Discrete Hopfield Neural Network Research Articles

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>

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.

Retracted: Performance Evaluation of Enterprise Supply Chain Management Based on the Discrete Hopfield Neural Network.

[This retracts the article DOI: 10.1155/2021/3250700.].

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.

An Intelligent Implementation of Multi-Sensing Data Fusion With Neuromorphic Computing for Human Activity Recognition

The increasing demand for considering multisensor data fusion technology has drawn attention for precise human activity recognition (HAR) over standalone technology due to its reliability and robustness. This article presents a framework that fuses data from multiple sensing systems and applies neuromorphic computing to sense and classify human activities. The data is collected by utilizing inertial measurement unit (IMU) sensors, software-defined radios, and radars, and feature extraction and selection are performed on the data. For each of the actions, such as sitting and standing, an activity matrix is generated, which is then fed into a discrete Hopfield neural network as a binary feature pattern for one-shot learning. Following the Hopfield network neurons’ feedback output, the conformity to the standard activity feature pattern is also determined. Following the Hopfield network neurons’ feedback output, the training of neurons is completed after two steps under the Hebbian learning law, and the conformity to the standard activity feature pattern is also determined. According to the probabilistic statistics on inference predictions, the proposed method, that is the neuromorphic computing of the three data fused framework, achieved the box plot for the highest lower quartile output of 95.34%, while the confusion matrix classification accuracy of the two activities was 98.98%. The results have shown that neuromorphic computing is most capable of multisensor data-fusion-based HAR. Furthermore, the proposed method can be enhanced by incorporating additional hardware signal processing in the system to enable the flexible integration of human activity data.

Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm

<abstract> <p>Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $ k = \mathrm{3, 2} $, $ k = \mathrm{3, 2}, 1 $ and $ k = \mathrm{3, 1} $. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $ k = \mathrm{3, 2} $ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase.</p> </abstract>

Optimal Deep Transfer Learning Based Colorectal Cancer Detection and Classification Model

Colorectal carcinoma (CRC) is one such dispersed cancer globally and also prominent one in causing cancer-based death. Conventionally, pathologists execute CRC diagnosis through visible scrutinizing under the microscope the resected tissue samples, stained and fixed through Haematoxylin and Eosin (H&E). The advancement of graphical processing systems has resulted in high potentiality for deep learning (DL) techniques in interpretating visual anatomy from high resolution medical images. This study develops a slime mould algorithm with deep transfer learning enabled colorectal cancer detection and classification (SMADTL-CCDC) algorithm. The presented SMADTL-CCDC technique intends to appropriately recognize the occurrence of colorectal cancer. To accomplish this, the SMADTL-CCDC model initially undergoes pre-processing to improve the input image quality. In addition, a dense-EfficientNet technique was employed to extract feature vectors from the pre-processed images. Moreover, SMA with Discrete Hopfield neural network (DHNN) method was applied for the recognition and classification of colorectal cancer. The utilization of SMA assists in appropriately selecting the parameters involved in the DHNN approach. A wide range of experiments was implemented on benchmark datasets to assess the classification performance. A comprehensive comparative study highlighted the better performance of the SMADTL-CDC model over the recent approaches.

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation燨perator

The effectiveness of the logic mining approach is strongly correlated to the quality of the induced logical representation that represent the behaviour of the data. Specifically, the optimum induced logical representation indicates the capability of the logic mining approach in generalizing the real datasets of different variants and dimensions. The main issues with the logic extracted by the standard logic mining techniques are lack of interpretability and the weakness in terms of the structural and arrangement of the 2 Satisfiability logic causing lower accuracy. To address the issues, the logical permutation serves as an alternative mechanism that can enhance the probability of the 2 Satisfiability logical rule becoming true by utilizing the definitive finite arrangement of attributes. This work aims to examine and analyze the significant effect of logical permutation on the performance of data extraction ability of the logic mining approach incorporated with the recurrent discrete Hopfield Neural Network. Based on the theory, the effect of permutation and associate memories in recurrent Hopfield Neural Network will potentially improve the accuracy of the existing logic mining approach. To validate the impact of the logical permutation on the retrieval phase of the logic mining model, the proposed work is experimentally tested on a different class of the benchmark real datasets ranging from the multivariate and time-series datasets. The experimental results show the significant improvement in the proposed logical permutation-based logic mining according to the domains such as compatibility, accuracy, and competitiveness as opposed to the plethora of standard 2 Satisfiability Reverse Analysis methods.

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

Real life logical rule is not always satisfiable in nature due to the redundant variable that represents the logical formulation. Thus, the intelligence system must be optimally governed to ensure the system can behave according to non-satisfiable structure that finds practical applications particularly in knowledge discovery tasks. In this paper, we a propose non-satisfiability logical rule that combines two sub-logical rules, namely Maximum 2 Satisfiability and Random 2 Satisfiability, that play a vital role in creating explainable artificial intelligence. Interestingly, the combination will result in the negative logical outcome where the cost function of the proposed logic is always more than zero. The proposed logical rule is implemented into Discrete Hopfield Neural Network by computing the cost function associated with each variable in Random 2 Satisfiability. Since the proposed logical rule is difficult to be optimized during training phase of DHNN, Election Algorithm is implemented to find consistent interpretation that minimizes the cost function of the proposed logical rule. Election Algorithm has become the most popular optimization metaheuristic technique for resolving constraint optimization problems. The fundamental concepts of Election Algorithm are taken from socio-political phenomena which use new and efficient processes to produce the best outcome. The behavior of Random Maximum 2 Satisfiability in Discrete Hopfield Neural Network is investigated based on several performance metrics. The performance is compared between existing conventional methods with Genetic Algorithm and Election Algorithm. The results demonstrate that the proposed Random Maximum 2 Satisfiability can become the symbolic instruction in Discrete Hopfield Neural Network where Election Algorithm has performed as an effective training process of Discrete Hopfield Neural Network compared to Genetic Algorithm and Exhaustive Search.

PRO2SAT: Systematic Probabilistic Satisfiability logic in Discrete Hopfield Neural Network

Satisfiability is prominent in the field of computer science and mathematics because SAT provides an alternative to represent the knowledge of any datasets. Fueled by this nature, recent paradigm tends to converge towards modelling Artificial Neural Network (ANN) through SAT. Despite extensive implementation of SAT in ANN, there are severely limited strategy to control the distribution of negative and positive literals in the logical rule. One of the most feasible approaches in controlling the behavior of the literal is by employing probabilistic behavior to each neuron in the ANN. In this paper, a novel logical rule namely Probabilistic 2 Satisfiability was proposed by implementing the probability to each variable in the 2 Satisfiability clause. In this context, the negativity of each variable will be determined using the probability which leads to higher search space. The proposed Probabilistic 2 Satisfiability was implemented into the special single layered Discrete Hopfield Neural Network where the cost function of each variable was derived by minimizing the inconsistency of the logic. The behavior of the proposed Probabilistic 2 Satisfiability was assessed based on various performance metrics including several newly introduced metrics. According to the experimental results, the proposed model has a probability of at least 81.8% in outperforming the existing method. Interestingly, the proposed model was reported to have the largest solution space when the ratio of positive was within [0.1, 0.4]. The comparison of experimental results with other state of the art logical rule demonstrates that the proposed model is promising in retrieving global neuron state.