  Geometric deep learning enables the encoding of physical symmetries in
modeling 3D objects. Despite rapid progress in encoding 3D symmetries into
Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness
of these networks through a local-to-global analysis lacks today. In this
paper, we propose a local hierarchy of 3D isomorphism to evaluate the
expressive power of equivariant GNNs and investigate the process of
representing global geometric information from local patches. Our work leads to
two crucial modules for designing expressive and efficient geometric GNNs;
namely local substructure encoding (LSE) and frame transition encoding (FTE).
To demonstrate the applicability of our theory, we propose LEFTNet which
effectively implements these modules and achieves state-of-the-art performance
on both scalar-valued and vector-valued molecular property prediction tasks. We
further point out the design space for future developments of equivariant graph
neural networks. Our codes are available at
\url{https://github.com/yuanqidu/LeftNet}.
