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Learning functions and their derivatives using Taylor series and neural networks

Hanselmann, T., Zaknich, A. and Attikiouzel, Y. (1999) Learning functions and their derivatives using Taylor series and neural networks. In: International Joint Conference on Neural Networks, IJCNN 99, 10 - 16 July, Washington, DC, USA pp. 409-412.

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This paper describes a design based on the Taylor series to approximate a function and its derivatives. After being trained, derivatives are obtained in a fast feedforward evaluation without the need for back propagation or forward perturbation. The Taylor network is basically an implementation of the Taylor series of a function. However, instead of only having one expansion point, it uses a function of expansion points and takes account of the order of the Taylor series by biasing individual terms of the Taylor series. A simple learning algorithm is given and demonstrated with a simple experiment to learn a sinusoid and its first derivative.

Item Type: Conference Paper
Publisher: IEEE
Copyright: © 1999 IEEE
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