Resolution of singularities via deep complex-valued neural networks
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4434
Abstract: It has been reported that training deep neural networks is more difficult than training shallow neural networks. Hinton et al. proposed deep belief networks with a learning algorithm that trains one layer at a time. A… read more here.
Keywords: valued neural; deep neural; neural networks; singular points ... See more keywords
Analysis of deep complex‐valued convolutional neural networks for MRI reconstruction and phase‐focused applications
Sign Up to like & getrecommendations! Published in 2021 at "Magnetic Resonance in Medicine"
DOI: 10.1002/mrm.28733
Abstract: Deep learning has had success with MRI reconstruction, but previously published works use real‐valued networks. The few works which have tried complex‐valued networks have not fully assessed their impact on phase. Therefore, the purpose of… read more here.
Keywords: phase; convolutional neural; mri reconstruction; valued convolutional ... See more keywords
Partial Fourier reconstruction of complex MR images using complex-valued convolutional neural networks.
Sign Up to like & getrecommendations! Published in 2021 at "Magnetic resonance in medicine"
DOI: 10.1002/mrm.29033
Abstract: PURPOSE To provide a complex-valued deep learning approach for partial Fourier (PF) reconstruction of complex MR images. METHODS Conventional PF reconstruction methods, such as projection onto convex sets (POCS), uses low-resolution image phase information from… read more here.
Keywords: reconstruction; phase; image; fourier reconstruction ... See more keywords
Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays
Sign Up to like & getrecommendations! Published in 2020 at "Circuits, Systems, and Signal Processing"
DOI: 10.1007/s00034-020-01428-4
Abstract: This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get… read more here.
Keywords: finite time; neural networks; time; time fixed ... See more keywords
Exponential stability analysis for delayed complex-valued memristor-based recurrent neural networks
Sign Up to like & getrecommendations! Published in 2017 at "Neural Computing and Applications"
DOI: 10.1007/s00521-017-3166-6
Abstract: The exponential stability problem for complex-valued memristor-based recurrent neural networks (CVMRNNs) with time delays is studied in this paper. As an extension of real-valued memristor-based recurrent neural networks, CVMRNNs can be separated into real and… read more here.
Keywords: valued memristor; based recurrent; memristor based; complex valued ... See more keywords
Fourier transforms on finite group actions and bent functions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-021-01057-3
Abstract: Highly nonlinear functions (bent functions, perfect nonlinear functions, etc.) on finite fields and finite (abelian or nonabelian) groups have been studied in numerous papers. As a generalization of bent functions on finite groups, bent functions… read more here.
Keywords: group; bent functions; functions finite; complex valued ... See more keywords
Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks
Sign Up to like & getrecommendations! Published in 2017 at "Neural Processing Letters"
DOI: 10.1007/s11063-017-9621-7
Abstract: In this paper, based on Wirtinger calculus, we introduce a quasi-Newton method for training complex-valued neural networks with analytic activation functions. Using the duality between Wirtinger calculus and multivariate real calculus, we prove a convergence… read more here.
Keywords: valued neural; method; quasi newton; newton method ... See more keywords
Robust State Estimation for Delayed Complex-Valued Neural Networks
Sign Up to like & getrecommendations! Published in 2017 at "Neural Processing Letters"
DOI: 10.1007/s11063-017-9626-2
Abstract: This paper is concerned with the state estimation problem for the uncertain complex-valued neural networks with time delays. The parameter uncertainties are assumed to be norm-bounded. Through available output measurements containing nonlinear Lipschitz-like terms, we… read more here.
Keywords: state; valued neural; neural networks; state estimation ... See more keywords
$$\alpha $$α-Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays
Sign Up to like & getrecommendations! Published in 2019 at "Neural Processing Letters"
DOI: 10.1007/s11063-018-9938-x
Abstract: This paper investigates the global $$\alpha $$α-exponential stability of impulsive fractional-order complex-valued neural networks with time delays. By constructing proper Lyapunov–Krasovskii functional and employing fractional-order complex-valued differential inequality, some sufficient conditions are obtained to ensure… read more here.
Keywords: alpha exponential; order; order complex; complex valued ... See more keywords
Exponential Stability and Sampled-Data Synchronization of Delayed Complex-Valued Memristive Neural Networks
Sign Up to like & getrecommendations! Published in 2019 at "Neural Processing Letters"
DOI: 10.1007/s11063-019-10082-0
Abstract: This paper is devoted to the global exponential stability (GES) and synchronization control of delayed complex-valued memristive neural networks (CVMNNs). The criterion on the existence, uniqueness and GES of the equilibrium point (EP) for delayed… read more here.
Keywords: neural networks; valued memristive; memristive neural; complex valued ... See more keywords
Robust Passivity and Stability Analysis of Uncertain Complex-Valued Impulsive Neural Networks with Time-Varying Delays
Sign Up to like & getrecommendations! Published in 2021 at "Neural Processing Letters"
DOI: 10.1007/s11063-020-10401-w
Abstract: In this article, we investigate the robust passivity and stability analysis of uncertain complex-valued impulsive neural network (UCVINN) models with time-varying delays. Many practical systems are subject to uncertainty in the real-world environments. As a… read more here.
Keywords: robust passivity; stability analysis; passivity stability; complex valued ... See more keywords