Built on

A. Müller, “Integral probability metrics and their generating classes of functions,” Advances in Applied Probability , vol. 29, no. 02, pp. 429–443, 1997
1997
Earlier work this paper cites.
B. Schölkopf and A. J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond . MIT press, 2002
2002
Earlier work this paper cites.
T. Hastie, S. Rosset, R. Tibshirani, and J. Zhu, “The entire regularization path for the support vector machine,” Journal of Machine Learning Research , vol. 5, no. Oct, pp. 1391–1415, 2004
2004
Earlier work this paper cites.
J. S. Marron, M. J. Todd, and J. Ahn, “Distance-weighted discrimination,” Journal of the American Statistical Association , vol. 102, no. 480, pp. 1267–1271, 2007
2007
Earlier work this paper cites.
B. K. Sriperumbudur, K. Fukumizu, A. Gretton, B. Schölkopf, and G. R. Lanckriet, “On integral probability metrics, ϕ \phi -divergences and binary classification,” arXiv preprint arXiv:0901.2698 , 2009
Original
2009
Earlier work this paper cites.
J. Ahn and J. Marron, “The maximal data piling direction for discrimination,” Biometrika , vol. 97, no. 1, pp. 254–259, 2010
2010
Earlier work this paper cites.
B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. Lanckriet, “Hilbert space embeddings and metrics on probability measures,” Journal of Machine Learning Research , vol. 11, no. Apr, pp. 1517–1561, 2010
2010
Earlier work this paper cites.
D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” arXiv preprint arXiv:1312.6114 , 2013
Original
2013
Earlier work this paper cites.

Similar

I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial nets,” in Advances in Neural Information Processing Systems , 2014, pp. 2672–2680
2014
Cited alongside, same era.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014
Original
2014
Cited alongside, same era.
Y. Li, K. Swersky, and R. Zemel, “Generative moment matching networks,” in Proceedings of The 32nd International Conference on Machine Learning , 2015, pp. 1718–1727
2015
Cited alongside, same era.
G. Dziugaite, D. Roy, and Z. Ghahramani, “Training generative neural networks via maximum mean discrepancy optimization,” in Uncertainty in Artificial Intelligence-Proceedings of the 31st Conference, UAI 2015 , 2015, pp. 258–267
2015
Cited alongside, same era.

Then

T. Che, Y. Li, A. P. Jacob, Y. Bengio, and W. Li, “Mode regularized generative adversarial networks,” arXiv preprint arXiv:1612.02136 , 2016
Original
2016
Later among the works it cites.
M. Arjovsky and L. Bottou, “Towards principled methods for training generative adversarial networks,” in NIPS 2016 Workshop on Adversarial Training. In review for ICLR , vol. 2016, 2017
2017
Closest in time.
M. Arjovsky, S. Chintala, and L. Bottou, “Wasserstein GAN,” arXiv preprint arXiv:1701.07875 , 2017
Original
2017
Closest in time.
Y. Mroueh, T. Sercu, and V. Goel, “McGan: Mean and covariance feature matching GAN,” arXiv preprint arXiv:1702.08398 , 2017
Original
2017
Closest in time.
I. Carmichael and J. Marron, “Geometric insights into support vector machine behavior using the KKT conditions,” arXiv preprint arXiv:1704.00767 , 2017

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2017

Geometric GAN

Lim, Jae Hyun, Ye, Jong Chul

Understand

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.

Built on

A. Müller, “Integral probability metrics and their generating classes of functions,” Advances in Applied Probability , vol. 29, no. 02, pp. 429–443, 1997
1997
Earlier work this paper cites.
B. Schölkopf and A. J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond . MIT press, 2002
2002
Earlier work this paper cites.
T. Hastie, S. Rosset, R. Tibshirani, and J. Zhu, “The entire regularization path for the support vector machine,” Journal of Machine Learning Research , vol. 5, no. Oct, pp. 1391–1415, 2004
2004
Earlier work this paper cites.
J. S. Marron, M. J. Todd, and J. Ahn, “Distance-weighted discrimination,” Journal of the American Statistical Association , vol. 102, no. 480, pp. 1267–1271, 2007
2007
Earlier work this paper cites.
B. K. Sriperumbudur, K. Fukumizu, A. Gretton, B. Schölkopf, and G. R. Lanckriet, “On integral probability metrics, ϕ \phi -divergences and binary classification,” arXiv preprint arXiv:0901.2698 , 2009
Original
2009
Earlier work this paper cites.
J. Ahn and J. Marron, “The maximal data piling direction for discrimination,” Biometrika , vol. 97, no. 1, pp. 254–259, 2010
2010
Earlier work this paper cites.
B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. Lanckriet, “Hilbert space embeddings and metrics on probability measures,” Journal of Machine Learning Research , vol. 11, no. Apr, pp. 1517–1561, 2010
2010
Earlier work this paper cites.
D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” arXiv preprint arXiv:1312.6114 , 2013
Original
2013
Earlier work this paper cites.

Similar

I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial nets,” in Advances in Neural Information Processing Systems , 2014, pp. 2672–2680
2014
Cited alongside, same era.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014
Original
2014
Cited alongside, same era.
Y. Li, K. Swersky, and R. Zemel, “Generative moment matching networks,” in Proceedings of The 32nd International Conference on Machine Learning , 2015, pp. 1718–1727
2015
Cited alongside, same era.
G. Dziugaite, D. Roy, and Z. Ghahramani, “Training generative neural networks via maximum mean discrepancy optimization,” in Uncertainty in Artificial Intelligence-Proceedings of the 31st Conference, UAI 2015 , 2015, pp. 258–267
2015
Cited alongside, same era.

Then

T. Che, Y. Li, A. P. Jacob, Y. Bengio, and W. Li, “Mode regularized generative adversarial networks,” arXiv preprint arXiv:1612.02136 , 2016
Original
2016
Later among the works it cites.
M. Arjovsky and L. Bottou, “Towards principled methods for training generative adversarial networks,” in NIPS 2016 Workshop on Adversarial Training. In review for ICLR , vol. 2016, 2017
2017
Closest in time.
M. Arjovsky, S. Chintala, and L. Bottou, “Wasserstein GAN,” arXiv preprint arXiv:1701.07875 , 2017
Original
2017
Closest in time.
Y. Mroueh, T. Sercu, and V. Goel, “McGan: Mean and covariance feature matching GAN,” arXiv preprint arXiv:1702.08398 , 2017
Original
2017
Closest in time.
I. Carmichael and J. Marron, “Geometric insights into support vector machine behavior using the KKT conditions,” arXiv preprint arXiv:1704.00767 , 2017

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

A. Radford, L. Metz, and S. Chintala, “Unsupervised representation learning with deep convolutional generative adversarial networks,” arXiv preprint arXiv:1511.06434 , 2015

Original

2015

Cited alongside, same era.

S. Nowozin, B. Cseke, and R. Tomioka, “f-GAN: Training generative neural samplers using variational divergence minimization,” in Advances in Neural Information Processing Systems , 2016, pp. 271–279

2016

Cited alongside, same era.

V. Dumoulin, I. Belghazi, B. Poole, A. Lamb, M. Arjovsky, O. Mastropietro, and A. C. Courville, “Adversarially learned inference,” arXiv preprint arXiv:1606.00704 , 2016

Original

2016

Cited alongside, same era.

L. Metz, B. Poole, D. Pfau, and J. Sohl-Dickstein, “Unrolled generative adversarial networks,” arXiv preprint arXiv:1611.02163 , 2016

Original

2016

Cited alongside, same era.

T. Tieleman and G. Hinton, “RMSprop Gradient Optimization,” http://www.cs.toronto.edu/t̃ijmen/csc321/slides/lecture-slides-lec6.pdf

Cited in the paper.