Splines, Rational Functions and Neural Networks

Part of Advances in Neural Information Processing Systems 4 (NIPS 1991)

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Robert C. Williamson, Peter Bartlett


Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.