A Theoretical Formulation of Many-body Message Passing Neural Networks
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Abstract (arXiv)
We present many-body Message Passing Neural Network (MPNN) framework that models higher-order node interactions (≥ 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.
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References · 9
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
- 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
- 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
- 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
- 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
- 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
- 2023Understanding Oversquashing in GNNs through the Lens of Effective Resistancecited by 94
- 2018MotifNet: a motif-based Graph Convolutional Network for directed graphscited by 63
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