Absolute stability of neural networks
Kiyotoshi Matsuoka · Systems and Computers in Japan · 1992
Abstract A sufficient condition for the state of a recurrent neural network to converge stably to an equilibrium state is the symmetry of the weights of connections between constituent units. However, generally, it imposes a strong restriction on the capability of the network. Although several stability conditions have been proposed for asymmetric recurrent networks, they are too strict and not useful for actual neural networks. Six new stability conditions are derived herein by using two types of Lyapunov functions. Some of them provide milder constraints on the connection weights than the conventional results, and others are particularly useful when the mutual connections between units have opposite signs of weights.