Quantifying Generalization in Linearly Weighted Neural Networks

Abst ract . Th e Vapn ik-Chervonenkis dimension has proven to be of great use in the theoret ical study of generalizat ion in artificial neural networks. Th e "probably approximately correct" learning framework is described and the importance of the Vapnik-Chervonenkis dimension is illustrated. We then investigate the Vapnik-Chervonenkis dimension of certain types of linearly weighted neural networks. First , we obtain bounds on the Vapnik-Chervonenkis dimensions of radial basis function networks with basis functions of several types. Secondly, we calculate the VapnikChervonenkis dimension of polynomial discriminant funct ions defined over both real and binary-valued inputs.