Adventures in cubic curve fitting: two optimization techniques and their application to the training of neural networks

Presents two optimization techniques based on cubic curve fitting; one based on function values and derivatives at two previous points, and another based on derivatives at three previous points. The latter approach is viewed from a derivative space perspective, obviating the need to compute the vertical translation of the cubic, thus simplifying the fitting problem. The authors demonstrate the effectiveness of the second method in training neural networks on parity problems of various sizes, and compare their results to a modified Quickprop algorithm and to gradient descent