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While the optimization problem behind deep neural networks is highlynon-convex, it is frequently observed in practice that training deep networksseems possible without getting stuck in suboptimal points. It has been arguedthat 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 areglobally optimal, for a fully connected network with squared loss and analyticactivation function given that the number of hidden units of one layer of thenetwork is larger than the number of training points and the network structurefrom this layer on is pyramidal.

The loss surface of deep and wide neural networks