Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion

2016 ◽  
Vol 20 (1) ◽  
pp. 132-138 ◽  
Author(s):  
Bolin Liao ◽  
◽  
Lin Xiao ◽  
Jie Jin ◽  
Lei Ding ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Hardware Implementation ◽  
Matrix Inversion ◽  
Matrix Inverse ◽  
Novel Complex ◽  
Simulation Results ◽  
Complex Valued ◽  
Gradient Neural Network

Static matrix inverse solving has been studied for many years. In this paper, we aim at solving a dynamic complex-valued matrix inverse. Specifically, based on the artful combination of a conventional gradient neural network and the recently-proposed Zhang neural network, a novel complex-valued neural network model is presented and investigated for computing the dynamic complex-valued matrix inverse in real time. A hardware implementation structure is also offered. Moreover, both theoretical analysis and simulation results substantiate the effectiveness and advantages of the proposed recurrent neural network model for dynamic complex-valued matrix inversion.

scholarly journals Design of a nonlinearly activated gradient-based neural network and its application to matrix inversion

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5095-5101
Author(s):  
Yongsheng Zhang ◽  
Lin Xiao ◽  
Lei Ding ◽  
Zhiguo Tan ◽  
KE. Chenc ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Network Models ◽  
Matrix Inversion ◽  
Activation Functions ◽  
Neural Network Models ◽  
Gradient Based ◽  
Simulation Results

Different from the traditional linearly activated gradient-based neural network model (GNN model), two nonlinear activation functions are presented and investigated to construct two nonlinear gradient-based neural network models (NGNN-1 model and NGNN-2 model) for matrix inversion in this paper. For comparative and illustrative purposes, the traditional GNN model is also used to solve matrix inversion problems under the same circumstance. In addition, the simulation results of the computer finally confirm the validity and superiority of the two nonlinear gradient-based neural network models specially activated by two nonlinear activation functions for matrix inversion, as compared with the traditional GNN model.

scholarly journals An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 19291-19302 ◽  
Author(s):  
Lei Ding ◽  
Lin Xiao ◽  
Kaiqing Zhou ◽  
Yonghong Lan ◽  
Yongsheng Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Neural Network Model ◽  
Sylvester Equation ◽  
Time Varying ◽  
Complex Valued

scholarly journals Asymmetric generalization in adaptation to target displacement errors in humans and in a neural network model

2015 ◽  
Vol 113 (7) ◽  
pp. 2360-2375 ◽  
Author(s):  
Stephanie Westendorff ◽  
Shenbing Kuang ◽  
Bahareh Taghizadeh ◽  
Opher Donchin ◽  
Alexander Gail
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Visual Target ◽  
Hand Position ◽  
Prediction Errors ◽  
Visually Guided ◽  
Target Error ◽  
Adaptation Mechanisms ◽  
Simulation Results

Different error signals can induce sensorimotor adaptation during visually guided reaching, possibly evoking different neural adaptation mechanisms. Here we investigate reach adaptation induced by visual target errors without perturbing the actual or sensed hand position. We analyzed the spatial generalization of adaptation to target error to compare it with other known generalization patterns and simulated our results with a neural network model trained to minimize target error independent of prediction errors. Subjects reached to different peripheral visual targets and had to adapt to a sudden fixed-amplitude displacement (“jump”) consistently occurring for only one of the reach targets. Subjects simultaneously had to perform contralateral unperturbed saccades, which rendered the reach target jump unnoticeable. As a result, subjects adapted by gradually decreasing reach errors and showed negative aftereffects for the perturbed reach target. Reach errors generalized to unperturbed targets according to a translational rather than rotational generalization pattern, but locally, not globally. More importantly, reach errors generalized asymmetrically with a skewed generalization function in the direction of the target jump. Our neural network model reproduced the skewed generalization after adaptation to target jump without having been explicitly trained to produce a specific generalization pattern. Our combined psychophysical and simulation results suggest that target jump adaptation in reaching can be explained by gradual updating of spatial motor goal representations in sensorimotor association networks, independent of learning induced by a prediction-error about the hand position. The simulations make testable predictions about the underlying changes in the tuning of sensorimotor neurons during target jump adaptation.

Sign in / Sign up

Export Citation Format

Share Document