title: The general critical analysis for continuous-time UPPAM recurrent neural networks.
abstract: The uniformly pseudo-projection-anti-monotone (UPPAM) neural network model, which can be considered as the unified continuous-time neural networks (CNNs), includes almost all of the known CNNs individuals. Recently, studies on the critical dynamics behaviors of CNNs have drawn special attentions due to its importance in both theory and applications. In this paper, we will present the analysis of the UPPAM network under the general critical conditions. It is shown that the UPPAM network possesses the global convergence and asymptotical stability under the general critical conditions if the network satisfies one quasi-symmetric requirement on the connective matrices, which is easy to be verified and applied. The general critical dynamics have rarely been studied before, and this work is an attempt to gain an meaningful assurance of general critical convergence and stability of CNNs. Since UPPAM network is the unified model for CNNs, the results obtained here can generalize and extend the existing critical conclusions for CNNs individuals, let alone those non-critical cases. Moreover, the easily verified conditions for general critical convergence and stability can further promote the applications of CNNs.
authors: School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, P.R. China and with the Department of Biomedical Engineering, Tulane University, New Orleans, LA, 70118, USA.
authors: Chen
authors: C
authors: Qiao
authors: School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, P.R. China.
authors: Wen-Feng
authors: WF
authors: Jing
authors: School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, P.R. China and with the Department of Biomedical Engineering, Tulane University, New Orleans, LA, 70118, USA.
authors: Jian
authors: J
authors: Fang
authors: Department of Biomedical Engineering, Tulane University, New Orleans, LA, 70118, USA and the Center of Genomics and Bioinformatics, Tulane University, New Orleans, LA, 70112, USA.
authors: Yu-Ping
authors: YP
authors: Wang
keywords: Continuous-time recurrent neural network; dynamical analysis; general critical condition; uniformly pseudo-projection-anti-monotone network