  We consider regression models involving multilayer perceptrons (MLP) with one
hidden layer and a Gaussian noise. The estimation of the parameters of the MLP
can be done by maximizing the likelihood of the model. In this framework, it is
difficult to determine the true number of hidden units because the information
matrix of Fisher is not invertible if this number is overestimated. However, if
the parameters of the MLP are in a compact set, we prove that the minimization
of a suitable information criteria leads to consistent estimation of the true
number of hidden units.
