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

There have been numerous recurrent neural network models diversely developed for modeling or simulating the associative memory behavior of human beings in the past decades, and the existing results for each model individual are in certain sense redundant with similarity. By utilizing the innate character of general activation operators, i.e., the uniformly pseudo-projection-anti-monotone property, a unified continuous-time recurrent neural network model is introduced, which can jointly cover almost all of the known continuous-time recurrent neural network individuals. Under the critical condition which is the intrinsic bounded line of stability and instability, we develop some convergence and stability theory for the unified recurrent neural network model when the time is continuous. 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 models and dynamics results of continuous-time RNNs.