Stabilizing GANs’ Training with Brownian Motion Controller

Tianjiao Luo, Ziyu Zhu, Jianfei Chen, Jun Zhu
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:23140-23156, 2023.

Abstract

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs’ training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-luo23g, title = {Stabilizing {GAN}s’ Training with Brownian Motion Controller}, author = {Luo, Tianjiao and Zhu, Ziyu and Chen, Jianfei and Zhu, Jun}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {23140--23156}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/luo23g/luo23g.pdf}, url = {https://proceedings.mlr.press/v202/luo23g.html}, abstract = {The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs’ training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.} }
Endnote
%0 Conference Paper %T Stabilizing GANs’ Training with Brownian Motion Controller %A Tianjiao Luo %A Ziyu Zhu %A Jianfei Chen %A Jun Zhu %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-luo23g %I PMLR %P 23140--23156 %U https://proceedings.mlr.press/v202/luo23g.html %V 202 %X The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs’ training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.
APA
Luo, T., Zhu, Z., Chen, J. & Zhu, J.. (2023). Stabilizing GANs’ Training with Brownian Motion Controller. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:23140-23156 Available from https://proceedings.mlr.press/v202/luo23g.html.

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