统一拓扑签名在图表示学习中的再利用
Repurposing Unified Topological Signatures for Graph Representation Learning
- BITS Pilani（比拉理工学院皮拉尼校区）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究将统一拓扑签名（UTS）集成到GNN训练中，通过增强、正则化和池化三种干预，突破了1-WL表达性限制，在三个基准上提升准确率最高达5.8%。
中文摘要 AI 辅助
消息传递图神经网络（GNNs）通过迭代传播和聚合局部邻域信息，随后进行全局读出，以学习图表示。然而，其判别能力受限于Weisfeiler-Lehman（1-WL）图同构测试的上界。这阻止了GNNs区分某些具有相同局部邻域结构的非同构图，常常导致相似的图表示。统一拓扑签名（UTS）捕获了由持续同调导出的全局图拓扑的紧凑、多尺度表示。我们引入了两种互补的UTS签名：Graph_UTS——输入图拓扑的静态签名，以及Embedding_UTS——演化嵌入拓扑的动态签名。它们编码了基于1-WL的消息传递GNNs无法访问的结构信息，但其能力仅被探索用于事后嵌入空间分析。我们将UTS集成到GNN训练中，通过三种架构干预：（i）UTS-Aug：用编码图真实拓扑的标准读出特征进行增强；（ii）UTS-Reg：约束表示坍缩的拓扑正则化器；（iii）UTS-Pool：保留结构关键节点的拓扑引导池化。我们进一步利用UTS作为逐层诊断工具，以量化GNN训练过程中的过平滑现象。理论上，我们证明了将UTS集成到GNN优化中严格扩展了GNN的表达能力，超越了1-WL层次。在三个图分类基准上的实验显示了一致的益处：Graph-UTS、Dual-UTS和UTS-Pool在所有三个数据集上提高了准确率，Embedding-UTS提供了较小但同样一致的增益，而UTS-Reg的益处因图域而异。使用Graph-UTS增强准确率最高提升5.8%，使用UTS-Reg最高提升1.9%，且使用UTS-Pool达到了与TOGL相当的性能。
英文摘要
Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative power is upper-bounded by the Weisfeiler--Lehman (1-WL) graph isomorphism test. This prevents GNNs from distinguishing certain non-isomorphic graphs with identical local neighborhood structures, often leading to similar graph representations. Unified Topological Signatures (UTS) capture compact, multi-scale representation of global graph topology derived from persistent homology. We introduce two complementary UTS signatures: Graph_UTS- a static signature of the input graph topology, and Embedding_UTS- a dynamic signature of the evolving embedding topology. They encode structural information inaccessible to 1-WL-based message-passing GNNs, yet their capabilities are explored solely for post-hoc embedding-space analysis. We integrate UTS into GNN training across three architectural interventions: (i) UTS-Aug: augmenting with standard readout feature that encodes graph's true topology; (ii) UTS-Reg: topological regularizer that constrains representation collapse; (iii) UTS-Pool: topology-guided pooling that retains structurally critical nodes. We further leverage UTS as a layer-wise diagnostic to quantify oversmoothing during GNN training. Theoretically, we show that integrating UTS into GNN optimization strictly extends GNN expressivity beyond the 1-WL hierarchy. Experiments on three graph classification benchmarks show consistent benefits: Graph-UTS, Dual-UTS, and UTS-Pool improve accuracy across all three datasets, Embedding-UTS provides smaller but similarly consistent gains, and UTS-Reg's benefit varies across graph domains. Accuracy improves by up to 5.8% with Graph-UTS augmentation, by up to 1.9% with UTS-Reg, and achieves comparable performance to TOGL with UTS-Pool.
