GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network

Abstract

One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity.

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation燨perator

“…By adapting various forms of 2SAT logical structure during the learning phase of HNN, P2SATRA outperfomed the 2SATRA, E2SATRA and RA approaches when being measured with the performance metrics such as the accuracy, precision, sensitivity, F-Score and MCC after the logic mining analysis with 11 different real datasets. For instance, it will be interesting to infuse different logical rule such as Maximum Satisfiability [20], Y-Type Random Satisfiability [8], G-Type Random Satisfiability [9] and Random k Satisfiability [5]. In terms of network architecture, it will be interesting if other learning mechanism such as in [21,22] were embeded into logic mining.…”

“…This shows that the interpretation of the 2SAT logical rule in DHNN can be further optimized using optimization algorithm. The implementation of 2SAT in various network inspires the emergence of other useful logic such as [5][6][7][8][9] in doing DHNN. Various type of logical rule creates optimal modelling of DHNN that has wide range of behavior.…”

Random Maximum 2 Satisfiability Logic in Discrete Hopfield Neural Network Incorporating Improved Election Algorithm

“…The chromosomes represent the possible solutions of the optimization problem. Next, to evaluate the quality of each chromosome, the fitness function of these chromosomes will be calculated based on Equation (21).…”

“…The proposed logic shows an interesting behavior because YRAN2SAT can be reduced to both 2SAT and RAN2SAT. On the other hand, Gao et al [21] extended the order of the clause in the logic by adding third order clause. Although the final energy for [20,21] tends to converge to local minimum energy (due to high number of neuron), both logics offer a wide range of flexibility to represent symbolic rule in HNN.…”

“…On the other hand, Gao et al [21] extended the order of the clause in the logic by adding third order clause. Although the final energy for [20,21] tends to converge to local minimum energy (due to high number of neuron), both logics offer a wide range of flexibility to represent symbolic rule in HNN. Despite rapid development in the field of logic in HNN, none of the mentioned studies consider the existence of a redundant variable in the logical rule.…”