离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络 模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳 定性进行了新的分析.证明了神经网络连接权矩阵在给定的约束条件下有唯一的而且是渐近 稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳 定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经 网络.所做的分析扩展了以前的稳定性结果.     

Adaptive competitive self-organizing associative memory

This work presents the design of an adaptive competitive self-organizing associative memory (ACSAM) system for use in classification and recognition of pattern information. Volterra and Lotka's models of interacting species in biology motivated the ACSAM model; a model based on a system of nonlinear ordinary differential equations (ODEs). Self-organizing behavior is modeled for unsupervised neural networks employing the concept of interacting/competing species in biology. In this model, self-organizing properties can be implicitly coded within the systems trajectory structure using only ODEs. Among the features of this continuous-time system are: 1) the dynamic behavior is well-understood and characterized; 2) the desired fixed points are the only asymptotically stable states of the system; 3) the trajectories of ACSAM derived from the weight activities of the gradient system have no periodic or homoclinic orbits; and 4) the heteroclinic orbits that exist between equilibrium states are structurally unstable and can be removed by small perturbations.     

具有时滞的双向联想记忆神经网络的定性分析

文中通过经入一个关键性条件研究了具有时滞的双向联想记忆神经的定性性质。这一关键性条件关联了网络双向的联结权系数。在这一条件下,证明了网络存在唯一的平衡态,并且这一平衡态是全局指数稳定的。当网络的外部输入具有周期性时,利用上述条件证明了网络存在全局平稳振荡。     

On the synthesis of brain-state-in-a-box neural models with application to associative memory

In this article we present techniques for designing associative memories to be implemented by a class of synchronous discrete-time neural networks based on a generalization of the brain-state-in-a-box neural model. First, we address the local qualitative properties and global qualitative aspects of the class of neural networks considered. Our approach to the stability analysis of the equilibrium points of the network gives insight into the extent of the domain of attraction for the patterns to be stored as asymptotically stable equilibrium points and is useful in the analysis of the retrieval performance of the network and also for design purposes. By making use of the analysis results as constraints, the design for associative memory is performed by solving a constraint optimization problem whereby each of the stored patterns is guaranteed a substantial domain of attraction. The performance of the designed network is illustrated by means of three specific examples.     

Equilibrium characterization of dynamical neural networks and asystematic synthesis procedure for associative memories

Several novel results concerning the characterization of the equilibrium conditions of a continuous-time dynamical neural network model and a systematic procedure for synthesizing associative memory networks with nonsymmetrical interconnection matrices are presented. The equilibrium characterization focuses on the exponential stability and instability properties of the network equilibria and on equilibrium confinement, viz., ensuring the uniqueness of an equilibrium in a specific region of the state space. While the equilibrium confinement result involves a simple test, the stability results given obtain explicit estimates of the degree of exponential stability and the regions of attraction of the stable equilibrium points. Using these results as valuable guidelines, a systematic synthesis procedure for constructing a dynamical neural network that stores a given set of vectors as the stable equilibrium points is developed.     

A synthesis procedure for brain-state-in-a-box neural networks

In this paper, some new qualitative properties of discrete-time neural networks based on the "brain-state-in-a-box" model are presented. These properties concern both the characterization of equilibrium points and the global dynamical behavior. Next, the analysis results are used as guidelines in developing an efficient synthesis procedure for networks that function as associative memories. A constrained design algorithm is presented that gives completely stable dynamical neural networks sharing some interesting features. It is guaranteed the absence of nonbinary stable equilibria, that is stable states with nonsaturated components. It is guaranteed that in close proximity (Hamming distance one) of the stored patterns there is no other binary equilibrium point. Moreover, the presented method allows one to optimize a design parameter that controls the size of the attraction basins of the stored vectors and the accuracy needed in a digital realization of the network.     

基于线性规划的联想记忆神经网络模型

提出一种基于优化线性函数的神经网络联想记忆器,打破了将待识别模式作为网络起始点的常规,它能保证渐近稳定的平衡点集与样本点集相同,吸引域分布合理,不渐近稳定的平衡点恰为实际的拒识模式,并且电路实现容易,对拒识模式有清楚的解释。理论分析和计算机模拟都表明本文的模型是理想的联想记忆器,还可降低对硬件的精度要求。     

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。     

基于约束区域的BSB联想记忆模型

提出一种根据联想记忆点设计基于约束区域的ＢＳＢ（Ｂｒａｉｎ－Ｓｔａｔｅ－ｉｎｍ－ａ－Ｂｏｘ）神经网络模型,它保证了渐近稳定的平衡点集与样本点集相同,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,从而将ＥＳＢ完善为理想的联想记忆器。     

含时延的联想记忆神经网络的指数吸引域和指数收敛速度

采用不等式技巧和非负矩阵性质, 给出了含时延的联想记忆神经网络平衡点的指数吸引域和指数收敛速度估计以及指数稳定的一些判断条件.     

非线性连续联想记忆神经网络的分析和优化设计

研究非线性连续联想记忆神经网络的渐近稳定性,得出几个定理.在此基础上,提出了一 种优化设计方法,并给出了理论证明.目前已有的若干结论是本文所得定理的特例.     

Synthesis of Brain-State-in-a-Box (BSB) based associative memories

Presents a novel synthesis procedure to realize an associative memory using the Generalized-Brain-State-in-a-Box (GBSB) neural model. The implementation yields an interconnection structure that guarantees that the desired memory patterns are stored as asymptotically stable equilibrium points and that possesses very few spurious states. Furthermore, the interconnection structure is in general non-symmetric. Simulation examples are given to illustrate the effectiveness of the proposed synthesis method. The results obtained for the GBSB model are successfully applied to other neural network models.     

Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis

In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.     

Design of GBSB neural associative memories using semidefiniteprogramming

This paper concerns reliable search for the optimally performing GBSB (generalized brain-state-in-a-box) neural associative memory given a set of prototype patterns to be stored as stable equilibrium points. First, we observe some new qualitative properties of the GBSB model. Next, we formulate the synthesis of GBSB neural associative memories as a constrained optimization problem. Finally, we convert the optimization problem into a semidefinite program (SDP), which can be solved efficiently by recently developed interior point methods. The validity of this approach is illustrated by a design example.     

Local and global stability analysis of an unsupervised competitive neural network.

Unsupervised competitive neural networks (UCNN) are an established technique in pattern recognition for feature extraction and cluster analysis. A novel model of an unsupervised competitive neural network implementing a multitime scale dynamics is proposed in this letter. The local and global asymptotic stability of the equilibrium points of this continuous-time recurrent system whose weights are adapted based on a competitive learning law is mathematically analyzed. The proposed neural network and the derived results are compared with those obtained from other multitime scale architectures.     

Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays

Bidirectional associative memory (BAM) models are two-layer heteroassociative networks. This paper is devoted to the investigation of the global asymptotic stability for BAM neural networks with S-type distributed signal transmission delays along the axon of a neuron. A theorem and corollary was obtained in which the boundedness and differentiability of the signal functions in some papers are deleted. Some sufficient conditions for the existence of global asymtotic stable equilibrium of the networks in this paper are better than the sufficient conditions in the quoted literature.     

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.     

An optimization approach to design of generalized BSB neural associative memories

This article is concerned with the synthesis of the optimally performing GBSB (generalized brain-state-in-a-box) neural associative memory given a set of desired binary patterns to be stored as asymptotically stable equilibrium points. Based on some known qualitative properties and newly observed fundamental properties of the GBSB model, the synthesis problem is formulated as a constrained optimization problem. Next, we convert this problem into a quasi-convex optimization problem called GEVP (generalized eigenvalue problem). This conversion is particularly useful in practice, because GEVPs can be efficiently solved by recently developed interior point methods. Design examples are given to illustrate the proposed approach and to compare with existing synthesis methods.     

The restricted influence of sparseness of coding on the capacity of familiarity discrimination networks

Much evidence indicates that the perirhinal cortex is involved in the familiarity discrimination aspect of recognition memory. It has been previously shown under selective conditions that neural networks performing familiarity discrimination can achieve very high storage capacity, being able to deal with many times more stimuli than associative memory networks can in associative recall. The capacity of associative memories for recall has been shown to be highly dependent on the sparseness of coding. However, previous work on the networks of Bogacz et al, Norman and O'Reilly and Sohal and Hasselmo that model familiarity discrimination in the perirhinal cortex has not investigated the effects of the sparseness of encoding on capacity. This paper explores how sparseness of coding influences the capacity of each of these published models and establishes that sparse coding influences the capacity of the different models in different ways. The capacity of the Bogacz et al model can be made independent of the sparseness of coding. Capacity increases as coding becomes sparser for a simplified version of the neocortical part of the Norman and O'Reilly model, whereas capacity decreases as coding becomes sparser for a simplified version of the Sohal and Hasselmo model. Thus in general, and in contrast to associative memory networks, sparse encoding results in little or no advantage for the capacity of familiarity discrimination networks. Hence it may be less important for coding to be sparse in the perirhinal cortex than it is in the hippocampus. Additionally, it is established that the capacities of the networks are strongly dependent on the precise form of the learning rules (synaptic plasticity) used in the network. This finding indicates that the precise characteristics of synaptic plastic changes in the real brain are likely to have major influences on storage capacity.     

Network capacity analysis for latent attractor computation

Attractor networks have been one of the most successful paradigms in neural computation, and have been used as models of computation in the nervous system. Recently, we proposed a paradigm called 'latent attractors' where attractors embedded in a recurrent network via Hebbian learning are used to channel network response to external input rather than becoming manifest themselves. This allows the network to generate context-sensitive internal codes in complex situations. Latent attractors are particularly helpful in explaining computations within the hippocampus--a brain region of fundamental significance for memory and spatial learning. Latent attractor networks are a special case of associative memory networks. The model studied here consists of a two-layer recurrent network with attractors stored in the recurrent connections using a clipped Hebbian learning rule. The firing in both layers is competitive--K winners take all firing. The number of neurons allowed to fire, K, is smaller than the size of the active set of the stored attractors. The performance of latent attractor networks depends on the number of such attractors that a network can sustain. In this paper, we use signal-to-noise methods developed for standard associative memory networks to do a theoretical and computational analysis of the capacity and dynamics of latent attractor networks. This is an important first step in making latent attractors a viable tool in the repertoire of neural computation. The method developed here leads to numerical estimates of capacity limits and dynamics of latent attractor networks. The technique represents a general approach to analyse standard associative memory networks with competitive firing. The theoretical analysis is based on estimates of the dendritic sum distributions using Gaussian approximation. Because of the competitive firing property, the capacity results are estimated only numerically by iteratively computing the probability of erroneous firings. The analysis contains two cases: the simple case analysis which accounts for the correlations between weights due to shared patterns and the detailed case analysis which includes also the temporal correlations between the network's present and previous state. The latter case predicts better the dynamics of the network state for non-zero initial spurious firing. The theoretical analysis also shows the influence of the main parameters of the model on the storage capacity.