Equivariant Graph Hierarchy-Based Neural Networks

TL;DR

This paper introduces Equivariant Hierarchy-based Graph Networks (EGHNs) that incorporate hierarchical pooling and updating mechanisms to enhance the modeling of complex physical systems, outperforming flat message passing approaches.

Contribution

The paper proposes a novel hierarchical framework for equivariant graph neural networks, including EMMP, E-Pool, and E-UpPool, to better capture spatial and dynamical hierarchies in physical systems.

Findings

EGHNs outperform flat EGNs in physical system modeling

Hierarchical pooling improves substructure discovery

Experimental results show enhanced accuracy in multi-object dynamics, motion capture, and protein modeling

Abstract

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-UpPool. 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-UpPool leverages the high-level information to update the dynamics of the low-level nodes. As their names imply, both E-Pool and E-UpPool are guaranteed to be equivariant to meet physic symmetry. Considerable experimental evaluations verify the effectiveness of our EGHN on several applications including multi-object dynamics simulation, motion capture, and protein dynamics modeling.