Several recent papers have recently shown that higher order graph neural networks can achieve better accuracy than their standard message passing counterparts, especially on highly structured graphs such as molecules. These models typically work by considering higher order representations of subgraphs contained within a given graph and then perform some linear maps between them. We formalize these structures as permutation equivariant tensors, or P-tensors, and derive a basis for all linear maps between arbitrary order equivariant P-tensors. Experimentally, we demonstrate this paradigm achieves state of the art performance on several benchmark datasets.

翻译：近期多篇论文表明，高阶图神经网络在处理分子等高结构化图时，其精度通常优于标准消息传递图神经网络。这类模型通常通过构建给定图中子图的高阶表示，并在这些表示之间执行线性映射来实现。我们将此类结构形式化为置换等变张量（P-tensors），并推导出任意阶等变P-tensor之间所有线性映射的基。实验表明，该范式在多个基准数据集上达到了当前最优性能。