A rigorous result about the off-line learning approximation

Summary form only given, as follows. The authors consider a mathematical justification of the offline approximation in continuous-time neural networks. In real-time models, a network behavior is characterized by two distinct dynamics evolving according to different time scales, the weight dynamics which is the `slow´ dynamics and the activation dynamics which is the `fast´ dynamics. The offline approximation consists in assuming that during the learning process neural activities are in their steady states. Such an approximation is a common dogma often used to provide an analysis of a network behavior. The authors considered convergent networks and proved that this approximation is valid on a large time scale on the order of 1/ε where ε is the learning rate parameter which controls the learning velocity