  Multilayer perceptrons (MLP) with one hidden layer have been used for a long
time to deal with non-linear regression. However, in some task, MLP's are too
powerful models and a small mean square error (MSE) may be more due to
overfitting than to actual modelling. If the noise of the regression model is
Gaussian, the overfitting of the model is totally determined by the behavior of
the likelihood ratio test statistic (LRTS), however in numerous cases the
assumption of normality of the noise is arbitrary if not false. In this paper,
we present an universal bound for the overfitting of such model under weak
assumptions, this bound is valid without Gaussian or identifiability
assumptions. The main application of this bound is to give a hint about
determining the true architecture of the MLP model when the number of data goes
to infinite. As an illustration, we use this theoretical result to propose and
compare effective criteria to find the true architecture of an MLP.
