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In this article, the problem of global exponential stability in Lagrange sense of neutral type complex‐valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay‐dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016

This article addresses stability analysis of a general class of memristor‐based complex‐valued recurrent neural networks (MCVNNs) with time delays. Some sufficient conditions to guarantee the boundedness on a compact set that globally attracts all trajectories of the MCVNNs are obtained by utilizing local inhibition. Moreover, some sufficient conditions for exponential stability and the global stability of the MCVNNs are established with the help of local invariant sets and linear matrix inequalities using Lyapunov–Krasovskii functional. The analysis results in the article, based on the results from the theory of differential equations with discontinuous right‐hand sides as introduced by Filippov. Finally, two numerical examples are also presented to show the effectiveness and usefulness of our theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–39, 2016

Currently, dealing directly with in-phase and quadrature time series data using the deep learning method is widely used in signal modulation classification. However, there is a relative lack of methods that consider the complex properties of signals. Therefore, to make full use of the inherent relationship between in-phase and quadrature time series data, a complex-valued hybrid neural network (CV-PET-CSGDNN) based on the existing PET-CGDNN network is proposed in this paper, which consists of phase parameter estimation, parameter transformation, and complex-valued signal feature extraction layers. The complex-valued signal feature extraction layers are composed of complex-valued convolutional neural networks (CNN), complex-valued gate recurrent units (GRU), squeeze-and-excite (SE) blocks, and complex-valued dense neural networks (DNN). The proposed network can improve the extraction of the intrinsic relationship between in-phase and quadrature time series data with low capacity and then improve the accuracy of modulation classification. Experiments are carried out on RML2016.10a and RML2018.01a. The results show that, compared with ResNet, CLDNN, MCLDNN, PET-CGDNN, and CV-ResNet models, our proposed complex-valued neural network (CVNN) achieves the highest average accuracy of 61.50% and 62.92% for automatic modulation classification, respectively. In addition, the proposed CV-PET-CSGDNN has a significant improvement in the misjudgment situation between 64QAM, 128QAM, and 256QAM compared with PET-CGDNN on RML2018.01a.

We present a new type of activation functions for a complex-valued neuralnetwork (CVNN). A proposed activation function is constructed such that itfixes a given ellipse. We obtain an application to a complex-valued Hopfieldneural network (CVHNN) using a special form of the introduced complexfunctions as an activation function. Considering the interesting geometricproperties of the plane curve ellipse such as focusing property, weemphasize that these properties may have possible applications in variousneural networks.

Remote and continuous biometric signal monitoring has become increasingly crucial for the prompt diagnosis of physiological disorders. However, traditional contact sensors might pose the risk of virus spread and cause discomfort, thereby impeding the continuous monitoring process. Furthermore, the enhancement of diagnostic performance using deep neural networks necessitates the use of large models, which could be a burden when developing embedded edge devices. Thus, we propose a multitask learning model to estimate the remote photoplethysmogram (PPG) and respiratory rate simultaneously based on facial videos using complex-valued neural networks. The RGB channel images are obtained from a region of interest of the facial video streams and a complex-numbered dataset is constructed. The multitask learning model designed for the complex domain can yield a small network architecture by reducing the number of parameters, which is advantageous for small embedded devices. Using a public dataset of face video streams from multiple participants, the proposed multitask learning model could simultaneously learn the remote PPG and respiratory rate with higher performance and a smaller structure compared with conventional real-valued neural networks. These results validate the potential of the proposed model for the accurate and efficient remote monitoring of physiological disorders.

In recent years, hyper-complex deep networks (such as complex-valued and quaternion-valued neural networks – QVNNs) have received a renewed interest in the literature. They find applications in multiple fields, ranging from image reconstruction to 3D audio processing. Similar to their real-valued counterparts, quaternion neural networks require custom regularisation strategies to avoid overfitting. In addition, for many real-world applications and embedded implementations, there is the need of designing sufficiently compact networks, with few weights and neurons. However, the problem of regularising and/or sparsifying QVNNs has not been properly addressed in the literature as of now. In this study, the authors show how to address both problems by designing targeted regularisation strategies, which can minimise the number of connections and neurons of the network during training. To this end, they investigate two extensions of $\\ell _1$ℓ1 and structured regularisations to the quaternion domain. In the authors’ experimental evaluation, they show that these tailored strategies significantly outperform classical (real-valued) regularisation approaches, resulting in small networks especially suitable for low-power and real-time applications.

Channel modeling plays a pivotal role in the field of communications, particularly in the optical communication networks of backbone communication systems. Recent studies on optical channel modeling have utilized real-valued neural network (RVNN) to extract channel characteristics, an approach that does not fully account for the properties of complex-valued signals. To address this limitation, we propose a complex-valued conditional generative adversarial network (C-CGAN) in this paper to comprehensively learn channel features. We describe the architecture and parameters of the C-CGAN and employ complex-valued windowed construction for input data. Subsequently, we evaluate the model’s accuracy and generalization capabilities using the normalized mean square error (NMSE) and benchmark it against the real-valued conditional generative adversarial network (R-CGAN). The results indicate that the C-CGAN achieves better generalization across various scenarios, including different dataset sizes, noise levels, and input feature complexities, while also exhibiting a more stable training process. The NMSE achieved by the C-CGAN remains below and outperforms the R-CGAN. Additionally, analysis from the perspective of floating-point operations (FLOPs) reveals that the computational complexity of the C-CGAN is relatively low. To further validate scalability, we introduce a self-loop cascading mechanism that, under constrained training datasets, improves NMSE performance by 22.48% compared to the R-CGAN.

This proposed research explores a novel approach to image classification by deploying a complex-valued neural network (CVNN) on a Field-Programmable Gate Array (FPGA), specifically for classifying 2D images transformed into polar form. The aim of this research is to address the limitations of existing neural network models in terms of energy and resource efficiency, by exploring the potential of FPGA-based hardware acceleration in conjunction with advanced neural network architectures like CVNNs. The methodological innovation of this research lies in the Cartesian to polar transformation of 2D images, effectively reducing the input data volume required for neural network processing. Subsequent efforts focused on constructing a CVNN model optimized for FPGA implementation, emphasizing the enhancement of computational efficiency and overall performance. The experimental findings provide empirical evidence supporting the efficacy of the image classification system developed in this study. One of the developed models, CVNN_128, achieves an accuracy of 88.3% with an inference time of just 1.6 ms and a power consumption of 4.66 mW for the classification of the MNIST test dataset, which consists of 10,000 frames. While there is a slight concession in accuracy compared to recent FPGA implementations that achieve 94.43%, our model significantly excels in classification speed and power efficiency—surpassing existing models by more than a factor of 100. In conclusion, this paper demonstrates the substantial advantages of the FPGA implementation of CVNNs for image classification tasks, particularly in scenarios where speed, resource, and power consumption are critical.

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.