E$^2$PN: Efficient SE(3)-Equivariant Point Network

This paper proposes a new point-cloud convolution structure that learns SE(3)-equivariant features. Compared with existing SE(3)-equivariant networks, our design is lightweight, simple, and flexible to be incorporated into general point-cloud learning networks. We strike a balance between the complexity and capacity of our model by selecting an unconventional domain for the feature maps. We further reduce the computational load by properly discretizing $\mathbb{R}^3$ to fully leverage the rotational symmetry. Moreover, we employ a permutation layer to recover the full SE(3) group from its quotient space. Experiments show that our method achieves comparable or superior performance in various tasks while consuming much less memory and running faster than existing work. The proposed method can foster the adoption of equivariant feature learning in various practical applications based on point clouds and inspire future developments of equivariant feature learning for real-world applications.