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. A.2 Proof of Theorem 2 Theorem 2. EMMP, E-Pool, and E-UnPool are all E( n)-equivariant. E( n)-invariant, which is crucial for maintaining the equivariance of the high-level EMMP .