Finite Memory Loading in Hairy Neurons

This paper presents a method to expand the basins of stable patterns in associative memory. It examines fully-connected associative memory geometrically and translate the learning process into an algebraic optimization procedure. It finds that locating all the patterns at certain stable corners of the neurons’ hypercube as far from the decision hyperplanes as possible can produce excellent error tolerance. It then devises a method based on this finding to develop the hyperplanes. This paper further shows that this method leads to the hairy model, or the deterministic analogue of the Gibb’s free energy model. Through simulations, it shows that this method gives better error tolerance than does the Hopfield model and the error-correction rule in both synchronous and asynchronous modes.     

Parametric identification of robotic systems with stable time-varying Hopfield networks

In this work, a novel method for on-line identification of non-linear systems is proposed based upon the optimisation methodology with Hopfield neural networks. The original Hopfield model is adapted so that the weights of the resulting network are time-varying. A rigorous analytical study proves that, under mild assumptions, the estimations provided by the method converge to the actual parameter values in the case of constant parameters, or to a bounded neighbourhood of the parameters when these are time-varying. Time-varying parameters, often appearing in mechanical systems, are dealt with by the neural estimator in a more natural way than by least squares techniques. Both sudden and slow continuous variations are considered. Besides, in contrast to the gradient method, the neural estimator does not critically depend on the adjustment of the gain. The proposed method is applied to the identification of a robotic system with a flexible link. A reduced output prediction error and an accurate estimation of parameters are observed in simulation results.This is a considerably extended version of a paper presented at the conference on Engineering Applications of Neural Networks (EANN), held in September 2003 at Málaga, Spain.     

基于离散Hopfield网络的自相关过程控制方法

对于自相关过程的统计控制,传统统计学方法虚发警报的概率较大,而BP人工神经网络方法权值训练困难,灵敏度不高。提出一种基于联想学习与离散Hopfield网络的自相关过程控制方法。不需任何训练样本,通过正交化编码将过程状态以吸引子的形式存储到Hopfield网络中,并利用网络的联想功能来检测自相关过程的阶跃型突变。算例研究表明,与Elman网络和EWMA方法相比,过程正常时,所提方法的平均链长（ARL）分别提高了27.9%和55.0%;过程异常时,所提方法的ARL分别降低了74.1%与81.8%以上。说明了方法的有效性与优越性。     

A Neural Paradigm for Motion Understanding

The main aim of this paper is to propose a new neural algorithm to perform a segmentation of an observed scene in regions corresponding to different moving objects, by analysing a time-varying image sequence. The method consists of a classification step, where the motion of small patches is recovered through an optimisation approach, and a segmen-tation step merging neighbouring patches characterised by the same motion. Classification of motion is performed without optical flow computation. Three-dimensional motion parameter estimates are obtained directly from the spatial and temporal image gradients by minimising an appropriate energy function with a Hopfield-like neural network. Network convergence is accelerated by integrating the quantitative estimation of the motion parameters with a qualitative estimate of dominant motion using the geometric theory of differential equations.     

Scheduling flow shops in the environment of multi-functional machine tools

The concept of virtual machine tool (VMT) is introduced in this paper to specify machining resources of multi-functional machine tools. A two-level model for makespan minimization in a flow shop is developed in multi-functional machine tool environments. The model is first optimized with an Hopfield neural network to find the optimal processing sequence for components to visit all the necessary VMTs. Secondly, according to a set of shop floor control rules, the VMTs for components machining are matched with real machine tools. This procedure is driven by the events taking place in components machining, such as the arriving or the finishing of a component. Numerical experiments are conducted in a number of flow shop scheduling problems up to 8×8 and the mean relative optimizing rate is employed to assess the results of numerical experiments.     

Optimization with the Hopfield network based on correlated noises: Experimental approach

This paper presents two simple optimization techniques based on combining the Langevin Equation with the Hopfield Model. Proposed models – referred as stochastic model (SM) and pulsed noise model (PNM) – can be regarded as straightforward stochastic extensions of the Hopfield optimization network. Both models follow the idea of stochastic neural network (Levy and Adams, IEEE Conference on Neural Networks, vol. III, San Diego, USA, 1987, pp. 681–689) and diffusion machine (Wong, Algorithmica 6 (1991) 466–478). They differ form the referred approaches by the nature of noises and the way of their injection. Optimization with stochastic model, unlike in the previous works, in which δ-correlated Gaussian noises were considered, is based on Gaussian noises with positive autocorrelation times. This is a reasonable assumption from a hardware implementation point of view. In the other model – pulsed noise model, Gaussian noises are injected to the system only at certain time instances, as opposed to continuously maintained δ-correlated noises used in the previous related works. In both models (SM and PNM) intensities of injected noises are independent of neurons’ potentials. Moreover, instead of impractically long inverse logarithmic cooling schedules, the linear cooling is tested. With the above strong simplifications neither SM nor PNM is expected to rigorously maintain thermal equilibrium (TE). However, numerical tests based on the canonical Gibbs–Boltzmann distribution show, that differences between rigorous and estimated values of TE parameters are relatively low (within a few percent). In this sense both models are said to perform quasithermal equilibrium. Optimization performance and quasithermal equilibrium properties of both models are presented based on the travelling salesman problem (TSP).     

Noise removal using hysteretic Hopfield tunnelling network in message transmission systems

A novel approach of two-tier noise removal scheme for message transmission systems is proposed with hysteretic Hopfield tunnelling network (HHTN). The proposed system increases the security of messages and reduces the complexity of recognition of characters due to external distortion or diffusion. Though there are many error detection codes, these codes request retransmission when there is an error. If the error rate is high the number of retransmissions is high which causes a delay in data communication. Kim et al. [Y.S. Kim, Y.M. Kim, J.Y. Choi, and D.K. Baik, Information hiding system stegowaveK for improving capacity, Parallel Distributed Comput. (2003), pp. 423–426] proposed an alternate two-tier communication system with code division multiple access (CDMA) technology and a mapping table. When HHTN is added to the system, the learning ability enables the network to remember patterns and enhances the speed. But when images of larger size are stored, the network fails to recognize, which leads to further research in this area.     

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.     

Chaos and hyperchaos in a Hopfield neural network

In this paper we investigate numerically the parameter-space of an autonomous system of four nonlinear first-order ordinary differential equations, which represents a Hopfield neural network with four neurons. The study considers three independent two-dimensional cross-sections of the three-dimensional parameter-space generated by this mathematical model, every constructed considering Lyapunov exponent values. We show that is possible to completely characterize the dynamics of the system based in these three plots, which are representative of the three-dimensional parameter-space as a whole.     

用Hopfield模型求解组合优化问题的拟人策略

文章对Hopfield网络状态的更新准则,提出了一个自适应的拟人策略。数值模拟表明,引入拟人策略的Hopfield模型对求解组合优化问题非常有效。