Generative Adversarial Symmetry Discovery

Jianke Yang, Robin Walters, Nima Dehmamy, Rose Yu
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:39488-39508, 2023.

Abstract

Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-yang23n, title = {Generative Adversarial Symmetry Discovery}, author = {Yang, Jianke and Walters, Robin and Dehmamy, Nima and Yu, Rose}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {39488--39508}, 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/yang23n/yang23n.pdf}, url = {https://proceedings.mlr.press/v202/yang23n.html}, abstract = {Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.} }
Endnote
%0 Conference Paper %T Generative Adversarial Symmetry Discovery %A Jianke Yang %A Robin Walters %A Nima Dehmamy %A Rose Yu %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-yang23n %I PMLR %P 39488--39508 %U https://proceedings.mlr.press/v202/yang23n.html %V 202 %X Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.
APA
Yang, J., Walters, R., Dehmamy, N. & Yu, R.. (2023). Generative Adversarial Symmetry Discovery. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:39488-39508 Available from https://proceedings.mlr.press/v202/yang23n.html.

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