The geometrical learning of multi-layer artificial neural networks with guaranteed convergence

A learning algorithm called geometrical expanding learning (GEL) is proposed to train multilayer artificial neural networks (ANNs) with guaranteed convergence for an arbitrary function in a binary field. It is noted that there has not yet been found a learning algorithm for a three-layer ANN which guarantees convergence. The most significant contribution of the proposed research is the development of a learning algorithm for multilayer ANNs which guarantees convergence and automatically determines the required number of neurons. The learning speed of the proposed GEL algorithm is much faster than that of the backpropagation learning algorithm in a binary field