In many applications of geometric deep learning, the choice of global
coordinate frame is arbitrary, and predictions should be independent of the
reference frame. In other words, the network should be equivariant with respect
to rotations and reflections of the input, i.e., the transformations of O(d).
We present a novel framework for building equivariant message passing
architectures and modifying existing non-equivariant architectures to be
equivariant. Our approach is based on local coordinate frames, between which
geometric information is communicated consistently by including tensorial
objects in the messages. Our framework can be applied to message passing on
geometric data in arbitrary dimensional Euclidean space. While many other
approaches for equivariant message passing require specialized building blocks,
such as non-standard normalization layers or non-linearities, our approach can
be adapted straightforwardly to any existing architecture without such
modifications. We explicitly demonstrate the benefit of O(3)-equivariance for a
popular point cloud architecture and produce state-of-the-art results on normal
vector regression on point clouds.

建立等变消息传递框架，实现几何深度学习中的任意维度欧几里得空间上的等变信息传递，通过局部坐标框架和张量对象在消息中保持几何信息一致性，并展示了 O (3) 等变性在点云架构上的优势及在法向量回归中的最新成果。