488 Solutions to the XOR Problem

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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Frans Coetzee, Virginia Stonick


A globally convergent homotopy method is defined that is capable of sequentially producing large numbers of stationary points of the multi-layer perceptron mean-squared error surface. Using this al(cid:173) gorithm large subsets of the stationary points of two test problems are found. It is shown empirically that the MLP neural network appears to have an extreme ratio of saddle points compared to local minima, and that even small neural network problems have extremely large numbers of solutions.