Optical reservoir computing(ORC)offers advantages,such as high computational speed,low power consumption,and high training speed,so it has become a competitive candidate for time series analysis in recent years.The cu...Optical reservoir computing(ORC)offers advantages,such as high computational speed,low power consumption,and high training speed,so it has become a competitive candidate for time series analysis in recent years.The current ORC employs single-dimensional encoding for computation,which limits input resolution and introduces extraneous information due to interactions between optical dimensions during propagation,thus constraining performance.Here,we propose complex-value encoding-based optoelectronic reservoir computing(CE-ORC),in which the amplitude and phase of the input optical field are both modulated to improve the input resolution and prevent the influence of extraneous information on computation.In addition,scale factors in the amplitude encoding can fine-tune the optical reservoir dynamics for better performance.We built a CE-ORC processing unit with an iteration rate of up to∼1.2 kHz using high-speed communication interfaces and field programmable gate arrays(FPGAs)and demonstrated the excellent performance of CE-ORC in two time series prediction tasks.In comparison with the conventional ORC for the Mackey–Glass task,CE-ORC showed a decrease in normalized mean square error by∼75%.Furthermore,we applied this method in a weather time series analysis and effectively predicted the temperature and humidity within a range of 24 h.展开更多
Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain su...Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.展开更多
In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. W...In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.展开更多
Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of fi...Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.展开更多
Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts ...Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.展开更多
Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative ...Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.展开更多
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. S...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.展开更多
Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance f...Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.展开更多
This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural ...This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.展开更多
In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active me...In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system.By using numerical measures,complex dynamical behaviors of the memristive laser system are uncovered.It appears the alternating appearance of quasi-periodic and chaotic oscillations.The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy.Interestingly,initial-values-oriented extreme multi-stability patterns are found,where the coexisting attractors have the same Lyapunov exponents.In addition,the introduction of a memristor greatly improves the complexity of the laser system.Moreover,to control the amplitude and offset of the chaotic signal,two kinds of geometric control methods including amplitude control and rotation control are designed.The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics.Finally,a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valu...Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.展开更多
Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link....Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.展开更多
In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued n...In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.展开更多
For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer...For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.展开更多
基金the National Natural Science Foundation of China(Grant Nos.62375171,62305208,62205189,62105203,and 62405182)the Shanghai Pujiang Program(Grant No.22PJ1407500)+4 种基金the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University(SJTU)(Grant No.SL2022ZD205)the National Key Research and Development Program of China(Grant No.2022YFC2806600)the Science Foundation of Donghai Laboratory(Grant Nos.DH-2022KF01001 and DH-2022KF01005)the Startup Fund for Young Faculty at SJTU(Grant No.24X010500120)the Science and Technology Commission of Shanghai Municipality(Grant No.20DZ2220400).
文摘Optical reservoir computing(ORC)offers advantages,such as high computational speed,low power consumption,and high training speed,so it has become a competitive candidate for time series analysis in recent years.The current ORC employs single-dimensional encoding for computation,which limits input resolution and introduces extraneous information due to interactions between optical dimensions during propagation,thus constraining performance.Here,we propose complex-value encoding-based optoelectronic reservoir computing(CE-ORC),in which the amplitude and phase of the input optical field are both modulated to improve the input resolution and prevent the influence of extraneous information on computation.In addition,scale factors in the amplitude encoding can fine-tune the optical reservoir dynamics for better performance.We built a CE-ORC processing unit with an iteration rate of up to∼1.2 kHz using high-speed communication interfaces and field programmable gate arrays(FPGAs)and demonstrated the excellent performance of CE-ORC in two time series prediction tasks.In comparison with the conventional ORC for the Mackey–Glass task,CE-ORC showed a decrease in normalized mean square error by∼75%.Furthermore,we applied this method in a weather time series analysis and effectively predicted the temperature and humidity within a range of 24 h.
基金support from the National Natural Science Foundation of China (Grant Nos.62027820,61975143,61735012,and 62205380).
文摘Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.
文摘In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.
文摘Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.
基金partially supported by the JSPS KAKENHI(JP22H03643,JP19K22891)。
文摘Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.
文摘Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503338,61573316,61374152,and 11302195)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.61072046)the Basic Scientific and Technological Frontier Project of Henan Province(No.1123004100322)
文摘Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.
基金Project supported by the Science and Technology Support Program of Xingtai,China(Grant No.2019ZC054)。
文摘This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.
基金Project supported by the National Natural Science Foundation of China(Grant No.61773010)Taishan Scholar Foundation of Shandong Province of China(Grant No.ts20190938)。
文摘In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system.By using numerical measures,complex dynamical behaviors of the memristive laser system are uncovered.It appears the alternating appearance of quasi-periodic and chaotic oscillations.The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy.Interestingly,initial-values-oriented extreme multi-stability patterns are found,where the coexisting attractors have the same Lyapunov exponents.In addition,the introduction of a memristor greatly improves the complexity of the laser system.Moreover,to control the amplitude and offset of the chaotic signal,two kinds of geometric control methods including amplitude control and rotation control are designed.The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics.Finally,a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62176189 and 62106181)the Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Grant No. Y202002)。
文摘Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.
文摘Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.
文摘In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.
文摘For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.
