In this paper the globally asymptotic stability of more general two-layer nonlinear feedback associative memory neural networks with time delays is examined. The sufficient conditions of existence, uniqueness and glob...In this paper the globally asymptotic stability of more general two-layer nonlinear feedback associative memory neural networks with time delays is examined. The sufficient conditions of existence, uniqueness and globally asymptotic stability of the equilibrum position are given. Finally, two interesting examples to illustrate the theory are given.展开更多
In this paper, the global exponential stability of an equilibrium position for general bidirectional associative memory neural networks are studied. The sufficient conditions of existence and uniqueness of the equilib...In this paper, the global exponential stability of an equilibrium position for general bidirectional associative memory neural networks are studied. The sufficient conditions of existence and uniqueness of the equilibrium position are given. The method of energy function is examined. Two examples are given to illustrate the theory.展开更多
A novel learning method for multi-valued associative memory network is introduced, which is based on Hebb rule, but utilizes more information. According to the current probe vector, the connection weights matrix could...A novel learning method for multi-valued associative memory network is introduced, which is based on Hebb rule, but utilizes more information. According to the current probe vector, the connection weights matrix could be chosen dynamically. Double-valued and multi-valued associative memory are all realized in our simulation experiment. The experimental results show that the method could enhance the associative success rate.展开更多
Based on current research on applications of chaotic neuron network for information processing, the stability and convergence of chaotic neuron network are proved from the viewpoint of energy function. Moreover, a new...Based on current research on applications of chaotic neuron network for information processing, the stability and convergence of chaotic neuron network are proved from the viewpoint of energy function. Moreover, a new auto-associative matrix is devised for artificial neural network composed of chaotic neurons, thus, an improved chaotic neuron network for associative memory is built up. Finally, the associative recalling process of the network is analyzed in detail and explanations of improvement are given.展开更多
In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. S...In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluat...The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluation of error-correction capability and the synthesis procedures for continuous-time associative memory neural networks.展开更多
In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stab...In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.展开更多
A unified bidirectional associative memory model (UBAM) isproposed- Its two special cases, UHOBAM and UEBAM, are the modifica-tions of intraconnected BAM (IBAM) and higher-order BAM (HOBAM),exponential BAM (EBAM) and ...A unified bidirectional associative memory model (UBAM) isproposed- Its two special cases, UHOBAM and UEBAM, are the modifica-tions of intraconnected BAM (IBAM) and higher-order BAM (HOBAM),exponential BAM (EBAM) and modified exponential BAM (MEBAM) , re-展开更多
A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of r...A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of realization is spent for the improvement.展开更多
This paper addressed a statistical analysis for the recall of parallel intraconnected bidirectional associative memory-Modified Intraconnected Bidirectional Associative Memory (MIBAM) and proved the conclusions: two M...This paper addressed a statistical analysis for the recall of parallel intraconnected bidirectional associative memory-Modified Intraconnected Bidirectional Associative Memory (MIBAM) and proved the conclusions: two MIBAM with the equal total number of neurons have the equal recalling probability for m pairs of stored pattern pairs if m is not too large. So they have the same capacity and same error correcting ability, i. e., their performances are statistically equivalent. The results of simulation support the conclusions well.展开更多
Asymptotical stability is an important property of the associative memory neural networks.In this comment,we demonstrate that the asymptotical stability analyses of the MVECAM and MV-eBAM in the asynchronous update ...Asymptotical stability is an important property of the associative memory neural networks.In this comment,we demonstrate that the asymptotical stability analyses of the MVECAM and MV-eBAM in the asynchronous update mode by Wang et al are not rigorous,and then we modify the errors and further prove that the two models are all asymptotically stable in both synchronous and asynchronous update modes.展开更多
A double-pattern associative memory neural network with “pattern loop” is proposed. It can store 2N bit bipolar binary patterns up to the order of 2 2N , retrieve part or all of the stored patterns which all have th...A double-pattern associative memory neural network with “pattern loop” is proposed. It can store 2N bit bipolar binary patterns up to the order of 2 2N , retrieve part or all of the stored patterns which all have the minimum Hamming distance with input pattern, completely eliminate spurious patterns, and has higher storing efficiency and reliability than conventional associative memory. The length of a pattern stored in this associative memory can be easily extended from 2N to kN.展开更多
A new bidirectional associative memory model named as HOMIBAM is introduced. The relationships of HOMIBAM with the models existed are pointed out. Both theoretical analysis and simulations show that the capacity and r...A new bidirectional associative memory model named as HOMIBAM is introduced. The relationships of HOMIBAM with the models existed are pointed out. Both theoretical analysis and simulations show that the capacity and recall performance of HOMIBAM are superior to that of modified intraconnected BAM (MIBAM), higher-order BAM (HOBAM ) greatly.展开更多
Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associativ...Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix_algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters,the connection matrix and the Lipschitz constant of the activation functions,are not only simple and practical,but also easier to check and less conservative than those imposed by similar results in recent literature.展开更多
Associative memory, one of the major cognitive functions in the hippocampal CA3 region, includes auto-associative memory and hetero-associative memory. Many previous studies have shown that Alzheimer's disease (AD)...Associative memory, one of the major cognitive functions in the hippocampal CA3 region, includes auto-associative memory and hetero-associative memory. Many previous studies have shown that Alzheimer's disease (AD) can lead to loss of functional synapses in the central nervous system, and associative memory functions in patients with AD are often impaired, but few studies have addressed the effect of AD on hetero-associative memory in the hippocampal CA3 region. In this study, based on a simplified anatomical structure and synaptic connections in the hippocampal CA3 region, a three-layered Hopfield-like neural network model of hippocampal CA3 was proposed and then used to simulate associative memory functions in three circumstances: normal, synaptic deletion and synaptic compensation, according to Ruppin's synaptic deletion and compensation theory. The influences of AD on hetero-associative memory were further analyzed. The simulated results showed that the established three-layered Hopfield-like neural network model of hippocampal CA3 has both auto-associative and hetero-associative memory functions. With increasing synaptic deletion level, both associative memory functions were gradually impaired and the mean firing rates of the neurons within the network model were decreased. With gradual increasing synaptic compensation, the associative memory functions of the network were improved and the mean firing rates were increased. The simulated results suggest that the Hopfield-like neural network model can effectively simulate both associative memory functions of the hippocampal CA3 region. Synaptic deletion affects both auto-associative and hetero-associative memory functions in the hippocampal CA3 region, and can also result in memory dysfunction. To some extent, synaptic compensation measures can offset two kinds of associative memory dysfunction caused by synaptic deletion in the hippocampal CA3 area.展开更多
This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can genera...This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.展开更多
We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics d...We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely eliminate crosstalk and spurious memories. The number of control qubits plays the role of an inverse fictitious temperature. The accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models thus solve the capacity shortage problem of classical associative memories, providing a polynomial improvement in capacity. The price to pay is the probabilistic nature of information retrieval.展开更多
文摘In this paper the globally asymptotic stability of more general two-layer nonlinear feedback associative memory neural networks with time delays is examined. The sufficient conditions of existence, uniqueness and globally asymptotic stability of the equilibrum position are given. Finally, two interesting examples to illustrate the theory are given.
基金Supported by the National Natural Science Foundation of China
文摘In this paper, the global exponential stability of an equilibrium position for general bidirectional associative memory neural networks are studied. The sufficient conditions of existence and uniqueness of the equilibrium position are given. The method of energy function is examined. Two examples are given to illustrate the theory.
文摘A novel learning method for multi-valued associative memory network is introduced, which is based on Hebb rule, but utilizes more information. According to the current probe vector, the connection weights matrix could be chosen dynamically. Double-valued and multi-valued associative memory are all realized in our simulation experiment. The experimental results show that the method could enhance the associative success rate.
基金National Natural Science Foundation of P.R.China(No. 69735101)
文摘Based on current research on applications of chaotic neuron network for information processing, the stability and convergence of chaotic neuron network are proved from the viewpoint of energy function. Moreover, a new auto-associative matrix is devised for artificial neural network composed of chaotic neurons, thus, an improved chaotic neuron network for associative memory is built up. Finally, the associative recalling process of the network is analyzed in detail and explanations of improvement are given.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503338,61573316,61374152,and 11302195)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金Supported by the National Natural Science Foundation of Chinathe Climb Project of China
文摘The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluation of error-correction capability and the synthesis procedures for continuous-time associative memory neural networks.
文摘In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.
文摘A unified bidirectional associative memory model (UBAM) isproposed- Its two special cases, UHOBAM and UEBAM, are the modifica-tions of intraconnected BAM (IBAM) and higher-order BAM (HOBAM),exponential BAM (EBAM) and modified exponential BAM (MEBAM) , re-
基金Supported by Climbing Program-National Key Project for Fundamental Research in China
文摘A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of realization is spent for the improvement.
基金Supported by Climbing Program-National Key Project for Fundamental Research in China
文摘This paper addressed a statistical analysis for the recall of parallel intraconnected bidirectional associative memory-Modified Intraconnected Bidirectional Associative Memory (MIBAM) and proved the conclusions: two MIBAM with the equal total number of neurons have the equal recalling probability for m pairs of stored pattern pairs if m is not too large. So they have the same capacity and same error correcting ability, i. e., their performances are statistically equivalent. The results of simulation support the conclusions well.
基金The project is supported by the National Natural Science Foundation of China (60873231 and 60973046)Major State Basic Research Development Pro-gram of China (2011CB302903)+2 种基金Natural Science Foundation of Jiangsu Province(BK2009426)Research and Innovation Plan for College Graduates of Jiangsu Province(CX10B_195Z) the Scientific Research Foundation of Nanjing University of Posts and Telecommunications(NY210043)
文摘Asymptotical stability is an important property of the associative memory neural networks.In this comment,we demonstrate that the asymptotical stability analyses of the MVECAM and MV-eBAM in the asynchronous update mode by Wang et al are not rigorous,and then we modify the errors and further prove that the two models are all asymptotically stable in both synchronous and asynchronous update modes.
文摘A double-pattern associative memory neural network with “pattern loop” is proposed. It can store 2N bit bipolar binary patterns up to the order of 2 2N , retrieve part or all of the stored patterns which all have the minimum Hamming distance with input pattern, completely eliminate spurious patterns, and has higher storing efficiency and reliability than conventional associative memory. The length of a pattern stored in this associative memory can be easily extended from 2N to kN.
基金Supported by Climbing Progamme-National Key Project for Fundamental Research in China
文摘A new bidirectional associative memory model named as HOMIBAM is introduced. The relationships of HOMIBAM with the models existed are pointed out. Both theoretical analysis and simulations show that the capacity and recall performance of HOMIBAM are superior to that of modified intraconnected BAM (MIBAM), higher-order BAM (HOBAM ) greatly.
文摘Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix_algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters,the connection matrix and the Lipschitz constant of the activation functions,are not only simple and practical,but also easier to check and less conservative than those imposed by similar results in recent literature.
基金the National Natural Science Foundation of China,No.30870649the Natural Science Foundation of Tianjin,No.08JCYBJC03300
文摘Associative memory, one of the major cognitive functions in the hippocampal CA3 region, includes auto-associative memory and hetero-associative memory. Many previous studies have shown that Alzheimer's disease (AD) can lead to loss of functional synapses in the central nervous system, and associative memory functions in patients with AD are often impaired, but few studies have addressed the effect of AD on hetero-associative memory in the hippocampal CA3 region. In this study, based on a simplified anatomical structure and synaptic connections in the hippocampal CA3 region, a three-layered Hopfield-like neural network model of hippocampal CA3 was proposed and then used to simulate associative memory functions in three circumstances: normal, synaptic deletion and synaptic compensation, according to Ruppin's synaptic deletion and compensation theory. The influences of AD on hetero-associative memory were further analyzed. The simulated results showed that the established three-layered Hopfield-like neural network model of hippocampal CA3 has both auto-associative and hetero-associative memory functions. With increasing synaptic deletion level, both associative memory functions were gradually impaired and the mean firing rates of the neurons within the network model were decreased. With gradual increasing synaptic compensation, the associative memory functions of the network were improved and the mean firing rates were increased. The simulated results suggest that the Hopfield-like neural network model can effectively simulate both associative memory functions of the hippocampal CA3 region. Synaptic deletion affects both auto-associative and hetero-associative memory functions in the hippocampal CA3 region, and can also result in memory dysfunction. To some extent, synaptic compensation measures can offset two kinds of associative memory dysfunction caused by synaptic deletion in the hippocampal CA3 area.
文摘This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.
文摘We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely eliminate crosstalk and spurious memories. The number of control qubits plays the role of an inverse fictitious temperature. The accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models thus solve the capacity shortage problem of classical associative memories, providing a polynomial improvement in capacity. The price to pay is the probabilistic nature of information retrieval.
基金This work was supported by the National Natural Science Foundation of China (61125303), the Program for Science and Technology in Wuhan, China (2014010101010004), the Program for Changjiang Scholars and Innovative Research Team in University of China (IRTt245), China Three Gorges University Science Foundation (KJ2013B020), Hubei Key Laboratory of Cascaded Hydropower Stations Operation and Control Program (2013KJX12), and Hubei Science and Technology Support Program (2015BAA106)