<![CDATA[A deeper understanding of the learning and retrieval phase of the Discrete Hopfield Neural Network (DHNN) is essential for advancing its application in intelligent systems. This study investigates the performance of a non-systematic logical rule, namely Conditional Random 2 Satisfiability logic (CRAN2SAT) in DHNN (DHNN-CRAN2SAT) in retrieving diverse and optimal final neuron states. The findings show that the Election Algorithm consistently retrieves the maximum global minimum solution value of 1 across all tested neuron sizes, outperforms Exhaustive Search. In addition, the implementation of a new updating rule during the retrieval phase significantly enhances the diversity of final neuron states. This improvement is reflected by lower Sokal–Sneath similarity indices with an average value of 0.3809 and increased neuron state variation with an average value of 8809. These results highlight the significance of both the learning algorithm and updating strategy in the retrieval phase of DHNN. By enabling a broader range of final neuron states, this approach offers meaningful improvements for logic mining models, particularly in addressing real-world classification challenges.]]>
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