NeurIPS 2019poster31 citations

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

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

Abstract

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.

BibTeX
@inproceedings{NEURIPS2019_a4ee59dd,
 author = {Fukumizu, Kenji and Yamaguchi, Shoichiro and Mototake, Yoh-ichi and Tanaka, Mirai},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Semi-flat minima and saddle points by embedding neural networks to overparameterization},
 url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/a4ee59dd868ba016ed2de90d330acb6a-Paper.pdf},
 volume = {32},
 year = {2019}
}