E(3)-Equivariant Mesh Neural Networks

Thuan Anh Trang, Nhat Khang Ngo, Daniel T. Levy, Thieu Ngoc Vo, Siamak Ravanbakhsh, Truong Son Hy
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:748-756, 2024.

Abstract

Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have addressed the need for geometric deep learning on 3D meshes. However, we observe that the complexities in many of these architectures do not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information and further improve it to account for long-range interactions through a hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive preprocessing. Our implementation is available at \url{https://github.com/HySonLab/EquiMesh}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-anh-trang24a, title = {E(3)-Equivariant Mesh Neural Networks}, author = {Anh Trang, Thuan and Ngo, Nhat Khang and Levy, Daniel T. and Ngoc Vo, Thieu and Ravanbakhsh, Siamak and Son Hy, Truong}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {748--756}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/anh-trang24a/anh-trang24a.pdf}, url = {https://proceedings.mlr.press/v238/anh-trang24a.html}, abstract = {Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have addressed the need for geometric deep learning on 3D meshes. However, we observe that the complexities in many of these architectures do not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information and further improve it to account for long-range interactions through a hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive preprocessing. Our implementation is available at \url{https://github.com/HySonLab/EquiMesh}.} }
Endnote
%0 Conference Paper %T E(3)-Equivariant Mesh Neural Networks %A Thuan Anh Trang %A Nhat Khang Ngo %A Daniel T. Levy %A Thieu Ngoc Vo %A Siamak Ravanbakhsh %A Truong Son Hy %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-anh-trang24a %I PMLR %P 748--756 %U https://proceedings.mlr.press/v238/anh-trang24a.html %V 238 %X Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have addressed the need for geometric deep learning on 3D meshes. However, we observe that the complexities in many of these architectures do not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information and further improve it to account for long-range interactions through a hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive preprocessing. Our implementation is available at \url{https://github.com/HySonLab/EquiMesh}.
APA
Anh Trang, T., Ngo, N.K., Levy, D.T., Ngoc Vo, T., Ravanbakhsh, S. & Son Hy, T.. (2024). E(3)-Equivariant Mesh Neural Networks. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:748-756 Available from https://proceedings.mlr.press/v238/anh-trang24a.html.

Related Material