Multivariable functional interpolation and adaptive networks. (English) Zbl 0657.68085

The relationship between “learning” in adaptive layered networks and the fitting of data with high dimensional surfaces is discussed. This leads naturally to a picture of “generalization” in terms of interpolation between known data points and suggests a rational approach to the theory of such networks. A class of adaptive networks is identified which makes the interpolation scheme explicit. This class has the property that learnig is equivalent to the solution of a set of linear equations. These networks thus represent nonlinear relationships while having a guaranteed learning rule.


68T05 Learning and adaptive systems in artificial intelligence
41A05 Interpolation in approximation theory