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.

翻译：我们提出了一种多体消息传递神经网络（MPNN）框架，用于建模高阶节点交互（涉及$\ge 2$个节点）。我们将高阶项建模为树形模体，该模体包含一个中心节点及其邻域，并在模体拉普拉斯矩阵上应用由全局边里奇曲率加权的局部谱滤波器。我们证明了该框架对邻域节点置换具有不变性，推导了其敏感度界限，并界定了所学图势能的范围。我们在图能量回归任务中验证了该框架在更深更广的网络拓扑结构下具有良好的可扩展性，并在具有异质性的合成图数据集上进行了分类实验，结果表明其狄利克雷能量始终保持高速增长。我们的代码已在 https://github.com/JThh/Many-Body-MPNN 开源。