用拉普拉斯谱编码解决图神经网络节点不可区分问题，提升模型表达能力。
Resolving Node Identifiability in Graph Neural Processes via Laplacian Spectral Encodings
- 引入不变于特征向量符号翻转的拉普拉斯谱编码，增强节点唯一性
- 仅需少量观测即可实现节点可辨识，样本复杂度显著优于传统方法
- 在药物相互作用任务中提升ROC-AUC与F1，验证理论优势的实际价值
消息传递图神经网络在图学习中广泛应用，但其表达能力受限于一维Weisfeiler-Lehman测试，难以区分结构不同的节点。本文提出一种对特征向量符号翻转和特征空间内基底旋转均不变的拉普拉斯位置编码，并证明该编码可在常数个观测下实现节点可辨识，建立与受Weisfeiler-Lehman测试约束架构的样本复杂度差异。分析结合最短路径与扩散距离的单调关联、基于固定锚点的谱三边定位，以及嵌入尺寸对数增长下的定量谱注入性。作为实例，将该编码与神经过程风格解码器结合，在化学图上的药物-药物相互作用任务中显著提升ROC-AUC与F1分数，验证了通过有原则的位置信息克服理论表达瓶颈的实用性。
原文摘要 · Abstract (English)
Message passing graph neural networks are widely used for learning on graphs, yet their expressive power is limited by the one-dimensional Weisfeiler-Lehman test and can fail to distinguish structurally different nodes. We provide rigorous theory for a Laplacian positional encoding that is invariant to eigenvector sign flips and to basis rotations within eigenspaces. We prove that this encoding yields node identifiability from a constant number of observations and establishes a sample-complexity separation from architectures constrained by the Weisfeiler-Lehman test. The analysis combines a monotone link between shortest-path and diffusion distance, spectral trilateration with a constant set of anchors, and quantitative spectral injectivity with logarithmic embedding size. As an instantiation, pairing this encoding with a neural-process style decoder yields significant gains on a drug-drug interaction task on chemical graphs, improving both the area under the ROC curve and the F1 score and demonstrating the practical benefits of resolving theoretical expressiveness limitations with principled positional information.
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