On the Flexible Dynamics Analysis for the Unified Discrete-Time RNNs

The uniformly pseudo-projection-anti-monotone (UPPAM) networks can jointly cover almost all of the known recurrent neural network individuals. In this paper, we develop some convergence theory for the UPPAM networks when the time is discrete. The results for convergence to an equilibrium as well as to the ring whose period is not greater than 2 for the UPPAM networks do not require the connective weight matrices to be symmetric anymore, which is the basic requirements for many existing dynamics analysis for the discrete-time recurrent neural network models. In addition, these theorems contain the least constraints, give the general determinate methods of convergence for UPPAM networks, and can be verified and utilized very easily. The study shows that the approach adopted in the present paper is powerful, particularly in the sense of unifying, simplifying and extending the currently existing various dynamics results for discrete-time RNNs.