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 W and 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 ΓW must 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.
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© 2007 Springer Berlin Heidelberg
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Qiao, C., Xu, ZB. (2007). New Critical Analysis on Global Convergence of Recurrent Neural Networks with Projection Mappings. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_18
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DOI: https://doi.org/10.1007/978-3-540-72395-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72394-3
Online ISBN: 978-3-540-72395-0
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