A High Order Neural Network to Solve Crossbar Switch Problem

Traditional Hopfield networking has been widely used to solve combinatorial optimization problems. However, high order Hopfiled networks, as an expansion of traditional Hopfield networks, are seldom used to solve combinatorial optimization problems. In theory, compared with low order networks, high order networks have better properties, such as stronger approximations and faster convergence rates. In this chapter, the authors focus on how to use high order networks to model combinatorial optimization problems. Firstly, the high order discrete Hopfield Network is introduced, then the authors discuss how to find the high order inputs of a neuron. Finally, the construction method of energy function and the neural computing algorithm are presented. In this chapter, the N queens problem and the crossbar switch problem, which are NP-complete problems, are used as examples to illustrate how to model practical problems using high order neural networks. The authors also discuss the performance of high order networks for modeling the two combinatorial optimization problems.

The Boolean Satisfiability Problem (BSAT) is one of the most important decision problems in mathematical logic and computational sciences for determining whether or not a solution to a Boolean formula.. Hopfield neural network (HNN) is one of the major type artificial neural network (NN) popularly known for it used in solving various optimization and decision problems based on its energy minimization machinism. The existing models that incorporate standalone network projected non-versatile framework as fundamental Hopfield type of neural network (HNN) employs random search in its training stages and sometimes get trapped at local optimal solution. In this study, Ants Colony Optimzation Algorithm (ACO) as a novel variant of probabilistic metaheuristic algorithm (MA) inspired by the behavior of real Ants, has been incorporated in the training phase of Hopfield types of the neural network (HNN) to accelerate the training process for Random Boolean kSatisfiability reverse analysis (RANkSATRA) based for logic mining. The proposed hybrid model has been evaluated according to robustness and accuracy of the induced logic obtained based on the agricultural soil fertility data set (ASFDS). Based on the experimental simulation results, it reveals that the ACO can effectively work with the Hopfield type of neural network (HNN) for Random 3 Satisfiability Reverse Analysis with 87.5 % classification accuracy

In this paper, we propose fuzzy control that leads to an ideal scheduling of changing the parameters in Hopfield's neural network. When a combinatorial optimization problem, such as the traveling salesman problem, is solved by Hopfield's neural network, it is efficient to change intentionally the parameters of the energy function and sigmoid function. By changing the parameters on purpose, this network can avoid being trapped at a local minima. However, it is difficult to determine how to change these parameters because there exists a complex relation among these parameters. First, we investigate a bad scheduling to change parameters by simple experiments and find several rules that may lead to a good scheduling. The rules extracted from the experimental results are then realized by fuzzy control. By using fuzzy control, we can judge bad scheduling from vague network's stages and correct the relation among the parameters. The traveling salesman problem is considered as an example to demonstrate its validity by computer simulations.

III.4 - Hopfield Model and Optimization Problems

Hopfield neural networks (HNN) and simulated annealing (SA) are two recent approaches to solving many combinatorial optimization problems. But, the disadvantages of HNN are that it can often converge at local minimum and the quality of solutions depends on the initial state because of sensitivity of parameterization. On the other hand, SA is designed to cope with the problem of convergence to a local minimum. SA, however, requires unacceptably large computing time. So, a new algorithm called mean field annealing (MFA) which can be interpreted as a generalization of HNN, is applied to optimization problems efficiently. In this paper, we propose a new approach based on MFA to solving of the minimization problem. Also we show that our approach can be applied to multi-layer as well as two-layer routing, and optimal solutions can be obtained by properly adjusting the parameter in the given energy function.

This paper investigates convergence theorems of (HNNMDs). (The discrete Hopfield network with multiple delays). We have demonstrated how to transform a network with multiple delays to a new network with a single delay. Based on serial rule updating mode, the conditions for convergence of a HNNMDs can be obtained.

Concerned with the slow learning problems of multilayer perceptrons, which utilise computationally intensive training algorithms like the backpropagation learning algorithm that can get trapped in local minima, this paper presents a novel type of higher-order recurrent neural networks, which is called the Dynamic Ridge Polynomial Neural Networks (DRPNN). The aim of the proposed network is to improve the performance of the Ridge Polynomial Neural Network by accommodating recurrent links structure. The network is tested for the prediction of non-linear and non-stationary financial signals. Three exchange rate time-series, which are the exchange rate time series between the British Pound and the Euro, the US dollar and the Euro as well as the exchange rate between the Japanese Yen and the Euro, are used in the simulation process. Simulation results showed that DRPNN generate higher profit returns with fast convergence when used to predict noisy financial time series.

In terms of the poor evaluation system of graduation theses, which is easy to be influenced by many human factors, we try to establish a more scientific and objective evaluation model and method of graduation thesis quality. Firstly, the index system of graduation thesis quality evaluation model was constructed, including topic selection, professional knowledge level, data collection capacity, ability to use knowledge, level of guidance teacher, and quality of the paper. Secondly, using expert scoring method, combining Matlab programming and applying AHP, the weight of the quality evaluation elements of graduation thesis was obtained, and the key factors affecting the quality level of graduation thesis were determined. Finally, a discrete Hopfield neural network model for the quality level of graduation thesis was established, and 120 graduation theses were selected for quality level simulation evaluation, and compared with the ideal evaluation results. The results showed that the discrete Hopfield neural network model is correct and it can effectively provide objective, scientific and normative evaluation for the quality of graduation theses. Key words: Undergraduate graduation thesis; AHP; Hopfield; Quality evaluation method

The Hopfield neural network is expected to act as the engine to solve the association problem or the optimization problem. In the associative processing using the Hopfield neural network, it is necessary that the precalculated weights should be memorized in the neural network. In the Hopfield neural network, however, there must be m2 weights, where m is the number of neurons. In other words, a tremendous memory capacity is required when m is increased. the weight can be stored either by an analog memory or a digital memory. the analog meomory, however, has problems of error and the decay of the memorized content. Then, digital memory must be used. In this case, the required number of memory elements is m2 × (data bits) and the hardware complexity increases in proportion to the number of data bits.Another point is that the hardware, such as the multiplier of the synapse, becomes more complicated with the increase of the number of bits. A remedy for those problems may be to reduce the number of bits for the weight. When a digital code of some 2 bits is used to represent the weight, for example, the memory capacity for storage can be reduced and the multiplication at the synapse can be simplified. One of the important issues then is how to determine the weight when the number of bits for the wieght is reduced. Since it is difficult to approximate the weight by a continuous variable, it is desirable to realize an efficint method which is differrent from the existing method of weight determination.With the foregoing as background, this paper discusses the weight determination method for the case where the weight determination method for the case where the weight can take only a few number of discrete values. In the proposed method, the evaluation function for the weight is examined and the weights are determined by optimization using an algorithm, which is an application of the branch‐and‐bound method. It is shown by simulation that a high associative ability is realized by the association processing using the weights obtained by the proposed method. Future applications can be expected.

Hopfield neural networks (HNNs) are one of the most well-known and widely used kinds of neural networks in optimization. In this article, the author focuses on building a deeper understanding of the working principle of the HNN during an optimization process. Our investigations yield several novel results giving some important insights into the working principle of both continuous and discrete HNNs. This article shows that what the traditional HNN actually does as energy function decreases is to divide the neurons into two classes in such a way that the sum of biased class volumes is minimized (or maximized) regardless of the types of the optimization problems. Introducing neuron-specific class labels, the author concludes that the traditional discrete HNN is actually a special case of the greedy asynchronous distributed interference avoidance algorithm (GADIA) [17] of Babadi and Tarokh for the 2-class optimization problems. The computer results confirm the findings.

Iterative learning control problem based on improved discrete-time Hopfield neural networks is considered in this paper. For the every process of iterative learning control, the neural networks execute a cycle that includes variable terms of learning time and training iterative number. The iterative learning control with improved Hopfield neural networks is formulated that can be described as a two-dimensional (2-D) Roesser model with variable coefficients. In terms of 2-D systems theory, sufficient conditions that iterative learning error approaches to zero are given. It has been shown that convergence of iterative learning control problem based on Hopfield neural networks is derived by 2-D systems theory instead of conventional algorithms that minimize a cost function.KeywordsRecurrent Neural NetworkIterative Learning ControlHopfield Neural NetworkNeural Network ControlRoesser ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper addresses the design and experimental characterization of a novel hybrid neural network, in which two distinct classical architectures interact: the Hopfield neural network and the Multi-Layer Perceptron. This hybrid neural system, named MLP+H (from MLP + Hopfield), presents a better performance than each one of the two classical architectures when considered in separate. In addition, it has the ability to deal with different classes of data than that normally allowed by the two conventional architectures. For example, while the Hopfield networks deal with binary patterns and the MLPs with information that always have some analog characteristics (due to the continuous nature of the MLP nodes), the MLP+H deals with analog inputs and purely digital outputs. Moreover, the MLP+H allows reduced training times when compared with the MLP architecture, also presenting compactness and flexibility in dealing with different applications, as implementation of anti-noise filters, an application currently under study.KeywordsConfusion MatrixInput PatternAnalog InputOutput PatternHybrid NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In 1984 Hopfield showed that the time evolution of a symmetric Hopfield neural networks are a motion in state space that seeks out minima in the energy function (i.e., equilibrium point set of Hopfield neural networks). Because high-order Hopfield neural networks have more extensive applications than Hopfield neural networks, and have been discussed on the convergence of the networks. In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the high-order neural network system still approacher some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic high-order neural network will approach its limit set. Our result cancels the requirement of symmetry of the connection weight matrix and includes the classic result on Hopfield neural networks, which is a special case of stochastic high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called modified sequential extension of section (MSES) that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the Hopfield neural networks.

The neural network system with terminal attractors is pro- posed for pattern recognition. By the introduction of the terminal attrac- tors, the spurious states of the energy function in the Hopfield neural networks can be avoided and a unique solution with global minimum is obtained. The computer simulations show the usefulness of the method for pattern recognition. Based on the terminal attractor neural network, we proposed the optical neural network with the terminal attractor model. The results show that the recognition rate is considerably enhanced by the introduction of the terminal attractors. © 1996 Society of Photo-Optical Instrumentation Engineers.