A LEARNING RESULT FOR CONTINUOUS-TIME RECURRENT NEURAL NETWORKS

The following learning problem is considered, for continuous-time recu rrent neural networks having sigmoidal activation functions. Given a ' 'black box'' representing an unknown system, measurements of output de rivatives are collected, for a set of randomly generated inputs, and a network is used to approximate the observed behavior. It is shown tha t the number of inputs needed for reliable generalization (the sample complexity of the learning problem) is upper bounded by an expression that grows polynomially with the dimension of the network and logarith mically with the number of output derivatives being matched. (C) 1998 Elsevier Science B.V. All rights reserved.