Minimal MLPs do not model the XOR logic

AbstractFitting the continuous valid logic of the exclusive OR (XOR) problem requires more than a minimal neural network configuration. This letter shows that the simplest logic to fit the XOR problem involves boundaries that cannot be mapped by a Multi-Layer Perceptron (MLP) with just two hidden nodes. This observation calls into question rule extraction methodologies based on pruning, since this practice can lock the network into a subspace of achievable continuous valued logic functions that prevent it from mapping the simplest logic to explain the data.