Supplementary Materials for Equivariant Graph Hierarchy-Based Neural Networks

A.1 Proof of Theorem 1 Theorem 1. EMMP can reduce to EGNN and GMN by specific choices of MLP in Eq. 3. Proof. We first prove that EMMP can reduce to GMN. [ ] This theorem basically implies that the expressivity of our EMMP is stronger than that of GMN or EGNN. A.2 Proof of Theorem 2 Theorem 2. EMMP, E-Pool, and E-UnPool are all E(n)-equivariant. We proceed the proof step by step, following the definition of EMMP in Eq. 3-6: Ẑ Indeed, with Theorem 2 we immediately have that any cascade of EMMP, E-Pool, and E-UnPool is also E(n)-equivariant. For the baselines, we leverage the codebases maintained by [4] We tune the hyper-parameters around the suggested hyper-parameters as specified in [4] and [6] for the baselines.