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Most supervised neural networks (NNs) are trained by minimizing the mean squared error (MSE) of the training set. In the presence of outliers, the resulting NN model can differ significantly from the underlying system that generates the data. Two different approaches are used to study the mechanism by which outliers affect the resulting models: influence function and maximum likelihood. The mean log squared error (MLSE) is proposed as the error criteria that can be easily adapted by most supervised learning algorithms. Simulation results indicate that the proposed method is robust against outliers