Comments on local minima free conditions in multilayer perceptrons

In this letter we point out that multilayer neural networks (MLP) with either sigmoidal units or radial basis functions can be given a canonical form with positive interunits weights, which does not restrict the well-known MLP universal computational capabilities. We give some results on the local minima of the error function using this canonical form. In particular, we prove that the local minima free conditions established in previous works can be relaxed significantly.