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arXiv 2009.00142cs.LGstat.ML
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Distance Encoding:设计可证明更强大的神经网络用于图表示学习

Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learning

Purdue University(普渡大学);Stanford University(斯坦福大学)

Pan Li, Yanbang Wang, Hongwei Wang, Jure Leskovec

摘要:

学习图中节点集的表示对于从节点角色发现到链接预测和分子分类的应用是至关重要的。图神经网络在图表示学习方面取得了巨大的成功。然而,GNN的表达能力受到1-Weisfeiler-Lehman(WL)测试的限制,因此GNN为实际上可能非常不同的图子结构生成相同的表示。最近通过模仿高阶WL测试提出的更强大的GNN只专注于表示整个图,并且它们在计算上效率低下,因为它们不能利用底层图的稀疏性。在这里,我们提出并数学分析了一般类的结构相关的功能,称为距离编码(DE)。DE帮助GNN表示任何节点集,同时提供比1-WL测试更严格的表达能力。DE捕获要学习其表示的节点集与图中每个节点之间的距离。为了捕获距离,DE可以应用各种图距离度量,例如最短路径距离或广义PageRank分数。我们提出了两种方式让GNN使用DE(1)作为额外的节点特征,以及(2)作为GNN中消息聚合的控制器。这两种方法都可以利用底层图的稀疏结构,从而提高计算效率和可扩展性。我们还证明了DE可以区分嵌入在几乎所有常规图中的节点集,而传统的GNN总是失败。我们评估DE在六个真实网络上的三个任务:结构角色预测,链接预测和三角预测。结果表明,我们的模型在准确性和AUROC方面优于没有DE的GNN高达15%。此外,我们的模型也明显优于其他专门为上述任务设计的最先进的方法。

英文摘要:

Learning representations of sets of nodes in a graph is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph representation learning. However, expressive power of GNNs is limited by the 1-Weisfeiler-Lehman (WL) test and thus GNNs generate identical representations for graph substructures that may in fact be very different. More powerful GNNs, proposed recently by mimicking higher-order-WL tests, only focus on representing entire graphs and they are computationally inefficient as they cannot utilize sparsity of the underlying graph. Here we propose and mathematically analyze a general class of structure-related features, termed Distance Encoding (DE). DE assists GNNs in representing any set of nodes, while providing strictly more expressive power than the 1-WL test. DE captures the distance between the node set whose representation is to be learned and each node in the graph. To capture the distance DE can apply various graph-distance measures such as shortest path distance or generalized PageRank scores. We propose two ways for GNNs to use DEs (1) as extra node features, and (2) as controllers of message aggregation in GNNs. Both approaches can utilize the sparse structure of the underlying graph, which leads to computational efficiency and scalability. We also prove that DE can distinguish node sets embedded in almost all regular graphs where traditional GNNs always fail. We evaluate DE on three tasks over six real networks: structural role prediction, link prediction, and triangle prediction. Results show that our models outperform GNNs without DE by up-to 15\% in accuracy and AUROC. Furthermore, our models also significantly outperform other state-of-the-art methods especially designed for the above tasks.

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。

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