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Journal articles on the topic 'Complex-valued neural networks'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Hirose, Akira. "Complex-valued Neural Networks." IEEJ Transactions on Electronics, Information and Systems 131, no. 1 (2011): 2–8. http://dx.doi.org/10.1541/ieejeiss.131.2.

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2

Guo, Song, and Bo Du. "Global Exponential Stability of Periodic Solution for Neutral-Type Complex-Valued Neural Networks." Discrete Dynamics in Nature and Society 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/1267954.

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This paper deals with a class of neutral-type complex-valued neural networks with delays. By means of Mawhin’s continuation theorem, some criteria on existence of periodic solutions are established for the neutral-type complex-valued neural networks. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are derived for the global exponential stability of periodic solutions to the neutral-type complex-valued neural networks. Finally, numerical examples are given to show the effectiveness and merits of the present results.

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3

Valle, Marcos Eduardo. "Complex-Valued Recurrent Correlation Neural Networks." IEEE Transactions on Neural Networks and Learning Systems 25, no. 9 (2014): 1600–1612. http://dx.doi.org/10.1109/tnnls.2014.2341013.

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4

Kobayashi, Masaki. "Symmetric Complex-Valued Hopfield Neural Networks." IEEE Transactions on Neural Networks and Learning Systems 28, no. 4 (2017): 1011–15. http://dx.doi.org/10.1109/tnnls.2016.2518672.

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5

Boonsatit, Nattakan, Santhakumari Rajendran, Chee Peng Lim, Anuwat Jirawattanapanit, and Praneesh Mohandas. "New Adaptive Finite-Time Cluster Synchronization of Neutral-Type Complex-Valued Coupled Neural Networks with Mixed Time Delays." Fractal and Fractional 6, no. 9 (2022): 515. http://dx.doi.org/10.3390/fractalfract6090515.

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The issue of adaptive finite-time cluster synchronization corresponding to neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A neutral-type coupled complex-valued neural network with mixed delays is more general than that of a traditional neural network, since it considers distributed delays, state delays and coupling delays. In this research, a new adaptive control technique is developed to synchronize neutral-type coupled complex-valued neural networks with mixed delays in finite time. To stabilize the resulting closed-loop system, the Lyapun

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6

Dong, Yu-Chao, Xi-Kun Li, Ming Yang, et al. "Quantum state classification via complex-valued neural networks." Laser Physics Letters 21, no. 10 (2024): 105206. http://dx.doi.org/10.1088/1612-202x/ad7246.

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Abstract To efficiently complete quantum information processing tasks, quantum neural networks (QNNs) should be introduced rather than the common classical neural networks, but the QNNs in the current noisy intermediate-scale quantum era cannot perform better than classical neural networks because of scale and the efficiency limits. So if the quantum properties can be introduced into classical neural networks, more efficient classical neural networks may be constructed for tasks in the field of quantum information. Complex numbers play an indispensable role in the standard quantum theory, and

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7

Flores, Alexandra Macarena, Víctor José Huilca, César Palacios-Arias, María José López, Omar Darío Delgado, and María Belén Paredes. "From Iterative Methods to Neural Networks: Complex-Valued Approaches in Medical Image Reconstruction." Electronics 14, no. 10 (2025): 1959. https://doi.org/10.3390/electronics14101959.

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Complex-valued neural networks have emerged as an effective instrument in image reconstruction, exhibiting significant advancements compared to conventional techniques. This study introduces an innovative methodology to tackle the difficulties related to image reconstruction within medical microwave imaging. Initially, in the estimation phase, the proposed methodology integrates the Born iterative method with quadratic programming. Subsequently, in the refinement stage, the study explores the application of complex-valued neural networks to enhance the quality of reconstructions. The research

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Nitta, Tohru. "Orthogonality of Decision Boundaries in Complex-Valued Neural Networks." Neural Computation 16, no. 1 (2004): 73–97. http://dx.doi.org/10.1162/08997660460734001.

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This letter presents some results of an analysis on the decision boundaries of complex-valued neural networks whose weights, threshold values, input and output signals are all complex numbers. The main results may be summarized as follows. (1) A decision boundary of a single complex-valued neuron consists of two hypersurfaces that intersect orthogonally, and divides a decision region into four equal sections. The XOR problem and the detection of symmetry problem that cannot be solved with two-layered real-valued neural networks, can be solved by two-layered complex-valued neural networks with

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9

Song, Qiankun, Qian Wu, and Yurong Liu. "Stabilization of chaotic quaternion-valued neutral-type neural networks via sampled-data control with two-sided looped functional approach." Nonlinear Analysis: Modelling and Control 29, no. 6 (2024): 1150–66. https://doi.org/10.15388/namc.2024.29.37852.

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The quaternion-valued neutral-type neural networks (QVNTNNs) stability problem through designing sampled-data controller is investigated in this paper. A main stability criterion of the considered neural networks (NNs) is obtained in the form of linear matrix inequalities (LMIs) based on the two-sided looped functional method. The effectiveness of the criterion is shown by a numerical example. It needs to be emphasized that the considered QVNTNNs model in this paper is not broken down into real-valued or complex-valued models in stability analysis, and the acquired criterion holds for both rea

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10

Kobayashi, Masaki. "Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks." Neural Computation 32, no. 11 (2020): 2237–48. http://dx.doi.org/10.1162/neco_a_01320.

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A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Comp

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11

Lee, ChiYan, Hideyuki Hasegawa, and Shangce Gao. "Complex-Valued Neural Networks: A Comprehensive Survey." IEEE/CAA Journal of Automatica Sinica 9, no. 8 (2022): 1406–26. http://dx.doi.org/10.1109/jas.2022.105743.

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12

Gorday, Paul E., Nurgun Erdol, and Hanqi Zhuang. "Complex-Valued Neural Networks for Noncoherent Demodulation." IEEE Open Journal of the Communications Society 1 (2020): 217–25. http://dx.doi.org/10.1109/ojcoms.2020.2970688.

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13

Kobayashi, Masaki. "Exceptional Reducibility of Complex-Valued Neural Networks." IEEE Transactions on Neural Networks 21, no. 7 (2010): 1060–72. http://dx.doi.org/10.1109/tnn.2010.2048040.

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14

Hirose, A. "Dynamics of fully complex-valued neural networks." Electronics Letters 28, no. 16 (1992): 1492. http://dx.doi.org/10.1049/el:19920948.

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15

Zhang, Yongliang, and He Huang. "Adaptive complex-valued stepsize based fast learning of complex-valued neural networks." Neural Networks 124 (April 2020): 233–42. http://dx.doi.org/10.1016/j.neunet.2020.01.011.

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16

Korzhov, Serhii O., and Valentyn S. Yesilevskyi. "Using complex-valued neural networks for aircraft identification." Applied Aspects of Information Technology 8, no. 1 (2025): 38–47. https://doi.org/10.15276/aait.08.2025.3.

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This paper presents an approach to aircraft recognition using complex-valued neural networks. The objective of the article is to study the effectiveness of complex-valued neural networks for aircraft identification tasks based on radar data, the efficiencyevaluated based on criteria such as classification accuracy, robustness to noise interference, the ability to maintain high accuracy with limited training data, and an optimal trade-off between accuracy and computational complexity.The study focuses on aircraft identification using phase and amplitude characteristics of radar signals, which a

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17

Popa, Călin-Adrian. "Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays." Fractal and Fractional 7, no. 11 (2023): 830. http://dx.doi.org/10.3390/fractalfract7110830.

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Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has appeared, namely octonion-valued neural networks (OVNNs), which are not a subset of ClVNNs. They are defined on the octonion algebra, which is an 8D algebra over the reals, and is also the only other normed division algebra that can be defined over the reals beside the complex and quaternion algebras. On the other hand, fractional-order neural ne

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18

Jayanthi, N., and R. Santhakumari. "Synchronization of time invariant uncertain delayed neural networks in finite time via improved sliding mode control." Mathematical Modeling and Computing 8, no. 2 (2021): 228–40. http://dx.doi.org/10.23939/mmc2021.02.228.

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This paper explores the finite-time synchronization problem of delayed complex valued neural networks with time invariant uncertainty through improved integral sliding mode control. Firstly, the master-slave complex valued neural networks are transformed into two real valued neural networks through the method of separating the complex valued neural networks into real and imaginary parts. Also, the interval uncertainty terms of delayed complex valued neural networks are converted into the real uncertainty terms. Secondly, a new integral sliding mode surface is designed by employing the master-s

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19

Dong, Wenjun, Yujiao Huang, Tingan Chen, Xinggang Fan, and Haixia Long. "Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays." Mathematics 10, no. 13 (2022): 2157. http://dx.doi.org/10.3390/math10132157.

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This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued neural networks into a real part and three imaginary parts, separating the quaternion field into 34n subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have 34n equilibrium points. According to the Hala

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20

Nitta, Tohru. "Learning Transformations with Complex-Valued Neurocomputing." International Journal of Organizational and Collective Intelligence 3, no. 2 (2012): 81–116. http://dx.doi.org/10.4018/joci.2012040103.

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The ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations has been applied to the estimation of optical flows and the generation of fractal images. The complex-valued neural network has the adaptability and the generalization ability as inherent nature. This is the most different point between the ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations and the standard techniques for 2D affine transformations such as the Fourier descriptor. It is important to clarify the properties of complex-valued neural networks in order to accel

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21

Hirose, Akira. "Nature of complex number and complex-valued neural networks." Frontiers of Electrical and Electronic Engineering in China 6, no. 1 (2011): 171–80. http://dx.doi.org/10.1007/s11460-011-0125-3.

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22

NITTA, TOHRU. "THE UNIQUENESS THEOREM FOR COMPLEX-VALUED NEURAL NETWORKS WITH THRESHOLD PARAMETERS AND THE REDUNDANCY OF THE PARAMETERS." International Journal of Neural Systems 18, no. 02 (2008): 123–34. http://dx.doi.org/10.1142/s0129065708001439.

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This paper will prove the uniqueness theorem for 3-layered complex-valued neural networks where the threshold parameters of the hidden neurons can take non-zeros. That is, if a 3-layered complex-valued neural network is irreducible, the 3-layered complex-valued neural network that approximates a given complex-valued function is uniquely determined up to a finite group on the transformations of the learnable parameters of the complex-valued neural network.

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23

Liu, Xin, Lili Chen, and Yanfeng Zhao. "Uniform Stability of a Class of Fractional-Order Fuzzy Complex-Valued Neural Networks in Infinite Dimensions." Fractal and Fractional 6, no. 5 (2022): 281. http://dx.doi.org/10.3390/fractalfract6050281.

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In this paper, the problem of the uniform stability for a class of fractional-order fuzzy impulsive complex-valued neural networks with mixed delays in infinite dimensions is discussed for the first time. By utilizing fixed-point theory, theory of differential inclusion and set-valued mappings, the uniqueness of the solution of the above complex-valued neural networks is derived. Subsequently, the criteria for uniform stability of the above complex-valued neural networks are established. In comparison with related results, we do not need to construct a complex Lyapunov function, reducing the c

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24

Goh, Su Lee, and Danilo P. Mandic. "A Complex-Valued RTRL Algorithm for Recurrent Neural Networks." Neural Computation 16, no. 12 (2004): 2699–713. http://dx.doi.org/10.1162/0899766042321779.

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A complex-valued real-time recurrent learning (CRTRL) algorithm for the class of nonlinear adaptive filters realized as fully connected recurrent neural networks is introduced. The proposed CRTRL is derived for a general complex activation function of a neuron, which makes it suitable for nonlinear adaptive filtering of complex-valued nonlinear and nonstationary signals and complex signals with strong component correlations. In addition, this algorithm is generic and represents a natural extension of the real-valued RTRL. Simulations on benchmark and real-world complex-valued signals support t

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25

Wang, Zengyun, Jinde Cao, Zhenyuan Guo, and Lihong Huang. "Generalized stability for discontinuous complex-valued Hopfield neural networks via differential inclusions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2220 (2018): 20180507. http://dx.doi.org/10.1098/rspa.2018.0507.

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Some dynamical behaviours of discontinuous complex-valued Hopfield neural networks are discussed in this paper. First, we introduce a method to construct the complex-valued set-valued mapping and define some basic definitions for discontinuous complex-valued differential equations. In addition, Leray–Schauder alternative theorem is used to analyse the equilibrium existence of the networks. Lastly, we present the dynamical behaviours, including global stability and convergence in measure for discontinuous complex-valued neural networks (CVNNs) via differential inclusions. The main contribution

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26

Kobayashi, Masaki. "Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules." Computational Intelligence and Neuroscience 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/4894278.

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Many models of neural networks have been extended to complex-valued neural networks. A complex-valued Hopfield neural network (CHNN) is a complex-valued version of a Hopfield neural network. Complex-valued neurons can represent multistates, and CHNNs are available for the storage of multilevel data, such as gray-scale images. The CHNNs are often trapped into the local minima, and their noise tolerance is low. Lee improved the noise tolerance of the CHNNs by detecting and exiting the local minima. In the present work, we propose a new recall algorithm that eliminates the local minima. We show t

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27

Linhardt, Timothy, Ananya Sen Gupta, Matthew Bays, and Ivars P. Kirsteins. "SONAR target classification with complex-valued neural networks." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A47. http://dx.doi.org/10.1121/10.0026751.

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Popular acoustic signal processing techniques analyze acoustic color, which is a magnitude representation of a frequency spectrum. This paradigm allows for easy visualization of results and simpler models at the cost of throwing out phase information. Analysis and modeling of complex-valued data does have inherent difficulty from the nature of complex numbers. Optimization on the complex field requires alternate partial derivative definitions to circumvent consequences of the Cauchy–Riemann equations regarding holomorphic functions. To make use of phase information, we demonstrate classifier m

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28

Caragea, Andrei, Dae Gwan Lee, Johannes Maly, Götz Pfander, and Felix Voigtlaender. "Quantitative Approximation Results for Complex-Valued Neural Networks." SIAM Journal on Mathematics of Data Science 4, no. 2 (2022): 553–80. http://dx.doi.org/10.1137/21m1429540.

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29

Scardapane, Simone, Steven Van Vaerenbergh, Amir Hussain, and Aurelio Uncini. "Complex-Valued Neural Networks With Nonparametric Activation Functions." IEEE Transactions on Emerging Topics in Computational Intelligence 4, no. 2 (2020): 140–50. http://dx.doi.org/10.1109/tetci.2018.2872600.

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30

HASHIMOTO, Naoki, Yasuaki KUROE, and Takehiro MORI. "On Energy Function for Complex-Valued Neural Networks." Transactions of the Institute of Systems, Control and Information Engineers 15, no. 10 (2002): 559–65. http://dx.doi.org/10.5687/iscie.15.559.

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31

Kaslik, Eva, and Ileana Rodica Rădulescu. "Dynamics of complex-valued fractional-order neural networks." Neural Networks 89 (May 2017): 39–49. http://dx.doi.org/10.1016/j.neunet.2017.02.011.

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32

Pandey, R. "Complex Valued Recurrent Neural Networks for Blind Equalization." International Journal of Modelling and Simulation 25, no. 3 (2005): 182–89. http://dx.doi.org/10.1080/02286203.2005.11442333.

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33

Nitta, Tohru. "Proposal of fully augmented complex-valued neural networks." Nonlinear Theory and Its Applications, IEICE 14, no. 2 (2023): 175–92. http://dx.doi.org/10.1587/nolta.14.175.

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34

Dong, Tao, and Tingwen Huang. "Neural Cryptography Based on Complex-Valued Neural Network." IEEE Transactions on Neural Networks and Learning Systems 31, no. 11 (2020): 4999–5004. http://dx.doi.org/10.1109/tnnls.2019.2955165.

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35

Pavlov, Stanislav, Dmitry Kozlov, Mikhail Bakulin, Aleksandr Zuev, Andrey Latyshev, and Alexander Beliaev. "Generalization of Neural Networks on Second-Order Hypercomplex Numbers." Mathematics 11, no. 18 (2023): 3973. http://dx.doi.org/10.3390/math11183973.

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The vast majority of existing neural networks operate by rules set within the algebra of real numbers. However, as theoretical understanding of the fundamentals of neural networks and their practical applications grow stronger, new problems arise, which require going beyond such algebra. Various tasks come to light when the original data naturally have complex-valued formats. This situation is encouraging researchers to explore whether neural networks based on complex numbers can provide benefits over the ones limited to real numbers. Multiple recent works have been dedicated to developing the

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36

Rattan, Sanjay S. P., and William W. Hsieh. "Complex-valued neural networks for nonlinear complex principal component analysis." Neural Networks 18, no. 1 (2005): 61–69. http://dx.doi.org/10.1016/j.neunet.2004.08.002.

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37

Chen, Xiaofeng, Qiankun Song, Yurong Liu та Zhenjiang Zhao. "Globalμ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays". Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/397532.

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The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the globalμ-stability of the complex-val

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38

Wang, Ruiting, Pengfei Wang, Chen Lyu, et al. "Multicore Photonic Complex-Valued Neural Network with Transformation Layer." Photonics 9, no. 6 (2022): 384. http://dx.doi.org/10.3390/photonics9060384.

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Photonic neural network chips have been widely studied because of their low power consumption, high speed and large bandwidth. Using amplitude and phase to encode, photonic chips can accelerate complex-valued neural network computations. In this article, a photonic complex-valued neural network (PCNN) chip is designed. The scale of the single-core PCNN chip is limited because of optical losses, and the multicore architecture of the chip is used to improve computing capability. Further, for improving the performance of the PCNN, we propose the transformation layer, which can be implemented by t

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39

Shu, Jinlong, Lianglin Xiong, Tao Wu, and Zixin Liu. "Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay." Mathematics 7, no. 1 (2019): 101. http://dx.doi.org/10.3390/math7010101.

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This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued s

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40

Tanaka, Gouhei. "Complex-Valued Neural Networks: Advances and Applications [Book Review]." IEEE Computational Intelligence Magazine 8, no. 2 (2013): 77–79. http://dx.doi.org/10.1109/mci.2013.2247895.

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41

Goh, Su Lee, and Danilo P. Mandic. "An augmented CRTRL for complex-valued recurrent neural networks." Neural Networks 20, no. 10 (2007): 1061–66. http://dx.doi.org/10.1016/j.neunet.2007.09.015.

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42

Dghais, Wael, Vitor Ribeiro, Zhansheng Liu, Zoran Vujicic, Manuel Violas, and António Teixeira. "Efficient RSOA modelling using polar complex-valued neural networks." Optics Communications 334 (January 2015): 129–32. http://dx.doi.org/10.1016/j.optcom.2014.08.031.

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43

Kobayashi, Masaki. "Fixed points of symmetric complex-valued Hopfield neural networks." Neurocomputing 275 (January 2018): 132–36. http://dx.doi.org/10.1016/j.neucom.2017.05.006.

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44

Kobayashi, Masaki. "Synthesis of complex- and hyperbolic-valued Hopfield neural networks." Neurocomputing 423 (January 2021): 80–88. http://dx.doi.org/10.1016/j.neucom.2020.10.002.

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45

Gong, Weiqiang, Jinling Liang, Xiu Kan, and Xiaobing Nie. "Robust State Estimation for Delayed Complex-Valued Neural Networks." Neural Processing Letters 46, no. 3 (2017): 1009–29. http://dx.doi.org/10.1007/s11063-017-9626-2.

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46

Georgiou, G. "Complex-Valued Neural Networks (Hirose, A.; 2006) [Book review]." IEEE Transactions on Neural Networks 19, no. 3 (2008): 544. http://dx.doi.org/10.1109/tnn.2008.919145.

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47

Wang, Huamin, Shukai Duan, Tingwen Huang, Lidan Wang, and Chuandong Li. "Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks." IEEE Transactions on Neural Networks and Learning Systems 28, no. 3 (2017): 766–71. http://dx.doi.org/10.1109/tnnls.2015.2513001.

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48

Zhang, Weiwei, Jinde Cao, Dingyuan Chen, and Fuad Alsaadi. "Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks." Entropy 20, no. 1 (2018): 54. http://dx.doi.org/10.3390/e20010054.

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49

Hirose, Akira. "Fractal variation of attractors in complex-valued neural networks." Neural Processing Letters 1, no. 1 (1994): 6–8. http://dx.doi.org/10.1007/bf02312393.

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50

Nitta, Tohru. "Resolution of singularities via deep complex-valued neural networks." Mathematical Methods in the Applied Sciences 41, no. 11 (2017): 4170–78. http://dx.doi.org/10.1002/mma.4434.

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