  Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry
in science, from classical and quantum physics to computational biology. It
enables robust and accurate prediction under arbitrary reference
transformations. In light of this, great efforts have been put on encoding this
symmetry into deep neural networks, which has been shown to improve the
generalization performance and data efficiency for downstream tasks.
Constructing an equivariant neural network generally brings high computational
costs to ensure expressiveness. Therefore, how to better trade-off the
expressiveness and computational efficiency plays a core role in the design of
the equivariant deep learning models. In this paper, we propose a framework to
construct SE(3) equivariant graph neural networks that can approximate the
geometric quantities efficiently. Inspired by differential geometry and
physics, we introduce equivariant local complete frames to graph neural
networks, such that tensor information at given orders can be projected onto
the frames. The local frame is constructed to form an orthonormal basis that
avoids direction degeneration and ensure completeness. Since the frames are
built only by cross product operations, our method is computationally
efficient. We evaluate our method on two tasks: Newton mechanics modeling and
equilibrium molecule conformation generation. Extensive experimental results
demonstrate that our model achieves the best or competitive performance in two
types of datasets.
