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. The domain of chemical and materials modeling is especially challenging because exact compliance with physical constraints is highly desirable for a model to be usable in practice. These constraints include smoothness and invariance with respect to translations, rotations, and permutations of identical atoms. If these requirements are not rigorously fulfilled, atomistic simulations might lead to absurd outcomes even if the model has excellent accuracy. Consequently, dedicated architectures, which achieve invariance by restricting their design space, have been developed. General-purpose point-cloud models are more varied but often disregard rotational symmetry. We propose a general symmetrization method that adds rotational equivariance to any given model while preserving all the other requirements. Our approach simplifies the development of better atomic-scale machine-learning schemes by relaxing the constraints on the design space and making it possible to incorporate ideas that proved effective in other domains. We demonstrate this idea by introducing 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.

翻译：点云作为三维物体的通用表示形式，已在科学和工程领域得到广泛应用。当前已提出众多基于点云输入的成功深度学习模型。化学与材料建模领域尤为特殊，因为模型在实际应用中必须严格满足物理约束条件，包括关于平移、旋转和同类原子置换的光滑性与不变性。若这些要求未能严格满足，即使模型精度优异，原子尺度模拟也可能导致荒谬结果。为此，研究者开发了通过限制设计空间实现不变性的专用架构。通用点云模型虽形式更为多样，但常忽略旋转对称性。我们提出一种通用对称化方法，可在保持其余所有要求的前提下为任意模型增加旋转等变性。该方法通过放宽设计空间约束，使得跨领域高效思想得以融合，从而简化了更优原子尺度机器学习方案的开发。为验证该构想，我们提出点边变换器（PET）架构——该架构虽非内在等变，却在多个分子与固体基准数据集上取得了当前最优性能。通过事后应用我们的通用对称化协议，PET在不显著改变精度的情况下实现了严格等变性。