  We present many-body Message Passing Neural Network (MPNN) framework that
models higher-order node interactions ($\ge 2$ nodes). We model higher-order
terms as tree-shaped motifs, comprising a central node with its neighborhood,
and apply localized spectral filters on motif Laplacian, weighted by global
edge Ricci curvatures. We prove our formulation is invariant to neighbor node
permutation, derive its sensitivity bound, and bound the range of learned graph
potential. We run regression on graph energies to demonstrate that it scales
well with deeper and wider network topology, and run classification on
synthetic graph datasets with heterophily and show its consistently high
Dirichlet energy growth.
  We open-source our code at https://github.com/JThh/Many-Body-MPNN.
