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In this article, the issue of exponential stability (ES) is investigated for a class of switched stochastic neural networks (SSNNs) with proportional delay (PD). The key feature of PD is an unbounded time-varying delay. By considering the comparison principle and combining the extended formula for the variation of parameters, we conquer the difficulty in consideration of PD effects for such networks for the first time, where the subsystems addressed may be stable or unstable. New delay-dependent conditions with respect to the mean-square ES of systems are established by employing the average dwell-time (ADT) technique, stochastic analysis theory, and Lyapunov approach. It is shown that the acquired minimum average dwell time (MADT) is not only relevant to the stable subsystems (SSs) and unstable subsystems (USs) but also dependent on the decay ratio (DR), increasing ratio (IR), as well as PD. Finally, the availability of the derived results under an average dwell-time-switched regulation (ADTSR) is illustrated through two numerical simulation examples.

In this paper, a class of stochastic neural networks with time delays is studied. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence of Stepanov-like almost periodic solutions for the stochastic neural networks under consideration. Then, by designing a novel state-feedback controller and constructing a suitable Lyapunov function, the global asymptotic synchronization and exponential stability of the stochastic neural networks are researched. Finally, two numerical examples are provided to show the feasibility of our results.

In this paper, we study the mean square exponential stability of discrete-time stochastic neural networks with partially unstable subsystems and mixed delays. The mixed delays under consideration involve discrete delay and distributed delay. Moreover, the discrete delay term satisfies the Bernoulli distribution . Different from the deterministic switching, we consider Markov switching and our system has partially unstable subsystems. By constructing a novel Lyapunov–Krasovskii functional and using the stationary distribution of Markov chain , we give sufficient conditions for the mean square exponential stability of the suggested system. Finally, two numerical examples are given to check the theory results.

Sports analytics in the wild (i.e., ubiquitously) is a thriving industry. Swing tracking is a key feature in sports analytics. Therefore, a centimeter-level tracking resolution solution is required. Recent research has explored deep neural networks for sensor fusion to produce consistent swing-tracking performance. This is achieved by combining the advantages of two sensor modalities (IMUs and depth sensors) for golf swing tracking. Here, the IMUs are not affected by occlusion and can support high sampling rates. Meanwhile, depth sensors produce significantly more accurate motion measurements than those produced by IMUs. Nevertheless, this method can be further improved in terms of accuracy and lacking information for different domains (e.g., subjects, sports, and devices). Unfortunately, designing a deep neural network with good performance is time consuming and labor intensive, which is challenging when a network model is deployed to be used in new settings. To this end, we propose a network based on Neural Architecture Search (NAS), called SwingNet, which is a regression-based automatic generated deep neural network via stochastic neural network search. The proposed network aims to learn the swing tracking feature for better prediction automatically. Furthermore, SwingNet features a domain discriminator by using unsupervised learning and adversarial learning to ensure that it can be adaptive to unobserved domains. We implemented SwingNet prototypes with a smart wristband (IMU) and smartphone (depth sensor), which are ubiquitously available. They enable accurate sports analytics (e.g., coaching, tracking, analysis and assessment) in the wild. Our comprehensive experiment shows that SwingNet achieves less than 10 cm errors of swing tracking with a subject-independent model covering multiple sports (e.g., golf and tennis) and depth sensor hardware, which outperforms state-of-the-art approaches.

In this paper, stability of a class of stochastic neural networks with switching signal is studied. Firstly, by means of the method of limiting average dwell time, we analyze the stability of switched systems which potentially contain unstable subsystems and stable subsystems simultaneously. Moreover, considering two types of switchings: stabilizing switchings and destabilizing switchings, we adopt time-dependent parameters to give a description of the relationship between two successive activated subsystems. Based on the obtained results for switched systems, some stability criteria for switched neural networks with stochastic disturbances are derived. At last, we present a numerical example to demonstrate the effectiveness of our results.

This paper focuses on the finite-time synchronization of stochastic memristor-based neural networks with time-varying discrete and distributed delays and discontinuous nonlinear functions via the adaptive state-feedback controller. Based on the theories of set-valued mappings and stochastic differential inclusions, the finite-time synchronization of the drive neural network and response neural network is transformed into the finite-time stabilization problem of the corresponding error stochastic neural network. By choosing an appropriate Lyapunov function and employing the theory of stochastic finite-time stability, we present a method to design the control gain parameters. Finally, an example verifies the validity of the proposed method.

In this paper, we first consider the stability problem for a class of stochastic quaternion-valued neural networks with time-varying delays. Next, we cannot explicitly decompose the quaternion-valued systems into equivalent real-valued systems; by using Lyapunov functional and stochastic analysis techniques, we can obtain sufficient conditions for mean-square exponential input-to-state stability of the quaternion-valued stochastic neural networks. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.

Context. To reduce the computational resource time in the problems of diagnosing and recognizing distorted images based on a fully connected stochastic pseudospin neural network, it becomes necessary to thin out synaptic connections between neurons, which is solved using the method of diagonalizing the matrix of synaptic connections without losing interaction between all neurons in the network. Objective. To create an architecture of a stochastic pseudo-spin neural network with diagonal synaptic connections without loosing the interaction between all the neurons in the layer to reduce its learning time. Method. The paper uses the Hausholder method, the method of compressing input images based on the diagonalization of the matrix of synaptic connections and the computer mathematics system MATLAB for converting a fully connected neural network into a tridiagonal form with hidden synaptic connections between all neurons. Results. We developed a model of a stochastic neural network architecture with sparse renormalized synaptic connections that take into account deleted synaptic connections. Based on the transformation of the synaptic connection matrix of a fully connected neural network into a Hessenberg matrix with tridiagonal synaptic connections, we proposed a renormalized local Hebb rule. Using the computer mathematics system “WolframMathematica 11.3”, we calculated, as a function of the number of neurons N, the relative tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network. Conclusions. We found that with an increase in the number of neurons, the tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network, decreases according to a hyperbolic law. Depending on the direction of pseudospin neurons, we proposed a classification of a renormalized neural network with a ferromagnetic structure, an antiferromagnetic structure, and a dipole glass.

The aim of this paper is to investigate the existence, uniqueness and stability of mild solutions to a stochastic delayed reaction–diffusion equation with spatial non-locality. This equation can be used to model the spatial–temporal evolution for age-structured spices perturbed by some random effects or the stochastic neural networks. The Banach fixed point theorem and a truncation method are adopted to establish the existence and uniqueness of mild solutions under both global and local Lipschitz conditions. Then, we explore the mean square exponential stability and almost sure exponential stability by employing the inequality techniques, the stochastic analysis techniques together with the properties of the nonlocal delayed term. Furthermore, we obtain the critical value of time delay $$\tau $$ that guarantees the stability of the mild solutions. At last, our theoretic results are illustrated by application to the stochastic non-local delayed Nicholson blowflies equation with numerical simulations.

This overview article describes Magnetoresistive Random Access Memory (MRAM) from a circuits and systems perspective. We discuss various tradeoffs and design challenges of MRAM in three broad application areas: 1) embedded non-volatile memory (eNVMs), 2) crossbar-based analog in-memory computing, and 3) stochastic computing. Certain MRAM characteristics, such as high retention, high endurance and fast read and write operations, make them ideal for replacing the standard CMOS memories for last-level cache applications with future scaling. However, various tradeoffs in power, performance and area pose conflicting requirements on MRAM design. We explore these challenges and various circuit techniques that have been developed to mitigate them. Further, we present various requirements of memristive crossbar arrays for accelerating matrix-vector-multiplication (MVM) operations in light of MRAM devices, and highlight various challenges, design considerations, and applicability of MRAM as crossbar arrays. Finally, we will elaborate on how inherent stochasticity of MRAM devices can be leveraged for implementing energy-efficient true random number generators (TRNGs) and stochastic units for performing certain tasks, such as developing fast solvers for combinatorial optimization, and stochastic neural networks.

In this paper, we investigate input-to-state stability (ISS) problem for a general model of hybrid stochastic systems with unbounded delays and impulsive effects, in which stochastic disturbances involve white noise and Markov chain. Firstly, we establish a novel differential inequality with unbounded delays and variable inputs, which extends and improves some existing results. Then, by using the obtained inequality, the sufficient conditions are derived to determine ISS properties on impulsive robustness and impulsive stabilization for the impulsive stochastic systems with unbounded delays. The results not only show that the ISS properties still remain under certain impulsive perturbations for some continuous stable systems, but also indicate that an unstable system can be successfully stabilized to be input-to-state stable by impulses even if the corresponding continuous system is unstable. The obtained criteria are applied to study the ISS problems for impulsive stochastic neural networks and the systems of energy-storing electrical circuit. Finally, two numerical examples and their simulations are given to illustrate the validity of theoretical results.

This study is related to the exponential synchronization problem of stochastic neural networks. A dynamic model of master-slave neural networks is established, which contains time-varying delays and Levy noises. The main purpose is to enable the slave system to follow the master system under the condition of limited communication capacity. Both the master system and the slave system are affected by random noises. Some sufficient conditions are given by means of linear matrix inequality methods which are established by applying Lyapunov functional together with the generalized Dynkin’s formula. Furthermore, a discrete event-triggered control is adopted in master-slave systems, which not only reduces the transmission resources but also avoids the Zeno phenomenon. At last, a numerical example is provided to verify the usefulness of judgment conditions in this study.

JJT and MAM acknowledge financial support from the Spanish Ministry of Science and Technology, and the Agencia Española de Investigación (AEI) under grant FIS2017-84256-P (FEDER funds) and from the Consejerı́a de Conocimiento, Investigación y Universidad, Junta de Andalucı́a and Euro- pean Regional Development Fund (ERDF), with reference SOMM17/6105/UGR. JMC acknowledges financial support from spanish Ministerio Economia, In- dustria y Competitividad and FEDER (grant DPI2016-79874-R) and from the Department of Economical Development and Infrastructure of the Basque Country (Elkartek Program, KK-2018/00032 and KK-2018/00090). JFM acknowledges financial support from the European Union’s Horizon 2020 Framework Program for Research and Innovation under the Specific Grant Agreement No. 945539 (Human Brain Project SGA3).

The Boltzmann machine (BM) and restricted Boltzmann machine (RBM) models are representative stochastic neural networks, in which neuron states are determined by stochastic activation functions. They are widely used in many applications. However, when analog circuits are used to realize a neural network, noise are not avoidable. The noise could come from external environments, such as power supplies and thermal noise, and they will affect the neurons’ stochastic behaviour in the BM and RBM models. Hence it is important to theoretically study how the noise affect the operation of the BM and RBM models. To best of our knowledge, there are little works related to the analysis on noisy BMs and noisy RBMs. This paper considers that there are additive noise in the inputs of the neurons, and theoretically studies the behaviors of the two models under this imperfect condition. It is found that the effect of additive noise is similar to increasing the temperature factors of the two models. Since the input noise may make the networks to have wrong stochastic behaviour, there is Kullback Leibler (KL) divergence loss in noisy BMs and noisy RBMs. Based on the Gaussian-distributed noise assumption, a noise compensation method is proposed to suppress the effect of additive noise. Experiments show that the proposed noise compensation method can greatly suppress the KL divergence loss. In addition, from the experimental results, our method is also effective for handling non-Gaussian noise.

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative studies of automatic and human speech recognition that associate standard non-adaptive feature extraction techniques with information loss which can adversely affect robustness. Stochastic neural networks, on the other hand, are a class of models capable of incorporating rich regularization mechanisms into the learning process. We consider a deep convolutional neural network that first decomposes speech into frequency sub-bands via an adaptive parametric convolutional block where filters are specified by cosine modulations of compactly supported windows. The network then employs standard non-parametric 1D convolutions to extract relevant spectro-temporal patterns while gradually compressing the structured high dimensional representation generated by the parametric block. We rely on a probabilistic parametrization of the proposed neural architecture and learn the model using stochastic variational inference. This requires evaluation of an analytically intractable integral defining the Kullback-Leibler divergence term responsible for regularization, for which we propose an effective approximation based on the Gauss-Hermite quadrature. Our empirical results demonstrate a superior performance of the proposed approach over comparable waveform-based baselines and indicate that it could lead to robustness. Moreover, the approach outperforms a recently proposed deep convolutional neural network for learning of robust acoustic models with standard FBANK features.

In this article, extended dissipative state estimation (EDSE) criteria is established for stochastic neural networks with variable delay states. The EDSE criteria includes passivity state estimation, dissipativity state estimation, H∞ state estimation and L 2 − L ∞ state estimation performances. Sufficient conditions for EDSE criteria are established by choosing Lyapunov–Krasovskii functionals (LKF) and using linear matrix inequality (LMIs) technique. New stochastic double integral inequality is applied for the integral term in the derivative of the chosen LKF in main results, which helps to establish EDSE criterion for delayed stochastic neural networks. The feasibility and superiority of the proposed approach is shown by providing numerical examples.

This paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient conditions on the existence and exponential stability of periodic solution for the stochastic neural networks are established. Moreover, a numerical example is presented to validate the theoretical results. Our results are also applicable to the existence and exponential stability of periodic solution for the corresponding deterministic systems.

In this paper, to investigate the exponential synchronization of stochastic neural networks, a new periodically intermittent discrete observation control (PIDOC) is first proposed. Different from the existing periodically intermittent control, our control in control time is feedback control based on discrete-time state observations (FCDSOs) instead of a continuous-time one. By employing the Lyapunov method, graph theory, and theory of differential inclusions, the exponential synchronization of stochastic neural networks with a discontinuous right-hand side is realized by PIDOC and some sufficient conditions are presented. Especially, when control width tends to control period, PIDOC will be reduced to a general FCDSO and we give some detailed discussions. Then, we provide some corollaries about synchronization in mean square, asymptotical synchronization in mean square, and exponential synchronization of stochastic neural networks under FCDSO. Finally, some numerical simulations are provided to demonstrate our analytical results.

In this paper, the robust stability problem for a class of uncertain stochastic complex-valued neural networks (USCVNNs) with additive time-varying delays (ATDs) is discussed. By constructing a suitable Lyapunov–Krasovskii functional (LKF), more time delay information is considered. By employing integral inequalities, some delay-dependent stability criteria are derived by converting USCVNNs into an equivalent real-valued uncertain stochastic neural networks. The obtained stability criterion is presented in the form of linear matrix inequalities (LMIs), which can be calculated through MATLAB LMI toolbox. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.