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

Dynamics analysis for generic projection continuous-time RNNs with bounded matrices

“…When one matrix H, which is the multiplication of the matrices determined by the RNNs and the critical condition, have bounded components, the critical global convergence as well as asymptotical stability will be achieved then. The results obtained here extend, to a large extent, most of the existing critical results given in [3,[5][6][7][8][9]. Furthermore, due to the easily verified characters of the bounded requirement of H, the presented dynamics results surely provide a wider application range for RNNs [10][11][12][13][14][15] .…”

“…The results in [9], i.e., the stability under the requirement that a nonlinear norm is less than 1, obviously is quite different to be verified here.…”

“…For all that, it should be pointed out that all these critical dynamics analysis are only for either the local field neural network model or for the static neural network model respectively, that is because the dynamics study for the generic continuous-time RNNs model (i.e., model (1)) should consider the affection of both two connective weight matrices: W and A at the same time, and which is much more difficult than the analysis for the local field neural network model or for the static neural network model. In [9], the stability of the general RNNs model (1) is presented, but it requires a nonlinear norm, which is deduced by the networks and can be regarded as a nonlinear generalization of the matrix norm, to be less than 1. In fact, this condition is quite hard to be verified in application.…”

Without Diagonal Nonlinear Requirements: The More GeneralP-Critical Dynamical Analysis for UPPAM Recurrent Neural Networks

“…Specially, we say is a ( , )-UPPAM whenever it is a -projection and -uniformly antimonotonous operator. It is worthwhile to note that the UPPAM operator provides a very appropriate, unified framework within which most of the known RNN models can be embedded and uniformly studied [21][22][23].…”

“…Thus, the UPPAM RNNs are called as the unified RNNs. Further, it is guessed that only the study of the dynamics of the UPPAM RNNs may achieve the outcome that we can discriminate the similarity and redundant of the dynamics results among those known RNNs individuals, and which is affirmed following in [22,23] for discrete-time RNNs as well as for continuous-time RNNs, respectively.…”