改进的指数双向联想记忆模型及性能估计

提出了一个新的改进型指数双向联想记忆模型(improved eBAM,简称IeBAM).通过定义有界且随状态改变而下降的能量函数,证明了IeBAM在状态的同、异步更新方式下的稳定性,一方面排除了Wang的修正指数BAM(modified eBAM,简称MeBAM)和Jeng的eBAM(exponential BAM)的稳定性证明中所作的不合理假设;另一方面,放宽了对BAM(bidirectional associative memory)的连续性假设的要求,并避免了补码问题.理论分析和计算机模拟结果表明,     

一个新的高阶双向联想记忆模型及其性能估计

提出了一个新的高阶双向联想记忆模型.它推广了由Tai及Jeng所提出的高阶双向联想记忆模型HOBAM(higher-order bidirectional associative memory)及修正的具有内连接的双向联想记忆模型MIBAM(modified intraconnected bidirectional associative memory),通过定义能量函数,证明了新模型在同步与异步更新方式下的稳定性,从而能够保证所有被训练模式对成为该模型的渐近稳定点.借助统计分析原理,估计了所提模型的存储容量.计算机模拟证实此模型不仅具有较高的存储容量,而且还具有较好的纠错能力.     

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

     

BAM Learning of Nonlinearly Separable Tasks by Using an Asymmetrical Output Function and Reinforcement Learning

Most bidirectional associative memory (BAM) networks use a symmetrical output function for dual fixed-point behavior. In this paper, we show that by introducing an asymmetry parameter into a recently introduced chaotic BAM output function, prior knowledge can be used to momentarily disable desired attractors from memory, hence biasing the search space to improve recall performance. This property allows control of chaotic wandering, favoring given subspaces over others. In addition, reinforcement learning can then enable a dual BAM architecture to store and recall nonlinearly separable patterns. Our results allow the same BAM framework to model three different types of learning: supervised, reinforcement, and unsupervised. This ability is very promising from the cognitive modeling viewpoint. The new BAM model is also useful from an engineering perspective; our simulations results reveal a notable overall increase in BAM learning and recall performances when using a hybrid model with the general regression neural network (GRNN).      

Second-order asymmetric BAM design with a maximal basin of attraction

Bidirectional associative memory (BAM) generalizes the associative memory (AM) to be capable of performing two-way recalling of pattern pairs. Asymmetric bidirectional associative memory (ABAM) is a variant of BAM relaxed with connection weight symmetry restriction and enjoys a much better performance than a conventional BAM structure. Higher-order associative memories (HOAMs) are reputed for their higher memory capacity than the first-order counterparts. The paper concerns the design of a second-order asymmetric bidirectional associative memory (SOABAM) with a maximal basin of attraction, whose extension to a HOABAM is possible and straightforward. First, a necessary and sufficient condition is derived for the connection weight matrix of SOABAM that can guarantee the recall of all prototype pattern pairs. A local training rule which is adaptive in the learning step size is formulated. Then derived is a theorem, designing a SOABAM further enlarging the quantities required to meet the complete recall theorem will enhance the capability of evolving a noisy pattern to converge to its association pattern vector without error. Based on this theorem, our algorithm is also modified to ensure each training pattern is stored with a basin of attraction as large as possible.     

Application of a bi-directional associative memory (BAM) network in computer assisted learning in chemistry

A computer assisted learning software based on a bi-directional associative memory (BAM) network was developed. The software was implemented to assist students in associating the names of the elements in the periodic table with their chemical symbols. The use of the BAM facilitates the analysis and interpretation of students' responses. The software package can be modified easily as an educational tool for other disciplines.     

A bidirectional heteroassociative memory for binary and grey-level patterns

Typical bidirectional associative memories (BAM) use an offline, one-shot learning rule, have poor memory storage capacity, are sensitive to noise, and are subject to spurious steady states during recall. Recent work on BAM has improved network performance in relation to noisy recall and the number of spurious attractors, but at the cost of an increase in BAM complexity. In all cases, the networks can only recall bipolar stimuli and, thus, are of limited use for grey-level pattern recall. In this paper, we introduce a new bidirectional heteroassociative memory model that uses a simple self-convergent iterative learning rule and a new nonlinear output function. As a result, the model can learn online without being subject to overlearning. Our simulation results show that this new model causes fewer spurious attractors when compared to others popular BAM networks, for a comparable performance in terms of tolerance to noise and storage capacity. In addition, the novel output function enables it to learn and recall grey-level patterns in a bidirectional way.     

双向联想记忆学习与回忆的研究

本文对双向联想记忆(BAM)的学习与回忆过程进行了详细的分析。在学习过程中,先是运用自适应非对称BAM算法进行学习,进而采用设置印象门限的反复记忆算法进行学习,本文从理论上证明了印象门限与样本吸引域之间的关系,指出反复记忆方法的理论依据。回忆过程中,采用非零阈值函数的运行方程,提出了阈值学习方法,并且从理论上证明了非零阈值函数的运行方程的采用,可进一步扩大吸引域。为了进一步扩大网络的信息存储量,本文引入了并联的BAM结构。本文方法的采纳,使得BAM网络的信息存储量、误差校正能力等得到很大程度的提高。     

CLAM: A new model of associative memory

We present a new associative memory model that stores arbitrary bipolar patterns without the problems we can find in other models like BAM or LAM. After identifying those problems we show the new memory topology and we explain its learning and recall stages. Mathematical demonstrations are provided to prove that the new memory model guarantees the perfect retrieval of every stored pattern and also to prove that whatever the input of the memory is, it operates as a nearest neighbor classifier. ©2000 John Wiley & Sons, Inc.     

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices P_k and Q_k are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

Robust stability of interval bidirectional associative memory neural network with time delays.

In this paper, the conventional bidirectional associative memory (BAM) neural network with signal transmission delay is intervalized in order to study the bounded effect of deviations in network parameters and external perturbations. The resultant model is referred to as a novel interval dynamic BAM (IDBAM) model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of unique equilibrium and robust stability are derived. These results are fairly general and can be verified easily. To go further, we extend our investigation to the time-varying delay case. Some robust stability criteria for BAM with perturbations of time-varying delays are derived. Besides, our approach for the analysis allows us to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as the usual C1-smooth sigmoids. We believe that the results obtained have leading significance in the design and application of BAM neural networks.     

模糊联想记忆网络的增强学习算法

针对 Kosko提出的最大最小模糊联想记忆网络存在的问题 ,通过对这种网络连接权学习规则的改进 ,给出了另一种权重学习规则 ,即把 Kosko的前馈模糊联想记忆模型发展成为模糊双向联想记忆模型 ,并由此给出了模糊快速增强学习算法 ,该算法能存储任意给定的多值训练模式对集 .其中对于存储二值模式对集 ,由于其连接权值取值 0或 1,因而该算法易于硬件电路和光学实现 .实验结果表明 ,模糊快速增强学习算法是行之有效的 .     

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Encoding method for bidirectional associative memory usingprojection on convex sets

The traditional encoding method of bidirectional associative memory (BAM) suggested by Kosko (1988) is based on the correlation method with which the capacity is very small. The enhanced Householder encoding algorithm (EHCA) presented here is developed on the basis of the Householder encoding algorithm (HCA) and projection on convex sets (POCS). The capacity of BAM with HCA tends to the dimension of the pattern pairs. Unfortunately, in BAM with HCA there are two different interconnection matrices and hence BAM with HCA may not converge when the initial stimulus is not one of the library patterns. In EHCA the two matrices found by HCA are reduced into one matrix by POCS. Hence, the convergent property of BAM can be maintained. Simulation results show that the capacity of BAM with EHCA is greatly improved.     

Guaranteed recall of all training pairs for bidirectionalassociative memory

Necessary and sufficient conditions are derived for the weights of a generalized correlation matrix of a bidirectional associative memory (BAM) which guarantee the recall of all training pairs. A linear programming/multiple training (LP/MT) method that determines weights which satisfy the conditions when a solution is feasible is presented. The sequential multiple training (SMT) method is shown to yield integers for the weights, which are multiplicities of the training pairs. Computer simulation results, including capacity comparisons of BAM, LP/MT BAM, and SMT BAM, are presented.     

内连式复值双向联想记忆模型及性能分析

Lee的复域多值双向联想记忆模型(complex domain bidirectional associative memory,简称CDBAM)不仅将Kosko的实域BAM(bidirectional associative memory)推广至复域,而且推广至多值情形,以利于多值模式(如灰级图像等)间的联想.在此基础上,提出了一个新的推广模型:复域内连式多值双向联想记忆模型(intraconnected CDBAM,简称ICDBAM),通过定义的能量函数证明了它在同步与异步更新方式下的稳定性,从而保证所有训练样本对成为其稳定点,克服了CDBAM所存在的补码问题.计算机模拟证明了该模型比CDBAM具有更高的存储容量和更好的纠错性能.     

The effect of weight fault on associative networks

In the past three decades, the properties of associative networks has been extensively investigated. However, most existing results focus on the fault-free networks only. In implementation, network faults can be exhibited in different forms, such as open weight fault and multiplicative weight noise. This paper studies the effect of weight fault on the performance of the bidirectional associative memory (BAM) model when multiplicative weight noise and open weight fault present. Assuming that connection weights are corrupted by these two common fault models, we study how many number of pattern pairs can be stored in a faulty BAM. Since one of important feature of associative network is error correction, we also study the number of pattern pairs can be stored in a faulty BAM when there are some errors in the initial stimulus pattern.     

Adaptation of the relaxation method for learning in bidirectionalassociative memory

An iterative learning algorithm called PRLAB is described for the discrete bidirectional associative memory (BAM). Guaranteed recall of all training pairs is ensured by PRLAB. The proposed algorithm is significant in many ways. Unlike many existing iterative learning algorithms, PRLAB is not based on the gradient descent technique. It is a novel adaptation from the well-known relaxation method for solving a system of linear inequalities. The algorithm is very fast. Learning 200 random patterns in a 200-200 BAM takes only 20 epochs on the average. PRLAB is highly insensitive to learning parameters and the initial configuration of a BAM. It also offers high scalability for large applications by providing the same high performance when the number of training patterns are increased in proportion to the size of the BAM. An extensive performance analysis of the new learning algorithm is included.     

An analysis of high-capacity discrete exponential BAM

An exponential bidirectional associative memory (eBAM) using an exponential encoding scheme is discussed. It has a higher capacity for pattern pair storage than conventional BAMs. A new energy function is defined. The associative memory takes advantage of the exponential nonlinearity in the evolution equations such that the signal-to-noise ratio (SNR) is significantly increased. The energy of the eBAM decreases as the recall process proceeds, ensuring the stability of the system. The increase of SNR consequently enhances the capacity of the BAM. The capacity of the exponential BAM is estimated.     

双向联想记忆神经网络抗噪声的能力

This paper analyzes noise sensitivity of bidirectional association memory (BAM) and shows that the anti-noise capability of BAM relates not only to the minimum absolute value of net inputs(MAV), as some researchers found, but also to the variance of weights associated with synapse connections. In fact, it is determined by the quotient of these two factors. On this base, a novel learning algorithm—small variance leaning for BAM(SVBAM) is proposed, which is to decrease the variance of the weights of synapse matrix. Simulation experiments show that the algorithm can decrease the variance of weights efficiently, therefore, noise immunity of BAM is improved. At the same time, perfect recall of all training pattern pairs still can be guaranteed by the algorithm.