Volterra characterization of neural networks

The authors analyze the application of the Volterra theory of nonlinear systems to neural networks. Expressions for efficiently computing the Volterra kernels of both a single hidden layer feedforward neural network and a recurrent one are presented. The authors also address the issue of functional representation of the recurrent neural network architecture and delineate a class of systems that can be approximated by this model. Computer simulations are also presented which indicate that neural networks characterization by their Volterra expansion may be useful in optimal architecture selection and assessment of learning and generalization