Discrete Hopfield Neural Network Research Articles

CONVERGENCE ANALYSIS OF A DISCRETE HOPFIELD NEURAL NETWORK WITH DELAY AND ITS APPLICATION TO KNOWLEDGE REFINEMENT

This paper investigates the convergence theorems that are associated with a Discrete Hopfield Neural Network (DHNN) with delay. We present two updating rules, one for serial mode and the other for parallel mode. The speed of convergence of these proposed updating rules is faster than all of the existing updating rules. It has been proved in this paper that a DHNN with delay will converge to a stable state when operating in a serial mode if the matrix of weights of the no-delay term is symmetric. In addition, it has been proved that they will converge to a stable state when operating in a parallel mode if the matrix of weights of the no-delay term is a symmetric and non-negative definite matrix. The condition for convergence of a DHNN without delay can been relaxed from the need to have a symmetric matrix to an even weaker condition of having a quasi-symmetric matrix. The results in this paper extend both the existing results concerning the convergence of a DHNN without delay and our previous findings. By means of the new network structure and its convergence theorems, we propose a local searching algorithm for combinatorial optimization. We also relate the maximum value of a bivariate energy function to the stable states of a DHNN with delay, which generalizes Hopfield's energy function. Moreover, for the serial model we give the relationship between the convergence of the energy function and the convergence of the corresponding network. One application is presented to demonstrate the higher rate of convergence and the accuracy of the classification using our algorithm.

Stability analysis of a discrete Hopfield neural network with delay

This letter investigates convergence theorems of a DHNN with delay. We present one generalized updating rule for serial mode. The condition for convergence of a DHNN without delay can be relaxed from a symmetric matrix to a quasi-symmetric matrix. One application is presented to demonstrate the higher convergence speed of our algorithm.

A Hopfield neural network approach for power optimization of real-time operating systems

The RTOS (Real-Time Operating System) is a critical component in the SoC (System-on-a-Chip), which is the main body for consuming total system energy. Power optimization based on hardware–software partitioning of a RTOS (RTOS–Power partitioning) can significantly minimize the energy consumption of a SoC. This paper presents a new model for RTOS–Power partitioning, which helps in understanding the essence of the RTOS–Power partitioning techniques. A discrete Hopfield neural network approach for implementing the RTOS–Power partitioning is proposed, where a novel energy function, operating equation and coefficients of the neural network are redefined. Simulations are carried out with comparison to other optimization techniques. Experimental results demonstrate that the proposed method can achieve higher energy savings up to 60% at relatively low costs of less than 4k PLBs while increasing the performance compared to the purely software realized SoC–RTOS.

Hardware–software partitioning of real-time operating systems using Hopfield neural networks

The hardware–software automated partitioning of a real-time operating system in the system-on-a-chip (SoC-RTOS partitioning) is a NP-complete problem, and a crucial step in the hardware–software co-design of SoC. In this paper, a new model for SoC-RTOS partitioning is introduced, which can help in understanding the essence of the SoC-RTOS partitioning. A discrete Hopfield neural network approach for implementing the SoC-RTOS partitioning is proposed, where a novel energy function, operating equation and coefficients of the neural network are redefined. Simulations are carried out with comparison to other optimization techniques. Experimental results demonstrate the feasibility and effectiveness of the proposed method.

An improved discrete Hopfield neural network for Max-Cut problems

In this paper, we proposed an improved discrete Hopfield neural network (DHNN) for Max-Cut problems. By introducing a nonlinear self-feedback term to the motion equation of the DHNN, the DHNN can escape from local minima and therefore get better solutions. Simulation results show that the proposed algorithm has superior ability for Max-Cut problems within reasonable number of iterations.

Efficient implementation of vector Preisach-type models using orthogonally coupled hysteresis operators

Vector hysteresis models are regarded as helpful tools that can be utilized in the simulation of multidimensional field-media interactions. Recently, substantial efforts have been focused on the refinement of vector Preisach-type models of hysteresis. The purpose of this paper is to present a computationally efficient vector Preisach-type hysteresis model constructed from only two scalar models having orthogonally inter-related elementary operators. Such a model is implemented via a linear neural network (LNN) fed from the outputs of discrete Hopfield neural network (DHNN) blocks having step activation functions. With this DHNN-LNN configuration, it is possible to carry out the identification process using well-established widely available algorithms. Details of the model, its identification, and experimental testing are presented.

A HOPFIELD-TYPE NEURAL NETWORK BASED MODEL FOR TEMPORAL CONSTRAINTS

In this paper we present an approximation method based on discrete Hopfield neural network (DHNN) for solving temporal constraint satisfaction problems. This method is of interest for problems involving numeric and symbolic temporal constraints and where a solution satisfying the constraints of the problem needs to be found within a given deadline. More precisely the method has the ability to provide a solution with a quality proportional to the allocated process time. The quality of the solution corresponds here to the number of satisfied constraints. This property is very important for real world applications including reactive scheduling and planning and also for over constrained problems where a complete solution cannot be found. Experimental study, in terms of time cost and quality of the solution provided, of the DHNN based method we propose provides promising results comparing to the other exact methods based on branch and bound and approximation methods based on stochastic local search.

Associative Memory Design via Path Embedding into a Graph

A graph theoretical procedure for storing a set of n-dimensional binary vectors as asymptotically stable equilibrium points of a discrete Hopfield neural network is presented. The method gives an auto-associative memory which stores an arbitrary memory set completely. Spurious memories might occur only in a small neighborhood of the original memory vectors, so cause small errors.

Identification and testing of an efficient hopfield neural network magnetostriction model

Magnetostriction models are indispensable to different crucial computational activities such as those dealing with active vibration damping devices and optimum clamping stresses for transformer sheets. This paper presents an efficient magnetostriction Preisach-type model based on the effective field approach. According to this approach, the total applied field may be regarded as a super position of the actual magnetic field and a stress-dependent feedback term. Construction and identification of the model is carried out by providing experimental training data to a modular discrete Hopfield neural network–linear neural network combination. Experimental testing suggests that this model can lead to good qualitative and quantitative simulation results.

A GENERAL UPDATING RULE FOR DISCRETE HOPFIELD-TYPE NEURAL NETWORK WITH TIME-DELAY AND THE CORRESPONDING SEARCH ALGORITHM

In this paper, the Hopfield neural network with delay (HNND) is studied from the standpoint of regarding it as an optimizing computational model. Two general updating rules for networks with delay (GURD) are given based on Hopfield-type neural networks with delay for optimization problems and characterized by dynamic thresholds. It is proved that in any sequence of updating rule modes, the GURD monotonously converges to a stable state of the network. The diagonal elements of the connection matrix are shown to have an important influence on the convergence process, and they represent the relationship of the local maximum value of the energy function to the stable states of the networks. All the ordinary discrete Hopfield neural network (DHNN) algorithms are instances of the GURD. It can be shown that the convergence conditions of the GURD may be relaxed in the context of applications, for instance, the condition of nonnegative diagonal elements of the connection matrix can be removed from the original convergence theorem. A new updating rule mode and restrictive conditions can guarantee the network to achieve a local maximum of the energy function with a step-by-step algorithm. The convergence rate improves evidently when compared with other methods. For a delay item considered as a noise disturbance item, the step-by-step algorithm demonstrates its efficiency and a high convergence rate. Experimental results support our proposed algorithm.

On permutation symmetries of hopfield model neural network

Discrete Hopfield neural network (DHNN) is studied by performing permutation operations on the synaptic weight matrix. The storable patterns set stored with Hebbian learning algorithm in a network without losing memories is studied, and a condition which makes sure all the patterns of the storable patterns set have a same basin size of attraction is proposed. Then, the permutation symmetries of the network are studied associating with the stored patterns set. A construction of the storable patterns set satisfying that condition is achieved by consideration of their invariance under a point group.

Neural network approaches to implementation of optimum multiuser detectors in code-division multiple-access channels

Two neural networks for implementing an optimum multiuser detector (MUD) in code-division multiple-access (CDMA) channels are proposed. By viewing the optimum MUD problem as an NP-complete combinatorial optimum problem, we apply the discrete Hopfield neural network (DHNN) which has the ability for fast optimization computing to solve this kind of optimum problem. This is the first neural network approach. Also, by viewing the optimum MUD problem in a CDMA channel as an optimum nonlinear classification decision problem, we apply a backpropagation neural network (BPNN) which, through arbitrary nonlinear transformations and adaptive learning, can implement this classification decision optimally and adaptively. Both neural networks have certain application potentials in implementing the optimum MUD in CDMA systems. The DHNN is more suitable for the case when the users in the system are stationary, while the BPNN is suitable for the case when users in the system are mobile, such as mobile cellular CDMA communication systems or personal communication systems (PCS).

Applying oonn to solve map-coloring problem

For solving the map-coloring problems, this paper presents an energy function, a more effective dynamic equation and a more simple convergence condition. For the first time we study the map-coloring problems in the way of connecting discrete Hopfield neural network with the orthogonal optimisation, and as a practical example, a color map of China is given.