Non-standard norms in genetically trained neural networks

We discuss alternative norms to train neural networks (NNs). We focus on the so called multilayer perceptrons (MLPs). To achieve this we rely on a genetic algorithm called an eclectic GA (EGA). By using the EGA we avoid the drawbacks of the standard training algorithm in this sort of NN: the backpropagation algorithm. We define four measures of distance: the mean exponential error (MEE); the mean absolute error (MAE); the maximum square error (MSE); and the maximum (supremum) absolute error (SAE). We analyze the behavior of an MLP NN on two kinds of problems: classification and forecasting. We discuss the results of applying an EGA to train the NNs and show that alternative norms yield better results than the traditional RMS norm. We also discuss the resilience of genetically trained NNs to the change of the transfer function in the output layer.