New critical analysis on global convergence of recurrent neural networks with projection mappings

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. © Springer-Verlag Berlin Heidelberg 2007.