Equivariant Graph Hierarchy-Based Neural Networks

Equivariant Graph neural Networks (EGNs) are powerful in characterizing the dynamics of multi-body physical systems. Existing EGNs conduct flat message passing, which, yet, is unable to capture the spatial/dynamical hierarchy for complex systems particularly, limiting substructure discovery and global information fusion. In this paper, we propose Equivariant Hierarchy-based Graph Networks (EGHNs) which consist of the three key components: generalized Equivariant Matrix Message Passing (EMMP), E-Pool and E-UnPool. In particular, EMMP is able to improve the expressivity of conventional equivariant message passing, E-Pool assigns the quantities of the low-level nodes into high-level clusters, while E-UnPool leverages the high-level information to update the dynamics of the low-level nodes. As their names imply, both E-Pool and E-UnPool are guaranteed to be equivariant to meet physic symmetry.