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GGAN

Geometric GAN

Abstract

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric steps: separating hyperplane search, discriminator parameter update away from the separating hyperplane, and the generator update along the normal vector direction of the separating hyperplane. This geometric intuition reveals the limitations of the existing approaches and leads us to propose a new formulation called geometric GAN using SVM separating hyperplane that maximizes the margin. Our theoretical analysis shows that the geometric GAN converges to a Nash equilibrium between the discriminator and generator. In addition, extensive numerical results show that the superior performance of geometric GAN.

Results and models

GGAN 64x64, CelebA-Cropped
Models Dataset SWD MS-SSIM FID Config Download
GGAN 64x64 CelebA-Cropped 11.18, 12.21, 39.16/20.85 0.3318 20.1797 config model | log
GGAN 128x128 CelebA-Cropped 9.81, 11.29, 19.22, 47.79/22.03 0.3149 18.7647 config model | log
GGAN 64x64 LSUN-Bedroom 9.1, 6.2, 12.27/9.19 0.0649 85.6629 config model | log

Note: In the original implementation of GGAN, they set G_iters to 10. However our framework does not support G_iters currently, so we dropped the settings in the original implementation and conducted several experiments with our own settings. We have shown above the experiment results with the lowest fid score.
Original settings and our settings:

Models Dataset Architecture optimizer lr_G lr_D G_iters D_iters
GGAN(origin) 64x64 CelebA-Cropped dcgan-archi RMSprop 0.0002 0.0002 10 1
GGAN(ours) 64x64 CelebA-Cropped dcgan-archi Adam 0.001 0.001 1 1
GGAN(origin) 64x64 LSUN-Bedroom dcgan-archi RMSprop 0.0002 0.0002 10 1
GGAN(ours) 64x64 LSUN-Bedroom lsgan-archi Adam 0.0001 0.0001 1 1

Citation

@article{lim2017geometric,
  title={Geometric gan},
  author={Lim, Jae Hyun and Ye, Jong Chul},
  journal={arXiv preprint arXiv:1705.02894},
  year={2017},
  url={https://arxiv.org/abs/1705.02894},
}