S-Type Random <i>k</i> Satisfiability Logic in Discrete Hopfield Neural Network Using Probability Distribution: Performance Optimization and Analysis

Abstract

Recently, a variety of non-systematic satisfiability studies on Discrete Hopfield Neural Networks have been introduced to overcome a lack of interpretation. Although a flexible structure was established to assist in the generation of a wide range of spatial solutions that converge on global minima, the fundamental problem is that the existing logic completely ignores the probability dataset’s distribution and features, as well as the literal status distribution. Thus, this study considers a new type of non-systematic logic termed S-type Random k Satisfiability, which employs a creative layer of a Discrete Hopfield Neural Network, and which plays a significant role in the identification of the prevailing attribute likelihood of a binomial distribution dataset. The goal of the probability logic phase is to establish the logical structure and assign negative literals based on two given statistical parameters. The performance of the proposed logic structure was investigated using the comparison of a proposed metric to current state-of-the-art logical rules; consequently, was found that the models have a high value in two parameters that efficiently introduce a logical structure in the probability logic phase. Additionally, by implementing a Discrete Hopfield Neural Network, it has been observed that the cost function experiences a reduction. A new form of synaptic weight assessment via statistical methods was applied to investigate the effect of the two proposed parameters in the logic structure. Overall, the investigation demonstrated that controlling the two proposed parameters has a good effect on synaptic weight management and the generation of global minima solutions.

Keywords

• discrete hopfield neural network
• non-systematic satisfiability
• probability distribution
• binomial distribution
• statistical learning
• optimization problems