New Critical Analysis on Global Convergence of Recurrent Neural Networks with Projection Mappings

Authors:
Chen Qiao;Zong-Ben Xu
Affiliations:
Institute for Information and System Science, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, 710049, P.R. China;Institute for Information and System Science, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, 710049, P.R. China
Venue:
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Year:
2007

Citing 5
Cited 2

On the stability of globally projected dynamical systems

Journal of Optimization Theory and Applications
New theorems on global convergence of some dynamical systems

Neural Networks
A reference model approach to stability analysis of neural networks

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Estimate of exponential convergence rate and exponential stability for neural networks

IEEE Transactions on Neural Networks
Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem

IEEE Transactions on Neural Networks

On the P-critical dynamics analysis of projection recurrent neural networks

Neurocomputing
The UPPAM continuous-time RNN model and its critical dynamics study

Neurocomputing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we present the general analysis of global convergence for the recurrent neural networks (RNNs) with projection mappings in the critical case that M(L,Γ), a matrix related with the weight matrix Wand the activation mapping of the networks, is nonnegative for a positive diagonal matrix Γ. In contrast to the existing conclusion such as in [1], the present critical stability results do not require the condition that ΓWmust be symmetric and can be applied to the general projection mappings other than nearest point projection mappings. An example has also been shown that the theoretical results obtained in the present paper have explicitly practical application.