Showing papers on "Bidirectional associative memory published in 2008"
TL;DR: In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method in terms of linear matrix inequality (LMI).
188 citations
TL;DR: Associative memory networks based on quaternionic Hopfield neural network are investigated and it is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternion networks.
Abstract: Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.
112 citations
05 Jun 2008
TL;DR: The higher‐order correlation model show dramatic improvement in its storage capity in comparison to the conventional binary correlation model, and opens up th posibility of storing spatial‐temporal patterns and symmetry invariant patterns.
Abstract: A neural network model of associative memory with higher order learning rule is presented. The new model could be fashioned to either the auto‐associative or the multiple associative mode. Energy function, asynchronous or synchronous dynamics can be constructed. The retrieval of the stored patterns or pattern sets from an incomplete input is monotonic guaranteed by a convergence theorem. The higher‐order correlation model show dramatic improvement in its storage capity in comparison to the conventional binary correlation model. It also opens up th posibility of storing spatial‐temporal patterns and symmetry invariant patterns.
93 citations
TL;DR: Based on the topological degree theory, Lyapunov functional method and some analysis techniques, the existence and global exponential stability of the equilibrium point of the Cohen-Grossberg bidirectional associative memory neural networks with delays and impulses was investigated in this article.
Abstract: Based on the topological degree theory, Lyapunov functional method and some analysis techniques, the existence and global exponential stability of the equilibrium point of Cohen–Grossberg bidirectional associative memory neural networks with delays and impulses is first investigated. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
79 citations
TL;DR: Based on the existence and stability analysis of the neural networks with or without delay, it was found that the 2n-dimensional networks can have 3 n equilibria and 2 n equilibrium of them are locally exponentially stable, where each layer of the BAM network has n neurons as mentioned in this paper.
65 citations
TL;DR: In the paper, the global robust asymptotic stability of bidirectional associative memory (BAM) neural networks with time-varying delays and uncertainties is investigated and a novel stability criterion is presented based on the Lyapunov method.
59 citations
TL;DR: An impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with distributed delays is studied and some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions.
Abstract: An impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with distributed delays is studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions. The approaches are based on Laypunov–Kravsovskii functional and homeomorphism theory. When our results are applied to the BAM neural networks, our results generalize some previously known results. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg-type bidirectional associative memory networks.
54 citations
TL;DR: A series of new and useful criteria on the existence and uniqueness of an equilibrium point and its global asymptotical stability are established and it is shown that in some special cases of the results, the stability criteria can be easily checked.
53 citations
TL;DR: In this article, a class of two-layer hetero-associative networks called bidirectional associative memory (BAM) networks with impulses is studied and sufficient conditions are established for the existence and globally exponential stability of a unique equilibrium, which generalize and improve the previously known results.
Abstract: In this paper, a class of two-layer heteroassociative networks called bidirectional associative memory (BAM) networks with impulses is studied. Some new sufficient conditions are established for the existence and globally exponential stability of a unique equilibrium, which generalize and improve the previously known results. The sufficient conditions are easy to verify and when the impulsive jumps are absent the results reduce to those of the non-impulsive systems. The approaches are based on employing Banach’s fixed point theorem, matrix theory and its spectral theory. Our results generalize and significantly improve the previous known results due to this method. Examples are given to show the feasibility and effectiveness of our results.
43 citations
TL;DR: A new dynamical model where synapses of the associative memory could be adjusted even after the training phase as a response to an input stimulus is described, providing some propositions that guarantee perfect and robust recall of the fundamental set of associations.
Abstract: The brain is not a huge fixed neural network, but a dynamic, changing neural network that continuously adapts to meet the demands of communication and computational needs. In classical neural networks approaches, particularly associative memory models, synapses are only adjusted during the training phase. After this phase, synapses are no longer adjusted. In this paper we describe a new dynamical model where synapses of the associative memory could be adjusted even after the training phase as a response to an input stimulus. We provide some propositions that guarantee perfect and robust recall of the fundamental set of associations. In addition, we describe the behavior of the proposed associative model under noisy versions of the patterns. At last, we present some experiments aimed to show the accuracy of the proposed model.
TL;DR: In this article, the global asymptotic stability of uncertain stochastic fuzzy bidirectional associative memory (BAM) neural networks with time-varying delays is analyzed.
TL;DR: In this article, a class of bidirectional associative memory (BAM) networks with transmission delays and nonlinear impulses are studied, and sufficient conditions are established for the existence and global exponential stability of a unique equilibrium, which generalize and improve the previously known results.
Abstract: In this paper, a class of bidirectional associative memory (BAM) networks with transmission delays and nonlinear impulses are studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium, which generalize and improve the previously known results. The sufficient conditions are easy to verify and when the impulsive jumps are linear or absent the results reduce to those of common impulsive or non-impulsive systems. Finally, an example is given to show the feasibility and effectiveness of our results.
16 Jul 2008
TL;DR: Kosko’s FAM suffers from an extremely low storage capacity of one rule per FAM matrix, which limits its applications to problems such as backing up a truck and trailer, target tracking, and voice cell control in ATM networks.
Abstract: Fuzzy associative memories (FAMs) belong to the class of fuzzy neural networks (FNNs). A FNN is an artificial neural network (ANN) whose input patterns, output patterns, and/or connection weights are fuzzy-valued [19, 11]. Research on FAM models originated in the early 1990’s with the advent of Kosko’s FAM [35, 37]. Like many other associative memory models, Kosko’s FAM consists of a single-layer feedforward FNN that stores the fuzzy rule “If x is Xk then y is Yk” using a fuzzy Hebbian learning rule in terms of max-min or max-product compositions for the synthesis of its weight matrix W . Despite successful applications of Kosko’s FAMs to problems such as backing up a truck and trailer [35], target tracking [37], and voice cell control in ATM networks [44], Kosko’s FAM suffers from an extremely low storage capacity of one rule per FAM matrix. Therefore, Kosko’s overall
TL;DR: Global exponential stability criteria are established for BAM NNs with time delays by applying Young's inequality and Holder's inequality techniques together with the properties of monotonic continuous functions.
Abstract: In this paper, we consider delayed bidirectional associative memory (BAM) neural networks (NNs) with Lipschitz continuous activation functions. By applying Young's inequality and Holder's inequality techniques together with the properties of monotonic continuous functions, global exponential stability criteria are established for BAM NNs with time delays. This is done through the use of a new Lyapunov functional and an M-matrix. The results obtained in this paper extend and improve previous results.
TL;DR: Based on the proper Lyapunov functions and the Jacobsthal liner inequality, some sufficient conditions are presented in this paper for global asymptotic stability of delay bidirectional associative memory neural networks with impulses.
Abstract: Based on the proper Lyapunov functions and the Jacobsthal liner inequality, some sufficient conditions are presented in this paper for global asymptotic stability of delay bidirectional associative memory neural networks with impulses. The obtained results are independently of the delay parameters and can be easily verified. Also, some remarks and an illustrative example are given to demonstrate the effectiveness of the obtained results.
TL;DR: It is shown that because of shrinking effects of impulse the DBAM may be globally exponentially stable even if the evolution of its continuous component deviates from the equilibrium point.
Abstract: This brief studies the stabilizing effects of impulses in delayed bidirectional associative memory (DBAM) neural networks when its continuous component does not converge asymptotically to the equilibrium point. A general criterion, which characterizes the aggregated effects of the impulse and the deviation of its continuous component from the equilibrium point on the exponential stability of the considered DBAM, is established by using Lyapunov-Razumikhin technique. It is shown that because of shrinking effects of impulse the DBAM may be globally exponentially stable even if the evolution of its continuous component deviates from the equilibrium point.
TL;DR: This is the first time applying the time scale calculus theory to unify and improve discrete-time and continuous-time bi-directional associate memory neural network under the same framework.
TL;DR: A new bidirectional hetero-associative memory model for true-color patterns that uses the associative model with dynamical synapses recently introduced in Vazquez and Sossa to guarantee perfect and robust recall of the fundamental set of associations.
Abstract: Classical bidirectional associative memories (BAM) have poor memory storage capacity, are sensitive to noise, are subject to spurious steady states during recall, and can only recall bipolar patterns. In this paper, we introduce a new bidirectional hetero-associative memory model for true-color patterns that uses the associative model with dynamical synapses recently introduced in Vazquez and Sossa (Neural Process Lett, Submitted, 2008). Synapses of the associative memory could be adjusted even after the training phase as a response to an input stimulus. Propositions that guarantee perfect and robust recall of the fundamental set of associations are provided. In addition, we describe the behavior of the proposed associative model under noisy versions of the patterns. At last, we present some experiments aimed to show the accuracy of the proposed model with a benchmark of true-color patterns.
TL;DR: Pseudo-relaxation learning algorithm is applied to CAM (Complex-valued Associative Memory) in order to improve the storage capacity of CAM by the Hebb rule.
Abstract: HAM (Hopfield Associative Memory) and BAM (Bidirectinal Associative Memory) are representative associative memories by neural networks. The storage capacity by the Hebb rule, which is often used, is extremely low. In order to improve it, some learning methods, for example, pseudo-inverse matrix learning and gradient descent learning, have been introduced. Oh introduced pseudo-relaxation learning algorithm to HAM and BAM. In order to accelerate it, Hattori proposed quick learning. Noest proposed CAM (Complex-valued Associative Memory), which is complex-valued HAM. The storage capacity of CAM by the Hebb rule is also extremely low. Pseudo-inverse matrix learning and gradient descent learning have already been generalized to CAM. In this paper, we apply pseudo-relaxation learning algorithm to CAM in order to improve the capacity.
TL;DR: In this article, the global asymptotic stability of delay bi-directional associative memory neural networks with impulses was studied and a sufficient condition which is independent with the delayed quantity was given.
TL;DR: The RKAM can outperform the aforementioned associative memory models, becoming equivalent to them when a dominance condition is fulfilled by the kernel matrix, and a statistical measure is proposed which can be easily computed from the probability distribution of the interpattern Hamming distance or directly estimated from the memory vectors.
Abstract: In this paper, we analyze a model of recurrent kernel associative memory (RKAM) recently proposed by Garcia and Moreno. We show that this model consists in a kernelization of the recurrent correlation associative memory (RCAM) of Chiueh and Goodman. In particular, using an exponential kernel, we obtain a generalization of the well-known exponential correlation associative memory (ECAM), while using a polynomial kernel, we obtain a generalization of higher order Hopfield networks with Hebbian weights. We show that the RKAM can outperform the aforementioned associative memory models, becoming equivalent to them when a dominance condition is fulfilled by the kernel matrix. To ascertain the dominance condition, we propose a statistical measure which can be easily computed from the probability distribution of the interpattern Hamming distance or directly estimated from the memory vectors. The RKAM can be used below saturation to realize associative memories with reduced dynamic range with respect to the ECAM and with reduced number of synaptic coefficients with respect to higher order Hopfield networks.
TL;DR: By utilizing the Lyapunov functional method, applying M-matrix, Young inequality technique and other analysis techniques, sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non-autonomous hybrid bidirectional associative memory (BAM) neural networks with Lipschitzian activation functions.
Abstract: In this paper, by utilizing the Lyapunov functional method, applying M-matrix, Young inequality technique and other analysis techniques, we analyze the exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses. Sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non-autonomous hybrid bidirectional associative memory (BAM) neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Finally, two examples are also provided to demonstrate the effectiveness of the results obtained.
TL;DR: In this paper, sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for bidirectional associative memory Hopfield-type neural networks with impulse, based on contraction principle and Gronwall-Bellman's inequality.
Abstract: In this paper, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for bidirectional associative memory Hopfield-type neural networks with impulse. The approaches are based on contraction principle and Gronwall–Bellman’s inequality. This paper is considering the almost periodic solution for impulsive Hopfield-type neural networks.
08 Jul 2008
TL;DR: The results show that DHGN offers lower computational complexity with better recall efficiency compared to the Hopfield network.
Abstract: In this paper, we conduct a comparative analysis of two associative memory-based pattern recognition algorithms We compare the established Hopfield network algorithm with our novel Distributed Hierarchical Graph Neuron (DHGN) algorithm The computational complexity and recall efficiency aspects of these algorithms are discussed The results show that DHGN offers lower computational complexity with better recall efficiency compared to the Hopfield network
TL;DR: The paper discusses the stability of non-autonomous bidirectional associative memory neural networks by using Gaines and Mawhin's continuation theorem of coincidence degree theory and criterions on asymptotic stability and exponential stability of periodic solutions of the neural networks are obtained.
TL;DR: In this paper, a discrete bidirectional associative memory neural network with delays is investigated and its dynamics are studied in terms of local analysis and Hopf bifurcation analysis.
Abstract: A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results.
TL;DR: This work derives some explicit equations based on the theory of dynamical systems, which relate the stability properties of fixed points to the network parameter values and proves that the proposed model needs much fewer neurons to store numerous stable fixed points, but also is able to learn asymmetric arrangement of fixed Points, whereas the SFNN model is limited to orthogonal arrangements.
03 Sep 2008
TL;DR: This work compares and contrast associative memory function in a network of biologically-based spiking neurons with previously published results for a simple artificial neural network model and investigates biologically plausible implementations of methods for improving recall under biologically realistic conditions, such as a sparsely connected network.
Abstract: Associative neural network models are a commonly used methodology when investigating the theory of associative memory in the brain. Comparisons between the mammalian hippocampus and neural network models of associative memory have been investigated [7]. Biologically based networks are complex systems built of neurons with a variety of properties. Here we compare and contrast associative memory function in a network of biologically-based spiking neurons [14] with previously published results for a simple artificial neural network model [6]. We investigate biologically plausible implementations of methods for improving recall under biologically realistic conditions, such as a sparsely connected network.
TL;DR: Using the drive-response concept, hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria based on Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) technique.
Abstract: This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, and covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, recurrent multilayer perceptrons (RMLPs). By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) technique, some exponential synchronization criteria are derived. Using the drive-response concept, hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria. Finally, detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.