Analytical Interpretation of Feed-Forward Nets outputs after Training

The minimization quadratic error criterion which gives rise to the back-propagation algorithm is studied using functional analysis techniques. With them, we recover easily the well-known statistical result which states that the searched global minimum is a function which assigns, to each input pattern, the expected value of its corresponding output patterns. Its application to classification tasks shows that only certain output class representations can be used to obtain the optimal Bayesian decision rule. Finally, our method permits the study of other error criterions, finding out, for instance, that absolute value errors lead to medians instead of mean values.