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

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Kenji Fukumizu, Shoichiro Yamaguchi, Yoh-ichi Mototake, Mirai Tanaka


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