A Theoretical Formulation of Many-body Message Passing Neural Networks
This work addresses the challenge of capturing complex interactions in graph neural networks for applications in heterophilic graph data, though it appears incremental as it builds on existing MPNN methods with novel extensions.
The authors tackled the problem of modeling higher-order node interactions in graphs by introducing a many-body Message Passing Neural Network framework that uses tree-shaped motifs and spectral filters weighted by edge Ricci curvatures, achieving scalability with deeper and wider networks and high Dirichlet energy growth in heterophilic graph classification.
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.