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We theoretically study the landscape of the training error for neuralnetworks in overparameterized cases. We consider three basic methods forembedding a network into a wider one with more hidden units, and discusswhether a minimum point of the narrower network gives a minimum or saddle pointof the wider one. Our results show that the networks with smooth and ReLUactivation have different partially flat landscapes around the embedded point.We also relate these results to a difference of their generalization abilitiesin overparameterized realization.

Semi-flat minima and saddle points by embedding neural networks to overparameterization