Existence and Global Attractivity of Stable Solutions in Neural Networks

The present paper shows that a su±cient condition for the existence of a stable solution to an autoregressive neural network model is the continuity and boundedness of the activation function of the hidden units in the multi layer perceptron (MLP). In addition, uniqueness of a stable solution is ensured by global lipschitzness and some conditions on the parameters of the system. In this case, the stable value is globally stable and convergence of the learning process occurs at exponential rate.