Special major 1, 3 satisfiability logic in discrete Hopfield neural networks

Currently, the discrete Hopfield neural network deals with challenges related to searching space and limited memory capacity. To address this issue, we propose integrating logical rules into the neural network to regulate neuron connections. This approach requires adopting a specific logic framework that ensures the network consistently reaches the lowest global energy state. In this context, a novel logic called major 1,3 satisfiability was introduced. This logic places a higher emphasis on third-order clauses compared to first-order clauses. The proposed logic is trained by the exhaustive search algorithm, aiming to minimize the cost function toward zero. To evaluate the proposed model effectiveness, we compare the model's learning and retrieval errors with those of the existing non-systematic logical structure, which primarily relies on first-order clauses. The similarity index measures the similarity benchmark neuron state with the existing and proposed model through extensive simulation studies. Certainly, the major random 1,3 satisfiability model exhibited a more extensive solution space when the ratio of third-order clauses exceeds 0.7% compared to first-order clauses. As we compared the experimental results with other state-of-the-art models, it became evident that the proposed model achieved significant results in capturing the overall neuron state. These findings emphasize the notable enhancements in the performance and capabilities of the discrete Hopfield neural network.