Classification of all Stationary Points on a Neural Network Error Surface

The artificial neural network with one hidden unit and the input nodes connected to the output node is considered. It is proven that the error surface of this network for the patterns of the XOR problem has minimum values with zero error and that all other stationary points of the error surface are saddle points. Also, the volume of the regions in weight space with saddle points is zero, hence training this network, using e.g. backpropagation with momentum, on the four patterns of the XOR problem, the correct solution with error zero will be reached in the limit with probability one.