Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to extract structural features from the graph. In this work, we propose to make GNNs universal by guiding the learning process with exact isomorphism solver techniques which operate on the paradigm of Individualization and Refinement (IR), a method to artificially introduce asymmetry and further refine the coloring when 1-WL stops. Isomorphism solvers generate a search tree of colorings whose leaves uniquely identify the graph. However, the tree grows exponentially large and needs hand-crafted pruning techniques which are not desirable from a learning perspective. We take a probabilistic view and approximate the search tree of colorings (i.e. embeddings) by sampling multiple paths from root to leaves of the search tree. To learn more discriminative representations, we guide the sampling process with particle filter updates, a principled approach for sequential state estimation. Our algorithm is end-to-end differentiable, can be applied with any GNN as backbone and learns richer graph representations with only linear increase in runtime. Experimental evaluation shows that our approach consistently outperforms leading GNN models on both synthetic benchmarks for isomorphism detection as well as real-world datasets.

翻译：消息传递图神经网络（GNN）已被证明在表达能力上受限于图同构的1-WL颜色精化测试。其他更具表达力的模型要么计算成本高昂，要么需要预处理来提取图的结构特征。本文提出通过引入精确同构求解器技术来指导学习过程，使GNN具备通用性。该技术基于个体化与精化（IR）范式——一种在1-WL停止时人为引入不对称性并进一步精化着色的方法。同构求解器会生成一个着色搜索树，其叶节点唯一标识该图。然而，该树呈指数级增长，需要人工设计剪枝技术，这从学习角度而言并不理想。我们采用概率视角，通过从搜索树的根节点到叶节点采样多条路径来近似着色（即嵌入）搜索树。为学习更具判别力的表示，我们使用粒子滤波更新（一种用于序贯状态估计的严谨方法）来指导采样过程。该算法支持端到端微分，可与任意GNN骨干网络结合使用，仅需线性时间开销即可学习更丰富的图表示。实验评估表明，我们的方法在同构检测的合成基准测试和真实数据集上均持续优于主流GNN模型。