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The Error Surface of the simplest XOR Network has no local Minima

By Ida G. Sprinkhuizen-Kuyper and E. J. W. Boers


The artificial neural network with one hidden unit and the input units connected to the output unit 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

Year: 1994
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