Point clouds are versatile representations of 3D objects and have found
widespread application in science and engineering. Many successful
deep-learning models have been proposed that use them as input. Some
application domains require incorporating exactly physical constraints,
including chemical and materials modeling which we focus on in this paper.
These constraints include smoothness, and symmetry with respect to
translations, rotations, and permutations of identical particles. Most existing
architectures in other domains do not fulfill simultaneously all of these
requirements and thus are not applicable to atomic-scale simulations. Many of
them, however, can be straightforwardly made to incorporate all the physical
constraints except for rotational symmetry. We propose a general symmetrization
protocol that adds rotational equivariance to any given model while preserving
all the other constraints. As a demonstration of the potential of this idea, we
introduce the Point Edge Transformer (PET) architecture, which is not
intrinsically equivariant but achieves state-of-the-art performance on several
benchmark datasets of molecules and solids. A-posteriori application of our
general protocol makes PET exactly equivariant, with minimal changes to its
accuracy. By alleviating the need to explicitly incorporate rotational symmetry
within the model, our method bridges the gap between the approaches used in
different communities, and simplifies the design of deep-learning schemes for
chemical and materials modeling.

本文介绍了一个通用的对称化协议，用于向任何给定模型添加旋转等变性，同时保留所有其他约束条件。我们将此方法应用于 Point Edge Transformer（PET）体系结构，并展示其在多个分子和固体基准数据集上实现了最先进的性能。通过减轻模型内显式纳入旋转对称性的需要，我们的方法弥合了不同社区所使用的方法之间的差距，并简化了化学和材料建模的深度学习方案的设计。