Weighted Random 2 Satisfiability Logic Training in Discrete Hopfield Neural Network via Election Algorithm
Nur Ezlin Zamri, Siti Syatirah Muhammad Sidik, Mohd Shareduwan Mohd Kasihmuddin, Mohd. Asyraf Mansor, Nurul Atiqah Romli · 2025
The advent of intelligent systems has revolutionized various fields, ranging from healthcare to finance. These systems usually leverage the mechanism of artificial intelligence (AI) approaches to enhance decision-making and extract insightful patterns from data. Among all known AI methods, neuro-symbolic models have emerged as a promising paradigm that implements the advantages of artificial neural networks (ANNs) and symbolic reasoning. This hybrid approach aims to counter the lack of transparency of most ANNs by introducing a formal language to govern the neurons. Due to the intricacy of this hybrid model, researchers usually implement robust learning capabilities in neuro-symbolic models to assure optimal optimization and interpretability qualities. However, the implementation of neuro-symbolic models in intelligent systems is fraught with several challenges and opportunities. This work explores this aspect by highlighting recent advancements of logical rule and training algorithms in an ANN model. Additionally, the development of each structure in the proposed neuro-symbolic model is discussed to expose potential avenues for future research and application. The discrete Hopfield neural network (DHNN) was initially introduced by Hopfield ( Hopfield, 1985 ) in solving the Travelling Salesman Problem (TSP). DHNN possessed single-layered neurons which were connected by the trained synaptic weight. Using the obtained synaptic weight, DHNN can retrieve correct final neuron states which also map to the convergence property of the network. However, the standard DHNN has a storage capacity problem when the number of neurons increases due to the large amounts of information which need to be stored. In this context, the retrieval capability of the DHNN is reduced to less than 50% which leads to a suboptimal solution (Folli et al., 2017 ). To solve this problem, Abdullah (1992) proposed logic to represent the neuron connection in DHNN.