2e4531a45b99f61947b23ccdd608303b-Paper-Conference.pdf

Equivariant Graph Neural Networks (GNNs) that incorporate the E(3) symmetry have achieved significant success in various scientific applications. As one of the most successful models, EGNN [1] leverages a simple scalarization technique to perform equivariant message passing over only Cartesian vectors (i.e., 1stdegree steerable vectors), enjoying greater efficiency and efficacy compared to equivariant GNNs using higher-degree steerable vectors. This success suggests that higher-degree representations might be unnecessary. In this paper, we disprove this hypothesis by exploring the expressivity of equivariant GNNs on symmetric structures, including k-fold rotations and regular polyhedra. We theoretically demonstrate that equivariant GNNs will always degenerate to a zero function if the degree of the output representations is fixed to 1 or other specific values. Based on this theoretical insight, we propose HEGNN, a high-degree version of EGNN to increase the expressivity by incorporating high-degree steerable vectors while still maintaining EGNN's advantage through the scalarization trick. Our extensive experiments demonstrate that HEGNN not only aligns with our theoretical analyses on a toy dataset consisting of symmetric structures, but also shows substantial improvements on other complicated datasets without obvious symmetry, including N-body and MD17.