GLOBAL DYNAMICS OF DELAYED BIDIRECTIONAL ASSOCIATIVE MEMORY (BAM) NEURAL NETWORKS

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.

STABILITY OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DELAYS

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.

QUALITATIVE ANALYSIS OF BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS

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.

Synthesization of high-capacity auto-associative memories using complex-valued neural networks

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.

Landslide displacement prediction based on optimized empirical mode decomposition and deep bidirectional long short-term memory network

There are two technical challenges in predicting slope deformation.The first one is the random displacement,which could not be decomposed and predicted by numerically resolving the observed accumulated displacement and time series of a landslide.The second one is the dynamic evolution of a landslide,which could not be feasibly simulated simply by traditional prediction models.In this paper,a dynamic model of displacement prediction is introduced for composite landslides based on a combination of empirical mode decomposition with soft screening stop criteria(SSSC-EMD)and deep bidirectional long short-term memory(DBi-LSTM)neural network.In the proposed model,the time series analysis and SSSC-EMD are used to decompose the observed accumulated displacements of a slope into three components,viz.trend displacement,periodic displacement,and random displacement.Then,by analyzing the evolution pattern of a landslide and its key factors triggering landslides,appropriate influencing factors are selected for each displacement component,and DBi-LSTM neural network to carry out multi-datadriven dynamic prediction for each displacement component.An accumulated displacement prediction has been obtained by a summation of each component.For accuracy verification and engineering practicability of the model,field observations from two known landslides in China,the Xintan landslide and the Bazimen landslide were collected for comparison and evaluation.The case study verified that the model proposed in this paper can better characterize the"stepwise"deformation characteristics of a slope.As compared with long short-term memory(LSTM)neural network,support vector machine(SVM),and autoregressive integrated moving average(ARIMA)model,DBi-LSTM neural network has higher accuracy in predicting the periodic displacement of slope deformation,with the mean absolute percentage error reduced by 3.063%,14.913%,and 13.960%respectively,and the root mean square error reduced by 1.951 mm,8.954 mm and 7.790 mm respectively.Conclusively,this model not only has high prediction accuracy but also is more stable,which can provide new insight for practical landslide prevention and control engineering.

DISCRETE BIDIRECTIONAL ASSOCIATIVE MEMORY WITH LEARNING FUNCTION

In this paper we propose a new discrete bidirectional associative memory (DBAM) which is derived from our previous continuous linear bidirectional associative memory (LBAM). The DBAM performs bidirectionally the optimal associative mapping proposed by Kohonen. Like LBAM and NBAM proposed by one of the present authors,the present BAM ensures the guaranteed recall of all stored patterns,and possesses far higher capacity compared with other existing BAMs,and like NBAM, has the strong ability to suppress the noise occurring in the output patterns and therefore reduce largely the spurious patterns. The derivation of DBAM is given and the stability of DBAM is proved. We also derive a learning algorithm for DBAM,which has iterative form and make the network learn new patterns easily. Compared with NBAM the present BAM can be easily implemented by software.

BIDIRECTIONAL ASSOCIATIVE MEMORY ENSEMBLE

The multiple classifier system （MCS）, composed of multiple diverse classifiers or feed-forward neural networks, can significantly improve the classification or generalization ability of a single classifier. Enlightened by the fundamental idea of MCS, the ensemble is introduced into the quick learning for bidirectional associative memory （QLBAM） to construct a BAM ensemble, for improving the storage capacity and the error-correction capability without destroying the simple structure of the component BAM. Simulations show that, with an appropriate ＂overproduce and choose＂ strategy or ＂thinning＂ algorithm, the proposed BAM ensemble significantly outperforms the single QLBAM in both storage capacity and noise-tolerance capability.

Multi-Valued Associative Memory Neural Network

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.

CHAOTIC NEURAL NETWORK FOR ASSOCIATIVE MEMORY

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.

A Hopfield-like hippocampal CA3 neural network model for studying associative memory in Alzheimer's disease

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.

Double-pattern associative memory neural network with pattern loop

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.

Seismic-inversion method for nonlinear mapping multilevel well–seismic matching based on bidirectional long short-term memory networks

In this paper,the recurrent neural network structure of a bidirectional long shortterm memory network(Bi-LSTM)with special memory cells that store information is used to characterize the deep features of the variation pattern between logging and seismic data.A mapping relationship model between high-frequency logging data and low-frequency seismic data is established via nonlinear mapping.The seismic waveform is infinitely approximated using the logging curve in the low-frequency band to obtain a nonlinear mapping model of this scale,which then stepwise approach the logging curve in the high-frequency band.Finally,a seismic-inversion method of nonlinear mapping multilevel well–seismic matching based on the Bi-LSTM network is developed.The characteristic of this method is that by applying the multilevel well–seismic matching process,the seismic data are stepwise matched to the scale range that is consistent with the logging curve.Further,the matching operator at each level can be stably obtained to effectively overcome the problems that occur in the well–seismic matching process,such as the inconsistency in the scale of two types of data,accuracy in extracting the seismic wavelet of the well-side seismic traces,and multiplicity of solutions.Model test and practical application demonstrate that this method improves the vertical resolution of inversion results,and at the same time,the boundary and the lateral characteristics of the sand body are well maintained to improve the accuracy of thin-layer sand body prediction and achieve an improved practical application effect.

Memory Chain in a Chaotic Autoassociative Neural Network

Memory chain is observed in a chaotic autoassociative neural network. The network recalls first stored pattern from a fragment of a memory, stays at this pattern for a while, transits to the second stored pattern that overlaps with the first recalled pattern.Then it stays at the second recalled pattern for a while, transits to the third stored pattern that overlaps with the second recalled pattern, and so on. Thus a memory chain is generated. The memory chain ends with the pattern that overlaps no other stored patten. This phenomenon is similar to the way of recalling process of human beings in some respects.

An Incremental Time-delay Neural Network for Dynamical Recurrent Associative Memory

An incremental time-delay neural network based on synapse growth, which is suitable for dynamic control and learning of autonomous robots, is proposed to improve the learning and retrieving performance of dynamical recurrent associative memory architecture. The model allows steady and continuous establishment of associative memory for spatio-temporal regularities and time series in discrete sequence of inputs. The inserted hidden units can be taken as the long-term memories that expand the capacity of network and sometimes may fade away under certain condition. Preliminary experiment has shown that this incremental network may be a promising approach to endow autonomous robots with the ability of adapting to new data without destroying the learned patterns. The system also benefits from its potential chaos character for emergence.

Almost periodic solutions of memristive multidirectional associative memory neural networks with mixed time delays

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.

An oscillatory neural network and dynamical associative memory

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LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks

Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).

Stability analysis of discrete-time BAM neural networks based on standard neural network models

To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.