Showing papers on "Bidirectional associative memory published in 2023"

Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

Abstract: Applying delayed dynamical models to characterize the dynamics of neural networks has attracted great interest from scientific community. In this current manuscript, a kind of new tri-neuron bidirectional associative memory (BAM) neural networks including delay are formulated. The properties of solution and Hopf bifurcation issue of the established tri-neuron BAM neural networks including delay are investigated. First, we check the existence and uniqueness of the solution to the formulated delayed tri-neuron BAM neural networks by virtue of fixed point theorem. Second, we seek the boundedness of the solution of the formulated delayed tri-neuron BAM neural networks in view of a suitable function and inequality skills. Third, the delay-independent criteria on stability and bifurcation of the formulated delayed tri-neuron BAM neural networks are acquired. Fourth, Hopf bifurcation control aspect of the formulated delayed tri-neuron BAM neural networks is explored via designing two proper hybrid controllers. To prove the accuracy of gained primary assertions, software simulation experiments are put into practice.

Finite-Time Estimation for Markovian BAM Neural Networks With Asymmetrical Mode-Dependent Delays and Inconstant Measurements

Abstract: The issue of finite-time state estimation is studied for discrete-time Markovian bidirectional associative memory neural networks. The asymmetrical system mode-dependent (SMD) time-varying delays (TVDs) are considered, which means that the interval of TVDs is SMD. Because the sensors are inevitably influenced by the measurement environments and indirectly influenced by the system mode, a Markov chain, whose transition probability matrix is SMD, is used to describe the inconstant measurement. A nonfragile estimator is designed to improve the robustness of the estimator. The stochastically finite-time bounded stability is guaranteed under certain conditions. Finally, an example is used to clarify the effectiveness of the state estimation.

Robustness Analysis of BAM Cellular Neural Network with Deviating Arguments of Generalized Type

Abstract: By generating equivalent integral equations, we analyze the existence and uniqueness of solutions of bidirectional associative memory cellular neural network (BAMCNN) with deviating arguments firstly. Secondly, the question of robustness of stability (RoS) of BAMCNN with deviating argument is studied. Using the Gronwall inequality, we calculate the upper bounds of the interference intensities that can maintain the initial stability of system. The perturbed BAMCNN will maintain its original stability if the strength of one or more perturbations is less than the upper bounds that we calculated in this study. To demonstrate the validity of the conjectural values, a variety of numerical illustrations are provided.

The Exponential Capacity of Dense Associative Memories

Abstract: Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another interesting feature of these networks is their connection to the attention mechanism which is part of the Transformer architectures widely applied in deep learning. In this work, we consider a generic family of pattern ensembles, and thanks to the statistical mechanics analysis of an auxiliary Random Energy Model, we are able to provide exact asymptotic thresholds for the retrieval of a typical pattern, $\alpha_1$, and lower bounds for the maximum of the load $\alpha$ for which all patterns can be retrieved, $\alpha_c$. Additionally, we characterize the size of the basins of attractions. We discuss in detail the cases of Gaussian and spherical patterns, and show that they display rich and qualitatively different phase diagrams.

Discrete time Hopfield neural network: convergence theorem: perturbation analysis

Abstract: <p>In this research paper, 𝜺−𝒑𝒆𝒓𝒕𝒖𝒓𝒃𝒂𝒕𝒊𝒐𝒏 of diagonal elements of symmetric synaptic weight matrix, 𝑾̅̅̅ ( with 𝜺>𝟎 ) of Hopfield Associative Memory (HAM) ( resulting in updated synaptic weight matrix 𝑾̂=𝑾̅̅̅+𝜺 𝑰 ) is assumed to ensure that the sufficient condition of convergence theorem is satisfied. It is proved that under such perturbation, stable states of HAMs based on synaptic weight matrices 𝑾̂,𝑾̅̅̅ are same. This result is generalized to prove that if 𝑾̂=𝑾̅̅̅+𝑹̅, ( where 𝑾̅̅̅,𝑹̅ have the same eigenvectors ), the stable states of HAMs based on 𝑾̂,𝑾̅̅̅ are same. It is proved that ( in a well defined sense ), if 𝑾̅̅̅ is positive definite, from the view point of dynamics of HAM the threshold vector can be assumed to be a zero vector. These results are interesting from the viewpoint of dynamics of HAM under practical perturbation models.</p>

Discrete Neural Network of Bidirectional Associative Memory

Abstract: The paper considers bidirectional associative memory, which is one of the known neural network paradigms. To simplify the implementation of the calculation of this paradigm, a discrete mathematical model of its functioning is proposed. Reducing the complexity is achieved by switching to integer calculations because Integer multiplication is several times simpler than real multiplication. The known neural network of bidirectional associative memory neural network was compared with the proposed one. The simulation was carried out in the VHDL language. For comparative evaluation, Spartan3E, Spartan6 and XC9500 chips were used. In the experimental part, it was shown that the hardware costs for the implementation of the neural network of bidirectional associative memory have decreased by more than 3 times compared to the known one. The proposed discrete model of BAM functioning does not narrow the scope of its application in comparison with the known model and can be used to build memory devices and restore distorted or noisy information.

State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

Abstract: For a class of discrete-time bidirectional associative memory neural networks (DTBAMNNs) with multiple time-varying delays, the issue of state estimation is studied. By propose a mathematical induction method, we first investigate novel delay-dependent and -independent global exponential stability (GES) criteria of the error system. The obtained GES criteria are described by linear scalar inequalities. Then, a state observer is derived via the theory of generalized matrix inverses. These exponential stability conditions are very simple, which is convenient to verify based on the standard software tools (for example, YALMIP). Finally, we present two illustrative examples to present the effectiveness of the theoretical results.

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

Abstract: 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.

Using Bidirectional Associative Memory Neural Networks to Solve the N-bit Task

Abstract: Nowadays, artificial neural networks can easily solve the N-bit parity problem. However, each time a different level must be learned, the network must be retrained. This, combined with the exponential increase of learning trials required as N grows, make these models too different from how their biological counterpart solves them. This is because humans learn to recognize patterns, count, and determine if numbers are odd or even. Once they have learned these tasks, they can have them interact to solve any level without further training. This behavior is akin to performing multiple associations of different tasks. Therefore, it is proposed that by using bidirectional associative memory neural networks, it would be possible to solve the N-bit parity problem in a similar fashion to humans. To achieve this, two networks interacted; one served as a task Identifier and the other as a memory Extractor, giving the desired behavior influenced by the Identifier. Results showed that the model could solve the 2- to 9-bit in linear time once the associations were learned. Moreover, this was possible with 97% fewer inputs and no retraining. In addition, because of the recurrent nature of the model, it could also solve the tasks even under high noise levels.

Extended dissipative output‐feedback control for discrete‐time bidirectional associative memory neural networks via delay‐partitioning approach

Abstract: This paper is concerned with the analysis of an extended dissipativity performance for a class of bidirectional associative memory (BAM) neural networks (NNs) having time-varying delays. To achieve this, the idea of the delay-partitioning approach is used, where the range of time-varying delay factors is partitioned into a finite number of equidistant subintervals. A delay-partitioning based Lyapunov–Krasovskii function is introduced on these intervals, and some new delay-dependent extended dissipativity results are established in terms of linear matrix inequalities, which also depend on the partition size of the delay factor. Further, numerical examples are performed to acknowledge the extended dissipativity performance of delayed discrete-time BAM NN; further, four case studies were explored with their simulations to validate the impact of the delay-partitioning approach.

Correction to: Multi-valued neural networks I: a multi-valued associative memory

Abstract: Here we provide a corrigendum on Theorem 2 to Article Title: Multi-Valued Neural Networks I: A Multi-Valued Associative Memory. https://doi.org/10.1007/s00521-021-05781-6.

Towards binary encoding in Bidirectional Associative Memories

Abstract: Bidirectional Associative Memories (BAMs) are Artificial Neural Networks frequently utilized in cognitive modeling. While bipolar encoding is commonly used in BAMs for optimal performance, binary encoding presents interesting properties. As such, this study introduces a novel transmission function for binary encoding and compares its performance to the conventional bipolar transmission function. To evaluate, an auto-association learning task and a noisy recall task were implemented. Results revealed that despite longer learning times, binary encoding preserves or enhances the properties observed in binary encoding. Findings are promising from a cognitive perspective, as they open the possibility of building intricate models of human cognition.

Optimization of Facial Images to Predict Gender Using HDSON and Bidirectional Associative Memory

Abstract: Objective: To enhance the Gender prophecy by employing facial images using imaginative algorithm and to resolve real time applications. Method: Initially, we make use of shared deep octonion network and the Octonion-Valued Neural Network (OVNN) to develop a generic framework for a Hybrid Deep Sparse Octonion Network (HDSON). Sparse Coding Octonion data Algorithm (SCOA) is exploited to depict the face images up to seven color channels and improves the weight of HDSON. Furthermore, to take advantage of the maximum storage we make use of Bidirectional Associative Memories (BAM). Findings: The proposed approach resolves both the issues of depiction of the facial image and its storage, since the present study combines the characteristics of SCOA to improve HDSON weight and BAM to enhance the storage. Moreover, the present study is simple to apply and effective in real time applications. Novelty: The proposed approach can be used in paramilitary to minimize cross border terrorism; in addition, the presented scheme can enhance the probability of child detection and may help local police to a large extent. Keywords: Automatic Gender Classification; BAM; DCN; HDSON; Octonion; SCOA; OVNN

Multidirectional Associative Memory Neural Network Circuit Based on Memristor

Abstract: Multidirectional associative memory neural network(MAMNN) is a direct extension of bidirectional associative memory neural network, which can handle multiple associations. In this work, a circuit of MAMNN based on memristor is proposed, which simulates the complex associative memory behavior more in line with the brain mechanism. Firstly, the basic associative memory circuit is designed, which is mainly composed of memristive weight matrix circuit, adder module and activation circuit. It realizes the associative memory function of single-layer neurons input and single-layer neurons output, so that the information can be transmitted unidirectionally between double-layer neurons. Secondly, on this basis, an associative memory circuit with multi-layer neurons input and single-layer neurons output is realized, which makes information transfer unidirectionally between multi-layer neurons. Finally, several identical circuit architectures are extended, and they are combined into a MAMNN circuit through the feedback connection from the output to the input, which realizes the bidirectional transmission of information between multi-layer neurons. Pspice simulation shows that: 1) When single-layer neurons are selected to input data, the circuit can associate data from other multi-layer neurons, realizing one-to-many associative memory function in the brain. 2) When multi-layer neurons are selected to input data, the circuit can associate the target data and realize the many-to-one associative memory function in the brain. The MAMNN circuit is applied to the field of image processing, which can associate and restore damaged binary images, showing strong robustness.

Parallel Technique on Bidirectional Associative Memory Cohen-Grossberg Neural Network

Abstract: The present paper is devoted to software analysis on applied method used on parallel technology, in particular CUDA and OpenMPI, to find stable areas of single mathematical model of Bidirectional Associative Memory (BAM) Cohen-Grossberg neural network with time-varying delays. The given type of neural networks give opportunity of modelling and study of biological problems.

Long Sequence Hopfield Memory

Abstract: Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where recurrent Hopfield-like neural networks are trained with temporally asymmetric Hebbian rules. However, these networks suffer from limited sequence capacity (maximal length of the stored sequence) due to interference between the memories. Inspired by recent work on Dense Associative Memories, we expand the sequence capacity of these models by introducing a nonlinear interaction term, enhancing separation between the patterns. We derive novel scaling laws for sequence capacity with respect to network size, significantly outperforming existing scaling laws for models based on traditional Hopfield networks, and verify these theoretical results with numerical simulation. Moreover, we introduce a generalized pseudoinverse rule to recall sequences of highly correlated patterns. Finally, we extend this model to store sequences with variable timing between states' transitions and describe a biologically-plausible implementation, with connections to motor neuroscience.

Periodic and Almost Periodic Solutions of Stochastic Inertial Bidirectional Associative Memory Neural Networks on Time Scales

Abstract: The stochastic inertial bidirectional associative memory neural networks (SIBAMNNs) on time scales are considered in this paper, which can unify and generalize both continuous and discrete systems. It is of primary importance to derive the criteria for the existence and uniqueness of both periodic and almost periodic solutions of SIBAMNNs on time scales. Based on that, the criteria for their exponential stability on time scales are studied. Meanwhile, the effectiveness of all proposed criteria is demonstrated by numerical simulation. The above study proposes a new way to unify and generalize both continuous and discrete SIBAMNNs systems, and is applicable to some other practical neural network systems on time scales.

Discrete time Hopfield neural network: convergence theorem: perturbation analysis

Abstract: <p>In this research paper, 𝜺−𝒑𝒆𝒓𝒕𝒖𝒓𝒃𝒂𝒕𝒊𝒐𝒏 of diagonal elements of symmetric synaptic weight matrix, 𝑾̅̅̅ ( with 𝜺>𝟎 ) of Hopfield Associative Memory (HAM) ( resulting in updated synaptic weight matrix 𝑾̂=𝑾̅̅̅+𝜺 𝑰 ) is assumed to ensure that the sufficient condition of convergence theorem is satisfied. It is proved that under such perturbation, stable states of HAMs based on synaptic weight matrices 𝑾̂,𝑾̅̅̅ are same. This result is generalized to prove that if 𝑾̂=𝑾̅̅̅+𝑹̅, ( where 𝑾̅̅̅,𝑹̅ have the same eigenvectors ), the stable states of HAMs based on 𝑾̂,𝑾̅̅̅ are same. It is proved that ( in a well defined sense ), if 𝑾̅̅̅ is positive definite, from the view point of dynamics of HAM the threshold vector can be assumed to be a zero vector. These results are interesting from the viewpoint of dynamics of HAM under practical perturbation models.</p>