Latent Space Symmetry Discovery

Jianke Yang, Nima Dehmamy, Robin Walters, Rose Yu
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:56047-56070, 2024.

Abstract

Equivariant neural networks require explicit knowledge of the symmetry group. Automatic symmetry discovery methods aim to relax this constraint and learn invariance and equivariance from data. However, existing symmetry discovery methods are limited to simple linear symmetries and cannot handle the complexity of real-world data. We propose a novel generative model, Latent LieGAN (LaLiGAN), which can discover symmetries of nonlinear group actions. It learns a mapping from the data space to a latent space where the symmetries become linear and simultaneously discovers symmetries in the latent space. Theoretically, we show that our model can express nonlinear symmetries under some conditions about the group action. Experimentally, we demonstrate that our method can accurately discover the intrinsic symmetry in high-dimensional dynamical systems. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-yang24g, title = {Latent Space Symmetry Discovery}, author = {Yang, Jianke and Dehmamy, Nima and Walters, Robin and Yu, Rose}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {56047--56070}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/yang24g/yang24g.pdf}, url = {https://proceedings.mlr.press/v235/yang24g.html}, abstract = {Equivariant neural networks require explicit knowledge of the symmetry group. Automatic symmetry discovery methods aim to relax this constraint and learn invariance and equivariance from data. However, existing symmetry discovery methods are limited to simple linear symmetries and cannot handle the complexity of real-world data. We propose a novel generative model, Latent LieGAN (LaLiGAN), which can discover symmetries of nonlinear group actions. It learns a mapping from the data space to a latent space where the symmetries become linear and simultaneously discovers symmetries in the latent space. Theoretically, we show that our model can express nonlinear symmetries under some conditions about the group action. Experimentally, we demonstrate that our method can accurately discover the intrinsic symmetry in high-dimensional dynamical systems. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.} }
Endnote
%0 Conference Paper %T Latent Space Symmetry Discovery %A Jianke Yang %A Nima Dehmamy %A Robin Walters %A Rose Yu %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-yang24g %I PMLR %P 56047--56070 %U https://proceedings.mlr.press/v235/yang24g.html %V 235 %X Equivariant neural networks require explicit knowledge of the symmetry group. Automatic symmetry discovery methods aim to relax this constraint and learn invariance and equivariance from data. However, existing symmetry discovery methods are limited to simple linear symmetries and cannot handle the complexity of real-world data. We propose a novel generative model, Latent LieGAN (LaLiGAN), which can discover symmetries of nonlinear group actions. It learns a mapping from the data space to a latent space where the symmetries become linear and simultaneously discovers symmetries in the latent space. Theoretically, we show that our model can express nonlinear symmetries under some conditions about the group action. Experimentally, we demonstrate that our method can accurately discover the intrinsic symmetry in high-dimensional dynamical systems. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
APA
Yang, J., Dehmamy, N., Walters, R. & Yu, R.. (2024). Latent Space Symmetry Discovery. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:56047-56070 Available from https://proceedings.mlr.press/v235/yang24g.html.

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