基于极大极小准则的Hopfield联想记忆学习算法*

基于联想记忆各记忆模式的吸引域之间应保持大小平衡的思想．提出了设计Hopfield联想记忆网络的极大极小准则，即设计出的对称连接权阵应使得网络最小的记忆模式吸引域达到最大．首先提出了一种快速学习算法;再发展了一个启发性迭代学习算法，称为约束感知器优化学习算法．大量实验结果表明了本文学习算法的优越性．     

联想记忆神经网络的训练

提出了一种联想记忆神经网络的优化训练方案,说明网络的样本吸引域可用阱深参数作 一定程度的控制,使网络具有尽可能好的容错性.计算表明,训练网络可达到α＜1(α=M/ N,N是神经元数,M是贮存样本数),而仍有良好的容错性,明显优于外积法、正交化外积法、 赝逆法等常用方案.文中还对训练网络的对称性与收敛性问题进行了讨论.     

对基于匹配滤波器的联想记忆模型的分析

近来,一些学者提出了用匹配滤波器实现的联想记忆模型,本文对这种模型进行了详细的分析。首先,讨论了模型中记忆样本模式的稳定性,提出了几个保证稳定性的充分条件;其次,分析了模型的误差校正能力,指出了当要求样本模式具有一定的吸引性时,模型中非线性加权函数应满足的约束条件;最后,利用信噪比分析了模型的记忆容量,并指出在取加权函效为指数函数的情况下,记忆容量与样本矢量的长度N成指数关系。     

基于遗传算法的Hopfield联想记忆吸引域的优化

由于一般离散Hopfield神经网络存在很多伪稳定点.使稳定点的吸引域变小.网络很难获得真正的最优解.因此,提出将遗传算法应用到Hopfield联想记忆神经网络中.利用遗传算法对复杂、多峰、非线性极不可微函数实现全局搜索性质.对Hopfield联想记忆吸引域进行优化,使待联想模式跳出伪模式的吸引域.使Hopfield网络在较高噪信比的情况下保持较高的联想成功率.仿真结果证明了该方法的有效性.     

一种新型双向联想记忆神经网络

提出了一种新型双向联想记忆神经网络,此网络将两个相互关联的模式以模式对的形式存储在由N个连接构成的模式环中,记忆容量为22N数量级,完全消除了假模式对、能够全部或部分地回忆出与输入模式对具有最小Hamming距的被记忆的模式对,同时具有较高的记忆效率和可靠性。连接由“连接状态”和“禁止路径”组成,前者直接存储二进制模式对向量的分量,后者用于消除假模式;此神经网络具有正向联想、逆向联想和自联想方式,使得网络能更灵活有效地满足不同的回忆要求。     

模拟反馈联想记忆的吸引域和指数收敛速度的估计及其应用

本文得到了若干关于模拟反馈联想记忆各记忆模式的吸引域及其中每一点趋向相应记忆模式的指数收敛速度的估计结果，它们可用于高效模拟反馈联想记忆的性能评价以及综合过程．     

具有二级模式的多状态神经元联想记忆网络

提出了一种新型的联想记忆神经网络,神经元的状态为向量,含N个神经元的网络中存储的模式由N个具有M个分量的二级模式组成,每个模式存储在一个由N个连接组成的“模式环”中,连接由“连接状态”和“禁止路径”组成,前者用于存储二级模式,后者用于消除假模式,回忆时允许输入不完整的模式,记忆容量为(N-1)！。     

讲座：人工神经网络：第四讲 反馈网络与联想记忆（续）

4基本学习规则Hopfield网络的学习，采用的是无导师学习。学习的过程相应于形成网络的连接权矩阵W。讨论的中心问题在于，如何使网络对于给定的问题进行学习，建立连接权矩阵，并使网络具有较强的联想记忆能力。假设需要存贮的记忆样本有P个X1，X2，…，XPXi∈{－1， 1}n（1）Hebb学习规则a．对一个模式的学习为了分析简便，首先考虑网络对一个模式的学习。这时需要存贮的记忆样本只有1个（设为X1），它将成为网络的稳定状态，并具有最大的吸引域，或者说具有最大的“纠错能力”。将记忆样本X1输入到网络，并作为网络的初始状态，经过…     

混沌在Hopfield联想记忆网络中的应用

将混沌应用到Hofield联想记忆网络中,利用混沌的遍历性和随机性等独特的性质,可以使待联想模式跳出伪模式的吸引域,而到达存储模式的吸引域内,从而解决了Hopfield网络在噪信比较高的情况下,联想成功率较低的问题。仿真结果证明了该方法的有效性。     

一种以环路作为存储单元的联想记忆神经网络

文章提出了一种新型联想记忆神经网络,每个模式被存储在一个通过网络中所有神经元的环路中,连接包括逻辑状态和一组神经元编号,网络中处理和传递的信号为神经元编号组成的序列,神经元执行一组处理这种序列的符号和逻辑运算;网络记忆容量为2N-2N、完全消除了假模式、同时具有更高的记忆效率和可靠性。     

关联优化存储下Hopfield网络的临界存储

本文通过对Ｈｏｐｆｉｅｌｄ神经网络存储相关信息的联想稳定性分析，给出了选取存储样本的优化规则，并得出Ｈｏｐｆｉｅｌｄ神经网络在优化存储规则下各存储样本均能纠一错的临床存储容量约为０．５Ｎ，比随机选取存储本的容量要强得多。     

A binary pattern classification using potts model

The paper offers a new kind of neural network for classifying binary patterns. Given the dimensionality of patterns, the memory capacity of the network grows exponentially with free parameter s. The paper considers the limitations for parameter s caused by the fact that greater values of demand large computer memory and decrease the basin of attraction we have. In contrast to similar models, the network enjoys larger memory capacity and better recognition capabilities—it can distinguish heavily distorted patterns and even cope with pattern correlation. The negative effect of the latter can be easily suppressed by taking a large enough value of s. A perceptron recognition system is considered to demonstrate the efficiency of the algorithm, yet the method is quite applicable in fully connected associative-memory networks. The article is published in the original.     

Long-term attraction in higher order neural networks

Recent results on the memory storage capacity of higher order neural networks indicate a significant improvement compared to the limited capacity of the Hopfield model. However, such results have so far been obtained under the restriction that only a single iteration is allowed to converge. This paper presents a indirect convergence (long-term attraction) analysis of higher order neural networks. Our main result is that for any kappa(d)相似文献   

Pattern storage and processing in attractor networks with short-time synaptic dynamics

Neurophysiological experiments show that the strength of synaptic connections can undergo substantial changes on a short time scale. These changes depend on the history of the presynaptic input. Using mean-field techniques, we study how short-time dynamics of synaptic connections influence the performance of attractor neural networks in terms of their memory capacity and capability to process external signals. For binary discrete-time as well as for firing rate continuous-time neural networks, the fixed points of the network dynamics are shown to be unaffected by synaptic dynamics. However, the stability of patterns changes considerably. Synaptic depression turns out to reduce the storage capacity. On the other hand, synaptic depression is shown to be advantageous for processing of pattern sequences. The analytical results on stability, size of the basins of attraction and on the switching between patterns are complemented by numerical simulations.     

The Object Perceptron Learning Algorithm on Generalised Hopfield Networks for Associative Memory

We present a study of generalised Hopfield networks for associative memory. By analysing the radius of attraction of a stable state, the Object Perceptron Learning Algorithm (OPLA) and OPLA scheme are proposed to store a set of sample patterns (vectors) in a generalised Hopfield network with their radii of attraction as large as we require. OPLA modifies a set of weights and a threshold in a way similar to the perceptron learning algorithm. The simulation results show that the OPLA scheme is more effective for associative memory than both the sum-of-outer produce scheme with a Hopfield network and the weighted sum-of-outer product scheme with an asymmetric Hopfield network.     

量子Hopfield神经网络及图像识别

传统的Hopfield网络的存储容量是神经元个数的0·14倍(P=0·14N)。由于它在识别大量的图像或模式时遇到了巨大的困难,所以研究人员一直在寻找新的方法。由量子计算和神经网络结合而产生的量子神经网络是新兴和前沿的学科之一。为了提高图像识别的速度和增加图像识别量,在分析了量子线性叠加特性的基础上,提出了一种用于存储矩阵元素的基于概率分布的量子Hopfield神经网络,它在存储容量或记忆容量上提高到了神经元个数的2N倍,比传统的Hopfield神经网络有了指数级的提高。通过图像识别的实例分析和仿真试验的结果表明,该量子Hopfield神经网络能有效地识别图像或模式,并且工作过程符合量子演化过程。     

基于约束区域的连续时间联想记忆神经网络

传统的联想记忆神经网络模型是根据联想记忆点设计权值。文中提出一种根据联想记忆点设计基于约束区域的神经网络模型,它保证了渐近稳定的平衡点集与样要点集相同,不渐近稳定的平衡点恰为实际的拒识状态,并且吸引域分布合理。它具有学习和遗忘能力,还具有记忆容量大和电路可实现优点,是理想的联想记忆器。     

Exact associative neural memory dynamics utilizing Boolean matrices

The exact dynamics of shallow loaded associative neural memories are generated and characterized. The Boolean matrix analysis approach is employed for the efficient generation of all possible state transition trajectories for parallel updated binary-state dynamic associative memories (DAMs). General expressions for the size of the basin of attraction of fundamental and oscillatory memories and the number of oscillatory and stable states are derived for discrete synchronous Hopfield DAMs loaded with one, two, or three even-dimensionality bipolar memory vectors having the same mutual Hamming distances between them. Spurious memories are shown to occur only if the number of stored patterns exceeds two in an even-dimensionality Hopfield memory. The effects of odd- versus even-dimensionality memory vectors on DAM dynamics and the effects of memory pattern encoding on DAM performance are tested. An extension of the Boolean matrix dynamics characterization technique to other, more complex DAMs is presented.     

Parallel Hopfield networks

We introduce a novel type of neural network, termed the parallel Hopfield network, that can simultaneously effect the dynamics of many different, independent Hopfield networks in parallel in the same piece of neural hardware. Numerically we find that under certain conditions, each Hopfield subnetwork has a finite memory capacity approaching that of the equivalent isolated attractor network, while a simple signal-to-noise analysis sheds qualitative, and some quantitative, insight into the workings (and failures) of the system.     

一种基于MRⅡ算法的三层二值双向联想记忆网络

传统的两层二值双向联想记忆(BAM)网络因其结构的限制存在着存储容量有限、区分小差别模式和存储非正交模式能力不足的缺陷,结构上将其扩展至三层网络是一个有效的解决思路,但是三层二值BAM网络的学习是一个难题,而三层连续型BAM网络又存在处理二值问题不方便的问题。为了解决这些问题,提出一种三层结构的二值双向联想记忆网络,创新之处是采用了二值多层前向网络的MRⅡ算法实现了三层二值BAM网络的学习。实验结果表明,基于MRⅡ算法的三层二值BAM网络极大地提高了网络的存储容量和模式区分能力,同时保留了二值网络特定的优势,具有较高的理论与实用价值。