  While the optimization problem behind deep neural networks is highly
non-convex, it is frequently observed in practice that training deep networks
seems possible without getting stuck in suboptimal points. It has been argued
that this is the case as all local minima are close to being globally optimal.
We show that this is (almost) true, in fact almost all local minima are
globally optimal, for a fully connected network with squared loss and analytic
activation function given that the number of hidden units of one layer of the
network is larger than the number of training points and the network structure
from this layer on is pyramidal.
