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Equivariance has been a long-standing concern in various fields ranging fromcomputer vision to physical modeling. Most previous methods struggle withgenerality, simplicity, and expressiveness -- some are designed ad hoc forspecific data types, some are too complex to be accessible, and some sacrificeflexible transformations. In this work, we propose a novel and simple frameworkto achieve equivariance for point cloud analysis based on the message passing(graph neural network) scheme. We find the equivariant property could beobtained by introducing an orientation for each point to decouple the relativeposition for each point from the global pose of the entire point cloud.Therefore, we extend current message passing networks with a module that learnsorientations for each point. Before aggregating information from the neighborsof a point, the networks transforms the neighbors' coordinates based on thepoint's learned orientations. We provide formal proofs to show the equivarianceof the proposed framework. Empirically, we demonstrate that our proposed methodis competitive on both point cloud analysis and physical modeling tasks. Codeis available at https://github.com/luost26/Equivariant-OrientedMP .

Equivariant Point Cloud Analysis via Learning Orientations for Message Passing