Hopfield Neural Network Research Articles

Multistable Memristor Synapse-Based Coupled Bi-Hopfield Neuron Model: Dynamic Analysis, Microcontroller Implementation and Image Encryption

The memristor, a revolutionary electronic component, mimics both neural synapses and electromagnetic induction phenomena. Recent study challenges are the development of effective neural models and discovering their dynamics. In this study, we propose a novel Hopfield neural network model leveraging multistable memristors, showcasing its efficacy in encoding biomedical images. We investigate the equilibrium states and dynamic behaviors of our designed model through comprehensive numerical simulations, revealing a rich array of phenomena including periodic orbits, chaotic dynamics, and homogeneous coexisting attractors. The practical realization of our model is achieved using a microcontroller, with experimental results demonstrating strong agreement with theoretical analyses. Furthermore, harnessing the chaos inherent in the neural network, we develop a robust biomedical image encryption technique, validated through rigorous computational performance tests.

Dynamics of Symmetrical Discontinuous Hopfield Neural Networks with Poisson Stable Rates, Synaptic Connections and Unpredictable Inputs

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence.

Recurrent neural networks for aerodynamic parameter estimation with Lyapunov stability analysis

ABSTRACT Aircraft parameter estimation is crucial for designing accurate and reliable flight dynamic models, essential for integration into flight simulators and developing effective control laws. These parameters, encompassing aerodynamic characteristics, play a pivotal role in enhancing aircraft performance, safety and overall operational efficiency. This paper explores aircraft parameter estimation using two Recurrent Neural Network (RNN) approaches: (i) the weight-bias method (RNN-WB) and (ii) the gradient-based method (RNN-Gradient). RNN-WB is based on the Hopfield neural network and relies on pre-computation of weight and bias information, applying non-linearity to the states of the network. RNN-Gradient computes direct gradients and applies non-linearity to the error. Simulated flight data is employed in MATLAB implementations to assess estimation results, considering both performance metrics and computation time. The estimated parameters were also compared with estimates obtained from Unscented Kalman Filter (UKF). A novel methodology is introduced to establish the asymptotic stability of RNN-WB and RNN-Gradient methods, utilizing the normalized Lyapunov energy functional. The asymptotic stability ensures the reliability and robustness of these techniques for parameter estimation. The RNN-Gradient shows a 20% performance improvement over RNN-WB. Satisfactory simulation results from both algorithms provide a promising foundation for their potential applications to real flight test data.

Symmetric multi-double-scroll attractors in Hopfield neural network under pulse controlled memristor

Symmetric multi-double-scroll attractors in Hopfield neural network under pulse controlled memristor

Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse

Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse

An Approach to Hopfield Network-Based Energy-Efficient RFID Network Planning

Abstract Radio Frequency IDentification (RFID) Network Planning (RNP) is the problem of placing RFID readers in a working area where a tag is interrogated by at least one reader and at the same time satisfies some constraints such as minimum number of placed readers, minimal interference, and minimal outside coverage. The RNP optimization has been proven NP-hard; thus, natural-inspired approaches are often used to find the optimal solution. The paper proposes an energy-efficient RNP approach in which the positions of placed readers are optimized by a Hopfield network, and the energy efficiency is achieved through a placement area restriction technique. A mechanism of redundant reader elimination is also added to minimize the number of placed readers. Simulation results show that the Hopfield network-based energy-efficient RNP approach achieves the maximum tag coverage and energy efficiency by reducing interference, outside coverage, and the number of placed readers.

Advancing urban water-energy demand predictions with a rotor hopfield neural network model optimized by contracted thermal exchange optimizer

ABSTRACT The relationship between urban water and energy demand is crucial for resource efficiency, sustainability, and environmental conservation. Rapid urbanization, population growth, and climate change necessitate integrated models that capture the complex interdependencies, feedback loops, and trade-offs between water and energy systems. This research addresses this intricate relationship by developing a modified Rotor Hopfield Neural Network (RHNN) Model using input indicators like population data, GDP, water consumption, precipitation, electricity consumption, wastewater discharge, and industrial coal usage. The model is optimized using a modified metaheuristic, called Contracted Thermal Exchange Optimizer (CTEO), resulting in a comprehensive forecast of urban water-energy demand. The model’s superior efficiency is demonstrated by comparing it with other contemporary methods. Upon comparison with alternative approaches, it is clear that the RHNN/CTEO model surpasses them, showcasing a mean relative error of 1.47% for water usage and 2.60% for energy consumption. This leads to an overall average MRE of 2.03%. This research contributes to the existing body of knowledge by offering an advanced model for urban water-energy demand forecasting, providing valuable insights for policymakers, urban planners, and stakeholders in making informed decisions related to resource allocation, infrastructure development, and sustainable urban development.

Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network’s dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviors such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural network. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations.

Modeling and Sentiment Analysis of Social Relationships in Elderly Smart Homes Based on Graph Neural Networks

With the expansion of Speech Emotion Recognition in the consumer domain, several devices, particularly those designed for managing smart home personal assistants for the elderly, have been widely available on the market. The increasing processing power and connection, together with the growing need to facilitate longer residency through technological interventions, highlight the potential benefits of smart home assistants. Enabling these assistants to recognize human emotions would greatly improve user-assistant communication, allowing the assistant to deliver more constructive and customized feedback to the user. In this research work, Modeling and Sentiment Analysis of Social Relationships in Elderly Smart Homes Based on Graph Neural Networks (SASR-MBHNN-BBOA) is proposed. The input data are collected from Social Recommendation Dataset. Then, input data are pre-processed utilizing Inverse Optimal Safety Filters (IOSF) for cleaning the data and removing the background noise. Then the pre-processed data are given to Memristive Bi-neuron Hopfield Neural Network (MBHNN) for predicting the sentiments like positive, negative and neutral. In general, MBHNN doesn’t express some adoption of optimization approaches for determining optimal parameters to predicting the sentiments accurately. Hence BBOA is proposed to optimize MBHNN classifier which precisely predicts the sentiments in elderly smart home. The proposed SASR-MBHNN-BBOA method is implemented in Python, and it assessed with numerous performance metrics such as accuracy, precision, recall, F1-score, ROC. The outcomes show SASR-MBHNN-BBOA attains 20.8%, 19.5%, and 29.6% higher Accuracy, 28.8%, 22.5%, and 32.6% higher Precision, 15.5%, 27.4%, and 18.2% higher Recall are analysed with existing methods such as, Emotional speech analysis in real time for smart home assistants.(SASR-CNN-SHA), Machine Learning to Investigate Elderly Care Requirements in China via the Lens of Family Caregivers (SASR-ML-IECR),Identifying User Emotions via Audio Conversations with Smart Assistants (SASR-DNN-EASA) methods respectively.

Clearance Nonlinear Control Method of Electro-Hydraulic Servo System Based on Hopfield Neural Network

The electro-hydraulic servo system has advantages such as high pressure, large flow, and high power, etc., which can also realize stepless regulation, so it is widely used in many engineering machineries. A linear model is sometimes only a simple approximation of an idealized model, but in an actual system, there may be nonlinear and transient variation characteristics in the systems. Coupling is reflected in the fact that the components or functional structures implemented by each system used for the design of hydraulic systems are not completely or independently related to each other, but affect each other. The nonlinear clearance between the actuator and the load reduces the control accuracy of the system and increases the impact, thus losing stable working conditions. In the paper, based on the nonlinear clearance problem of the electro-hydraulic servo system, a mathematical transfer model with clearance is established, and on this basis, a clearance compensation method based on the Hopfield neural network is proposed. In this way, clearance compensation can be realized by adjusting the parameters of neural network nodes, through simple and convenient operation. Finally, by setting different clearance values, the results of the step response and sine response curve before and after clearance compensation of the hydraulic system are compared, and the effectiveness of Hopfield neural network compensation clearance control is verified based on the comparison simulation results.

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.

Dynamic analysis and hardware implementation of multi-scroll Hopfield neural networks with three different memristor synapses

Dynamic analysis and hardware implementation of multi-scroll Hopfield neural networks with three different memristor synapses

A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

Abstract Compared to conventional single-scroll or double-scroll attractors, multi-scroll chaotic attractors possess wide potential for application due to their adjustability and complex topology. However, neural network models for generating multiple scrolls are often implemented using memristors with piecewise nonlinear functions. To further explore multi-scroll attractors with different working mechanisms,a unique memristor containing a group of hyperbolic tangent functions is designed and then applied in a three-dimensional Hopfield neural network (HNN). The proposed memristive Hopfield neural network (MHNN) has multi-scroll chaotic attractors, where the number and parity of the scrolls be changed by adjusting the control parameters of the memristor. The complex dynamical behaviors of MHNN are studied by utilizing diverse numerical modeling approaches like bifurcation diagrams, Lyapunov exponents and phase plot. In addition, the proposed MHNN also has a complicated offset boosting coexisting behavior. By selecting suitable parameters, multiple coexisting chaotic attractors could be obtained. Homogeneous coexisting multi-scroll attractors can be shifted in multiple directions including unidirectional, planar and spatial ones. Moreover, theoretically speaking, there could be an infinite number of coexisting attractors. Finally, experimental results are validated through numerical simulations and circuit experiments to confirm the feasibility of the proposed MHNN model.

Memristive Hopfield neural network with multiple controllable nonlinear offset behaviors and its medical encryption application

Memristors possess inherent nonlinearity and synaptic attributes, rendering them more suited for integration as synapses within neural networks compared to resistors. Furthermore, their utilization induces significant alterations in the dynamic behavior of neural networks, hence bestowing considerable value in the realm of secure communication applications. In this paper, an improved cosine memristor is proposed, three representative memristor Hopfield neural networks (MHNNs) are constructed using it as synapse. The MHNNs exhibit rich initial offset boost behaviors, we summarize these phenomena into four types based on the offset characteristics. In particular, these offset types can be converted by adjusting internal parameters of the memristor. In addition, the MHNNs are constructed and tested using both software and hardware components, validating the accuracy of theoretical simulation and the implementation of systems. Ultimately, a set of bit-plane level medical image encryption algorithm is proposed on the basis of MHNNs, which has excellent encryption performance and can effectively protect the privacy of patients.

A sparse quantized hopfield network for online-continual memory

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed way. Further, synaptic plasticity in the brain depends only on information local to synapses. Deep networks, on the other hand, typically use non-local learning algorithms and are trained in an offline, non-noisy, independent, identically distributed setting. Understanding how neural networks learn under the same constraints as the brain is an open problem for neuroscience and neuromorphic computing. A standard approach to this problem has yet to be established. In this paper, we propose that discrete graphical models that learn via an online maximum a posteriori learning algorithm could provide such an approach. We implement this kind of model in a neural network called the Sparse Quantized Hopfield Network. We show our model outperforms state-of-the-art neural networks on associative memory tasks, outperforms these networks in online, continual settings, learns efficiently with noisy inputs, and is better than baselines on an episodic memory task.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Implementing Optical Analog Computing and Electrooptic Hopfield Network by Silicon Photonic Circuits

Implementing Optical Analog Computing and Electrooptic Hopfield Network by Silicon Photonic Circuits

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

In Search of Dispersed Memories: Generative Diffusion Models Are Associative Memory Networks.

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. Similar to associative memory systems, these networks define a dynamical system that converges to a set of target states. In this work, we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is (asymptotically) identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Leveraging this connection, we formulate a generalized framework for understanding the formation of long-term memory, where creative generation and memory recall can be seen as parts of a unified continuum.

Reconciling quantum and classical spectral theories of ultrastrong coupling: role of cavity bath coupling and gauge corrections

Cavity quantum-electrodynamics (QED) is a rich area of optical physics, where extreme light–matter coupling can give rise to ultrastrong coupling. The ultrastrong coupling regime presents some fascinating uniquely quantum mechanical effects, such as ground state virtual photons and vacuum squeezing. Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrong coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling, which has so far not been identified. We also show the impact of this bath model on the quantum Rabi model, which has no classical analog in ultrastrong coupling. These results can be used to guide emerging experiments and significantly impact current models and interpretations of ultrastrong coupling between light and matter.