近这些问题ķ为可满足ķ在 Hopfield 神经网络 (HNN) 中≤ 3。对此，在现有网络中引入 3 Satisfiability 逻辑规则，增加了李雅普诺夫能量函数和局部场中的突触权重维度。在这项研究中，我们提出了一种选举算法（EA）来优化 HNN 的学习阶段，以补偿学习阶段的高计算复杂度。这项研究使用各种性能指标广泛评估了所提出的模型。本研究的主要发现表明，随机 3 可满足性逻辑表示在学习和检索阶段通过 EA 与 HNN 在错误评估、能量分析、相似性指数和可变性度量方面的兼容性和性能。