  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.
