ON THE STATISTICAL PHYSICS OF RADIAL BASIS FUNCTION NETWORKS

Techniques from statistical physics have been applied successfully in recent years to the analysis of the generalization performance of neural networks. However, most of the analysis to date has been for perceptron-like networks or simple generalizations thereof such as committee machines, and none of the networks studied are used to any significant extent in practice. This letter presents results obtained in applying techniques from statistical physics to a popular class of neural networks that has been used successfully in many practical applications: the Gaussian radial basis function networks. We obtain expressions for the learning curves exhibited by these networks in the high-temperature limit for both realizable and unrealizable target rules.