Learning functions and their derivatives using Taylor series and neural networks

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.