Smooth, exact rotational symmetrization for deep learning on point clouds
This addresses the need for physically compliant models in atomistic simulations, enabling more versatile and accurate deep learning applications in science and engineering.
The authors tackled the problem of ensuring exact rotational symmetry in deep learning models for point clouds, particularly in chemical and materials modeling, by proposing a general symmetrization method that adds rotational equivariance to any model while preserving other physical constraints, and demonstrated it with the Point Edge Transformer (PET) architecture achieving state-of-the-art performance on benchmark datasets.
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.