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We expand on a recent paper by Courrieu which introduces three algorithms for determin- ing the distance between any point and the interpolation domain associated with a feedforward neural network. This has been shown to have a significant relation with the network's generalization capa- bility. A further neural-like relaxation algorithm is presented here, which is proven to naturally solve the problem originally posed by Courrieu. The algorithm is based on a powerful result developed in the context of Markov chain theory, and turns out to be a special case of a more general relaxation model which has long become a standard technique in the machine vision domain. Some experiments are presented which conhrm the validity of the proposed approach.

A relaxation algorithm for estimating the domain of validity of feedforward neural networks