Testing the number of parameters with multidimensional MLP

This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example the case when the number of hidden units is know. In this framework, we show that we get a simple asymptotic distribution, if we use the logarithm of the determinant of the empirical error covariance matrix as cost function.