Thuan Trang

Thuan N. A. Trang, Thieu N. Vo, Khuong D. Nguyen

This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The main challenge when designing equivariant models for point clouds is how to trade-off the performance of the model and the complexity. Existing equivariant models are either too complicate to implement or very high complexity. The main aim of this study is to build a general procedure to introduce group equivariant property to SOTA models for 3D point clouds. The group equivariant models built form our procedure are simple to implement, less complexity in comparison with the existing ones, and they preserve the strengths of the original SOTA backbone. From the results of the experiments on object classification, it is shown that our methods are superior to other group equivariant models in performance and complexity. Moreover, our method also helps to improve the mIoU of semantic segmentation models. Overall, by using a combination of only-finite-rotation equivariance and augmentation, our models can outperform existing full $SO(3)$-equivariance models with much cheaper complexity and GPU memory. The proposed procedure is general and forms a fundamental approach to group equivariant neural networks. We believe that it can be easily adapted to other SOTA models in the future.

Thuan Trang, Nhat Khang Ngo, Daniel Levy et al.

Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric deep learning on 3D mesh. However, we observe that the complexities in many of these architectures does 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 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 pre-processing. Our implementation is available at https://github.com/HySonLab/EquiMesh