Discrete Hopfield Neural Network Research Articles

НЕЙРОМЕРЕЖЕВІ МАТЕМАТИЧНІ МОДЕЛІ ЛЮДИНОМАШИННОГО СПІЛКУВАННЯ ТА РОЗПІЗНАВАННЯ

The study is devoted to the neural network interpretation of the task of human-machine communication and recognition by multiple criteria, considered as a task of assignment. The main goal is to reduce this problem to a standard form, where the number of criteria groups is equal to the number of ranked documents. The study defined the architecture of a neural network and proposed the use of a network of binary neurons, which is a matrix of a certain dimension. The proposed ranking model is based on a neural network that contains arbitrary feedback. This allows the excitation to be transmitted back to the neuron, which contributes to the repeated performance of its function. However, in dynamic neural networks instability occurs, which is manifested in a random change in the states of neurons without reaching stationary states. The question of stability of the dynamics of such systems remains open. The considered discrete Hopfield neural network has the following characteristics: one layer of elements, each element is connected to all others, but not to itself; only one element is updated per stage; elements are updated in random order, but each is updated with the same frequency; the output function is binary (value "0" or "1"). A Hopfield neural network is recurrent: the output of the network is reused as input until a steady state is reached. After starting, the neural network changes its state, gradually moving to a stable mode, which allows identifying a plan for evaluating the process of human-machine communication according to a set of criteria. Random search procedures are used to refine the results. The proposed energy function is minimized to ensure that the constraints are met and the problem is solved. The constructed function reaches a minimum only in the states corresponding to the assignment plans. The definition of the network parameters is carried out by comparing the obtained functions with the energy function in general form. The practical implementation of the model demonstrated that Hopfield's neural network can be successfully applied to document ranking in human-machine communication and recognition systems, providing high accuracy and efficiency in solving ranking problems.

Study on the construction and application of a community emergency capacity evaluation model based on a combined weighting-discrete Hopfield neural network

To accurately evaluate community emergency capability and solve the problems with the existing index system, which has been declared unreasonable with respect to components, unclear in meaning and unreliable in terms of empowerment results caused by a single algorithm, a triangle model of community safety and resilience is introduced to construct an emergency capability index system suitable for communities with frequent geological disasters in Yunnan Province. Additionally, a combined empowerment model is constructed to improve the accuracy of the empowerment results. First, according to the relevant information and the results of expert consultations and field investigations, the index system is determined. Second, three weighting methods, the G1-entropy weight, G1-CRITIC and G1-coefficient of variation, are used to calculate the index weight and perform a comparative analysis, after which the best weighting method is selected and combined with the discrete Hopfield neural network model to construct a weighting-evaluation model. Finally, the model is applied to evaluate the emergency capability of a community with frequent geological disasters in Yunnan Province. The results show that the index of monitoring and early warning ability of geological disasters is added, which makes the index more targeted, and thus, the result obtained using the G1-CRITIC combination weighting model is more accurate. The evaluation model constructed in this paper accurately evaluates community emergency capacity and is further popularized and applied in communities with frequent geological disasters in Yunnan Province.

Binary ant colony optimization algorithm in learning random satisfiability logic for discrete hopfield neural network

This study introduced a novel ant colony optimization algorithm that implements the population selection strategy of the Estimation of Distribution Algorithm and a new pheromone updating formula. It aimed to optimize the performance of G-type random high-order satisfiability logic structures embedded in Discrete Hopfield Neural Networks, thereby enhancing the efficiency of the Hopfield Neural Network learning algorithm. Through comparative analysis with other metaheuristic algorithms, our model demonstrated superior performance in terms of global convergence, time complexity, and algorithm complexity. Additionally, we evaluated the learning phase, retrieval phase, and similarity analysis using various ratios of literals and clauses. It was shown that our proposed model exhibits stronger search ability compared to other metaheuristic algorithms and Exhaustive Search. Our model enhanced the efficiency of the learning phase, resulting in the number of global solutions accounting for 100 %, and significantly improved the global solution diversity. These advancements contributed to the efficiency of the model in convergence, rendering it applicable to a wide range of nonlinear classification and prediction problems.

Dual optimization approach in discrete Hopfield neural network

Having effective learning and retrieval phases of satisfiability logic in Discrete Hopfield Neural Network models ensures optimal synaptic weight management, which consequently leads to the production of optimal final neuron states. However, the problem with this model is that different initial states can affect the biasedness of the retrieval phase since the model memorizes final states without generating new ones and produces suboptimal final neuron states. To date, there is no recent research that solves this issue by improving both phases in the Discrete Hopfield Neural Network that involves first-order satisfiability logic. Therefore, this research contributes to the improvement of the learning and retrieval phases by integrating the Hybrid Differential Evolution Algorithm and Swarm Mutation respectively. This research utilizes Y-Type Random 2 Satisfiability, which combines first and second-order clauses to expand the storage capacity of DHNN models, facilitating the retrieval of optimal final neuron states. To evaluate the effectiveness of the Hybrid Differential Evolution Algorithm and Swarm Mutation in the learning and retrieval phases, several performance metrics are employed in terms of synaptic weight management, learning errors, testing errors, energy profiles, solution variations, and similarity for 10 different cases. Quantitative evaluations show that the proposed model successfully enhances the optimization of both phases, ranking first compared to 10 recent algorithms for all metrics. In terms of convergence analysis, the proposed model progressed fast towards the optimal solution with only one iteration for all cases. Additionally, the proposed model can generate a 100 % global minima ratio when dealing with a high number of neurons for Case 5.

Industrial technology network security measurement in international trade under discrete hopfield neural network

As global economic integration continues to advance, international trade has become increasingly vital for the economic development and growth of nations. This research aims to assess the trends in industrial technology security within China’s international trade and provide practical guidance for policy-making, corporate strategies, and international cooperation. The significance of the rising trend in security within China’s international trade industry lies in its establishment of a robust foundation for the long-term development of China’s international trade, contributing to its cooperation and competitiveness with other countries. In addressing the limitations of traditional measurement methods and providing a more comprehensive and accurate assessment of industrial technology security, this research presents an approach based on a discrete Hopfield Neural Network (HNN) for evaluating industrial technology security in international trade. This method integrates multiple indicators, including technology gap rates, to construct the Superior Quality Engineering (SQE) comprehensive evaluation model. The research employs a combination model of “entropy-grey relational-Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)-discrete HNN” to assess industrial technology security. This research evaluates international trade industry technology security using patent data from 2015 to 2022 as samples. The results indicate an overall upward trend in security in China’s international trade industry. Within this trend, the research observes a stepwise increase in scale components, leading to continuous improvement in security. In terms of quality components, although security develops relatively slowly overall, it exhibits a trend of initial gradual decline followed by rapid growth. Regarding efficiency components, there is overall slow growth with periodic fluctuations. This research outcome provides substantial support for the research of industrial technology in international trade. The proposed method can assist businesses in evaluating their technological security in international trade and offer robust support for international trade decision-making.

J-type random 2,3 satisfiability: a higher-order logical rule in discrete hopfield neural network

J-type random 2,3 satisfiability: a higher-order logical rule in discrete hopfield neural network

A novel associative memory model based on semi-tensor product (STP).

A good intelligent learning model is the key to complete recognition of scene information and accurate recognition of specific targets in intelligent unmanned system. This study proposes a new associative memory model based on the semi-tensor product (STP) of matrices, to address the problems of information storage capacity and association. First, some preliminaries are introduced to facilitate modeling, and the problem of information storage capacity in the application of discrete Hopfield neural network (DHNN) to associative memory is pointed out. Second, learning modes are equivalently converted into their algebraic forms by using STP. A memory matrix is constructed to accurately remember these learning modes. Furthermore, an algorithm for updating the memory matrix is developed to improve the association ability of the model. And another algorithm is provided to show how our model learns and associates. Finally, some examples are given to demonstrate the effectiveness and advantages of our results. Compared with mainstream DHNNs, our model can remember learning modes more accurately with fewer nodes.

A novel processor for dynamic evolution of constrained SAT problems: The dynamic evolution variant of the discrete Hopfield neural network satisfiability model

The Boolean satisfiability problem, a renowned NP-complete challenge in computer science, has recently garnered interest in the Discrete Hopfield Neural Network - Satisfiability model. This model adeptly integrates logical rules into Hopfield networks, excelling in locating global minima for traditional SAT problems. However, it faces efficiency challenges when dealing with SAT problems characterized by dynamic evolution constraints due to its static network architecture. During dynamic evolution iterations, there is a significant exponential increase in the computational costs due to redundant and repetitive computations.In order to address this challenge, this paper introduces a dynamic evolution variant of the Discrete Hopfield Neural Network - Satisfiability model. In extensive simulation experiments, we progressively augmented the number of constraint clauses from 1 to 1500, seeking global minima for CNF problems. The proposed model exhibited congruent performance with the traditional model, achieving a Global Minimum Ratio of 1 and a Hamming distance of 0. Crucially, the proposed model minimized CPU utilization and neared zero error metrics, while the traditional model experienced exponential CPU and error metric escalation. These outcomes affirm the proposed model's robust global search capabilities and high precision, aligning with the traditional model. Furthermore, owing to this model's incorporation of not only temporal constraint increment operator but also innovative real-time learning techniques and clever integration methods, along with the establishment of a novel real-time decision mechanism, the proposed model effectively addresses the issues of redundancy and repeated calculations inherent in traditional models. This results in a stable and significantly improved computational speed. Additionally, this model's dynamic evolution network architecture is specifically designed to accommodate arbitrary and efficient extensions of dynamic constraints, while also featuring a built-in preprocessing function to filter out duplicate variables. In the future, as a dynamic evolution processor, this model exhibits immense potential for solving large-scale SAT problems with dynamic evolution constraints and holds broad application prospects in emerging fields such as automated reasoning, intelligent recommendation systems, and machine learning.

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

<abstract> <p>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.</p> </abstract>

Conditional random <i>k</i> satisfiability modeling for <i>k</i> = 1, 2 (CRAN2SAT) with non-monotonic Smish activation function in discrete Hopfield neural network

<abstract> <p>The current development of logic satisfiability in discrete Hopfield neural networks (DHNN)has been segregated into systematic logic and non-systematic logic. Most of the research tends to improve non-systematic logical rules to various extents, such as introducing the ratio of a negative literal and a flexible hybrid logical structure that combines systematic and non-systematic structures. However, the existing non-systematic logical rule exhibited a drawback concerning the impact of negative literal within the logical structure. Therefore, this paper presented a novel class of non-systematic logic called conditional random <italic>k</italic> satisfiability for <italic>k</italic> = 1, 2 while intentionally disregarding both positive literals in second-order clauses. The proposed logic was embedded into the discrete Hopfield neural network with the ultimate goal of minimizing the cost function. Moreover, a novel non-monotonic Smish activation function has been introduced with the aim of enhancing the quality of the final neuronal state. The performance of the proposed logic with new activation function was compared with other state of the art logical rules in conjunction with five different types of activation functions. Based on the findings, the proposed logic has obtained a lower learning error, with the highest total neuron variation <italic>TV</italic> = 857 and lowest average of Jaccard index, <italic>JSI</italic> = 0.5802. On top of that, the Smish activation function highlights its capability in the DHNN based on the result ratio of improvement <italic>Zm</italic> and <italic>TV</italic>. The ratio of improvement for Smish is consistently the highest throughout all the types of activation function, showing that Smish outperforms other types of activation functions in terms of <italic>Zm</italic> and <italic>TV.</italic> This new development of logical rule with the non-monotonic Smish activation function presents an alternative strategy to the logic mining technique. This finding will be of particular interest especially to the research areas of artificial neural network, logic satisfiability in DHNN and activation function.</p> </abstract>

Unsupervised logic mining with a binary clonal selection algorithm in multi-unit discrete Hopfield neural networks via weighted systematic 2 satisfiability

<p>Evaluating behavioral patterns through logic mining within a given dataset has become a primary focus in current research. Unfortunately, there are several weaknesses in the research regarding the logic mining models, including an uncertainty of the attribute selected in the model, random distribution of negative literals in a logical structure, non-optimal computation of the best logic, and the generation of overfitting solutions. Motivated by these limitations, a novel logic mining model incorporating the mechanism to control the negative literal in the systematic Satisfiability, namely Weighted Systematic 2 Satisfiability in Discrete Hopfield Neural Network, is proposed as a logical structure to represent the behavior of the dataset. For the proposed logic mining models, we used ratio of <italic>r</italic> to control the distribution of the negative literals in the logical structures to prevent overfitting solutions and optimize synaptic weight values. A new computational approach of the best logic by considering both true and false classification values of the learning system was applied in this work to preserve the significant behavior of the dataset. Additionally, unsupervised learning techniques such as Topological Data Analysis were proposed to ensure the reliability of the selected attributes in the model. The comparative experiments of the logic mining models by utilizing 20 repository real-life datasets were conducted from repositories to assess their efficiency. Following the results, the proposed logic mining model dominated in all the metrics for the average rank. The average ranks for each metric were Accuracy (7.95), Sensitivity (7.55), Specificity (7.93), Negative Predictive Value (7.50), and Mathews Correlation Coefficient (7.85). Numerical results and in-depth analysis demonstrated that the proposed logic mining model consistently produced optimal induced logic that best represented the real-life dataset for all the performance metrics used in this study.</p>

Synergizing intelligence and knowledge discovery: Hybrid black hole algorithm for optimizing discrete Hopfield neural network with negative based systematic satisfiability

<p>The current systematic logical rules in the Discrete Hopfield Neural Network encounter significant challenges, including repetitive final neuron states that lead to the issue of overfitting. Furthermore, the systematic logical rules neglect the impact on the appearance of negative literals within the logical structure, and most recent efforts have primarily focused on improving the learning capabilities of the network, which could potentially limit its overall efficiency. To tackle the limitation, we introduced a Negative Based Higher Order Systematic Logic to the network, imposing restriction on the appearance of negative literals within the clauses. Additionally, a Hybrid Black Hole Algorithm was proposed in the retrieval phase to optimize the final neuron states. This ensured that the optimized states achieved maximum diversity and reach global minima solutions with the lowest similarity index, thereby enhancing the overall performance of the network. The results illustrated that the proposed model can achieve up to 10,000 diversified and global solutions with an average similarity index of 0.09. The findings indicated that the optimized final neuron states are in optimal configurations. Based on the findings, the development of the new systematic SAT and the implementation of the Hybrid Black Hole algorithm to optimize the retrieval capabilities of DHNN to achieve multi-objective functions result in updated final neuron states with high diversity, high attainment of global minima solutions, and produces states with a low similarity index. Consequently, this proposed model could be extended for logic mining applications to tackle classification tasks. The optimized final neuron states will enhance the retrieval of high-quality induced logic, which is effective for classification and knowledge extraction.</p>

Modeling of 3 SAT discrete Hopfield neural network optimization using genetic algorithm optimized K-modes clustering

<p>The discrete Hopfield neural network 3-satisfiability (DHNN-3SAT) model represents an innovative application of deep learning techniques to the Boolean SAT problem. Existing research indicated that the DHNN-3SAT model demonstrated significant advantages in handling 3SAT problem instances of varying scales and complexities. Compared to traditional heuristic algorithms, this model converged to local minima more rapidly and exhibited enhanced exploration capabilities within the global search space. However, the model faced several challenges and limitations. As constraints in SAT problems dynamically increased, decreased, or changed, and as problem scales expanded, the model's computational complexity and storage requirements may increase dramatically, leading to reduced performance in handling large-scale SAT problems. To address these challenges, this paper first introduced a method for designing network synaptic weights based on fundamental logical clauses. This method effectively utilized the synaptic weight information from the original SAT problem within the DHNN network, thereby significantly reducing redundant computations. Concrete examples illustrated the design process of network synaptic weights when constraints were added, removed, or updated, offering new approaches for managing the evolving constraints in SAT problems. Subsequently, the paper presented a DHNN-3SAT model optimized by genetic algorithms combined with K-modes clustering. This model employed genetic algorithm-optimized K-modes clustering to effectively cluster the initial space, significantly reducing the search space. This approach minimized the likelihood of redundant searches and reduced the risk of getting trapped in local minima, thus improving search efficiency. Experimental tests on benchmark datasets showed that the proposed model outperformed traditional DHNN-3SAT models, DHNN-3SAT models combined with genetic algorithms, and DHNN-3SAT models combined with imperialist competitive algorithms across four evaluation metrics. This study not only broadened the application of DHNN in solving 3SAT problems but also provided valuable insights and guidance for future research.</p>

A novel Hybrid Exhaustive Search and data preparation technique with multi-objective Discrete Hopfield Neural Network

The primary objective in building predictive analytics models is to achieve optimal accuracy with real datasets. The limitations of existing models lie in their storage capacity, which hinders the progress of generating high accuracy. When a model storage capacity is limited, it may struggle to process large datasets and encounter underfitting issues, preventing it from capturing the complexities of the data. Hence, this paper addresses these challenges by introducing a novel approach to predictive analytics, focusing on expanding the storage capacity of the Discrete Hopfield Neural Network (DHNN). First, this paper employs satisfiability logic to represent the attributes of a dataset in the DHNN. This logic representation enables the model to establish a connection between neurons and attributes, enabling efficient information processing. Second, to introduce a multi-objective DHNN, a key innovation that enhances the model’s storage capacity. In this context, a novel training algorithm named Hybrid Exhaustive Search is developed to optimize the DHNN’s training phase. Third, this paper introduces new data preparation techniques, including feature selection and a method for identifying the best-induced logic. This best-induced logic explains and extracts dataset relationships. Finally, the proposed model is evaluated based on four reputable metrics and a variety of datasets primarily collected from the UCI Repository. The performance of the proposed model is compared with three existing models. Through extensive experiments and rigorous evaluation, the proposed model can outperform existing models in all metrics demonstrating the effectiveness of expanded storage capacity and novel data preparation techniques employed.

A modified reverse-based analysis logic mining model with Weighted Random 2 Satisfiability logic in Discrete Hopfield Neural Network and multi-objective training of Modified Niched Genetic Algorithm

Over the years, the study on logic mining approach has increased exponentially. However, most logic mining models disregarded any efforts in expanding the search space which led to poor generalizability property of the retrieved induced logic. In light of this gap, this paper initiated the hybridization of logic mining approach with a multi-objective training algorithm namely Modified Niche Genetic Algorithm. The core impetus of this algorithm is to ensure optimal production of multiple superstrings via Wan Abdullah method resulting in multiple units associative memory feature of the Discrete Hopfield Neural Network. Therefore, the storage capacity of DHNN increases which directed towards larger search space of locating optimal induced logic. Additionally, several modifications were imposed to counter other issues such as, rigid logical rule, outdated quality of best logic, and high dependency on the supervised attributes selection method. Experimentation was done on 20 repository datasets from reputable machine learning repositories. Results showed that the proposed model outperformed all baseline methods in terms of accuracy = 0.8727, precision = 0.9845, specificity = 0.9988, and Matthew’s correlation coefficient = 0.5815.

A 4D discrete Hopfield neural network-based image encryption scheme with multiple diffusion modes

A novel 4D chaotic map is proposed in this paper using the model of a self-feedback Discrete Hopfield Neural Network (DHNN) with nonlinear synaptic ICMIC (4D-IDHNN). Based on an analysis of chaos characteristics, including attractors, Lyapunov exponents, Bifurcation, Sample Entropy and CO algorithms, the 4D-IDHNN system demonstrates reasonable stochasticity and ergodicity, alongside a broad spectrum of hyperchaotic parameters. Based on the 4D-IDHNN system, we design a new Pixel-dependent bit-plane Chaotic random Diffusion (PbCrD) algorithm with high diffusion capability and security. To begin, the 4D-IDHNN system generates pseudo-random sequences to confuse the plaintext image pixel positions with Chaotic Magic Random Scramble (CMRS). Subsequently, the PbCrD algorithm can be employed to diffuse pixel values. With the initial value of 4D-IDHNN generated using the SHA-256 hash of plaintext image, the ability to resist plaintext attacks can be enhanced. The algorithm includes 24 diffusion modes, which is three times greater than the number of DNA rules, thereby enhancing the complexity of decryption. The proposed encryption algorithm has good effectiveness, robustness, and resistance to differential attacks based on simulations and security analyses.

Chaos in a two dimensional fractional discrete Hopfield neural network and its control

A novel two-dimensional fractional discrete Hopfield neural network is presented in this study, which is based on discrete fractional calculus. This network incorporates both constant and variable orders, and its behavior is examined using phase plots, time evolution, bifurcation, Lyapunov exponents, and complexity analysis. Compared to integer and constant fractional orders, the numerical simulations demonstrate that the proposed variable-order fractional HNN exhibits more complex characteristics, and by selecting different fractional variable orders, novel attractors with chaotic behavior can be obtained. Additionally, a control scheme is proposed to stabilize the suggested neural network by utilizing the stability theorem for fractional discrete time systems. This control scheme is applied to both states in the study.

Log-Linear-Based Logic Mining with Multi-Discrete Hopfield Neural Network

Choosing the best attribute from a dataset is a crucial step in effective logic mining since it has the greatest impact on improving the performance of the induced logic. This can be achieved by removing any irrelevant attributes that could become a logical rule. Numerous strategies are available in the literature to address this issue. However, these approaches only consider low-order logical rules, which limit the logical connection in the clause. Even though some methods produce excellent performance metrics, incorporating optimal higher-order logical rules into logic mining is challenging due to the large number of attributes involved. Furthermore, suboptimal logical rules are trained on an ineffective discrete Hopfield neural network, which leads to suboptimal induced logic. In this paper, we propose higher-order logic mining incorporating a log-linear analysis during the pre-processing phase, the multi-unit 3-satisfiability-based reverse analysis with a log-linear approach. The proposed logic mining also integrates a multi-unit discrete Hopfield neural network to ensure that each 3-satisfiability logic is learned separately. In this context, our proposed logic mining employs three unique optimization layers to improve the final induced logic. Extensive experiments are conducted on 15 real-life datasets from various fields of study. The experimental results demonstrated that our proposed logic mining method outperforms state-of-the-art methods in terms of widely used performance metrics.

Multi-unit Discrete Hopfield Neural Network for higher order supervised learning through logic mining: Optimal performance design and attribute selection

In the perspective of logic mining, the attribute selection, and the objective function of the best logic is the two main factors that identifies the effectiveness of our proposed logic mining model. The non-significant attributes selected will cause the Discrete Hopfield Neural Network to learned and obtain wrong synaptic weight. Thus, this will result to suboptimal solution. Although we might select the correct attributes, the conventional objective function of the best logic limits the search space to obtained more induced logic during the retrieval phase of Discrete Hopfield Neural Network. Therefore, this paper proposes a novel logic mining by integrating statistical analysis in the pre-processing phase to ensure that only optimal attributes will be selected. Supervised learning approach via correlation analysis is implemented for the purpose of attribute selection. Additionally, permutation operator serves to enhance the probability of the higher order satisfiability logical rule to be satisfied by having finite arrangement of attributes. During the learning phase, we proposed multi-unit Discrete Hopfield Neural Network to enhance the search space which leads to optimal solution. The efficiency of the proposed model is tested on 15 real-life datasets by comparing the performance of the model with existing works in logic mining using five performance metrics including accuracy, sensitivity, precision, Matthews Correlation Coefficient (MCC) and F1 Score. According to the results, the proposed model has its own strength by dominating most of the average rank of the performance metrics. This demonstrates that the proposed model can differentiate across all domains in the confusion matrix. Additionally, the p-value obtained based on the five-performance metrics indicate that there is a significantly difference between the proposed model and all existing works since the value obtained for accuracy (0.000), sensitivity (0.001), precision (0.000), F1 score (0.000) and MCC (0.000) are less than 0.05. This finding statistically prove that the proposed model is more effective compared with existing works in logic mining.

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

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.