SUPERVISED TRAINING OF NEURAL NETWORKS VIA ELLIPSOID ALGORITHMS

In this paper we show that two ellipsoid algorithms can be used to tra in single-layer neural networks with general staircase nonlinearities. The ellipsoid algorithms have several advantages over other conventio nal training approaches including (1) explicit convergence results and automatic determination of linear separability, (2) an elimination of problems with picking initial values for the weights, (3) guarantees that the trained weights are in some ''acceptable region,'' (4) certai n ''robustness'' characteristics, and (5) a training approach for neur al networks with a wider variety of activation functions. We illustrat e the training approach by training the MAJ function and then by showi ng how to train a controller for a reaction chamber temperature contro l problem.