arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2401.17752cs.LGcs.AI
收藏

PF-GNN:基于可微粒子滤波的通用图表示近似

PF-GNN: Differentiable particle filtering based approximation of universal graph representations

School of Computing, National University of Singapore(新加坡国立大学计算机学院);PayPal Innovation Lab(PayPal创新实验室)

Mohammed Haroon Dupty, Yanfei Dong, Wee Sun Lee

AI总结:

针对消息传递GNN表达能力受1-WL测试限制的问题,提出基于可微粒子滤波的PF-GNN,通过采样IR范式的着色搜索树近似通用图表示,端到端可微且仅线性增加耗时,在合成与真实数据集上性能优于主流GNN。

摘要:

众所周知,消息传递图神经网络(GNNs)的表达能力受限于图同构的1-WL颜色细化测试。其他表达能力更强的模型要么计算成本高昂,要么需要进行预处理以从图中提取结构特征。在本研究中,我们提出通过采用基于个体化与细化(Individualization and Refinement, IR)范式的精确同构求解器技术来引导学习过程,使GNN具备通用性——IR是一种在1-WL方法失效时人为引入不对称性并进一步细化着色的方法。同构求解器会生成一个着色搜索树,其叶节点可唯一标识图结构。然而,该搜索树会呈指数级增长,且需要手工设计的剪枝技术,这从学习的角度来看并不理想。我们从概率视角出发,通过对搜索树中从根节点到叶节点的多条路径进行采样,来近似着色搜索树(即嵌入)。为学习更具判别性的表示,我们采用粒子滤波更新来引导采样过程,这是一种用于序列状态估计的 principled 方法。我们的算法是端到端可微的,可适配任意GNN作为骨干网络,且仅需线性的运行时间增长就能学习到更丰富的图表示。实验评估表明,我们的方法在同构检测的合成基准以及真实世界数据集上,均始终优于主流的GNN模型。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑