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Semi-flat minima and saddle points by embedding neural networks to overparameterization
Kenji Fukumizu · Shoichiro Yamaguchi · Yoh-ichi Mototake · Mirai Tanaka

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #216

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.

Author Information

Kenji Fukumizu (Institute of Statistical Mathematics / Preferred Networks / RIKEN AIP)
Shoichiro Yamaguchi (Preferred Networks)
Yoh-ichi Mototake (Institute of Statistical Mathematics)
Mirai Tanaka (The Institute of Statistical Mathematics / RIKEN)

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