The Research on the GC Property for RNNs with Limited Matrix 2-Norm

The global convergence (GC) analysis of recurrent neural networks (RNNs) is a first and necessary step for any practical applications of them. In the present paper, when the connecting matrix of the RNNs with projection mapping owning limited norm, the GC property is assured under the critical condition. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.