提出新方法PiPE，融合位置编码与拓扑特征提升图神经网络性能
Positional Encoding meets Persistent Homology on Graphs
- 将位置编码与持久同调结合，设计可学习的PiPE方法
- 在分子属性预测等任务上表现优于传统位置编码和拓扑方法
- 适合需要强结构感知的图学习场景，如化学分子分析
消息传递图神经网络（GNN）的局部归纳偏置限制了其对关键结构信息（如连通性与环路）的利用。位置编码（PE）和持久同调（PH）作为两种有前景的解决方案，分别赋予GNN位置感知能力与多尺度拓扑特征。然而，两者相对优劣的严格理论分析仍不明确。本文通过构建新例证，证明二者表达能力互不包含，并据此提出新型可学习方法PiPE（Persistence-informed Positional Encoding），其理论表达能力超越单一的PE与PH。PiPE在分子属性预测、图分类及分布外泛化等多种任务中表现优异，推动图表示学习发展。代码已开源：https://github.com/Aalto-QuML/PIPE。
原文摘要 · Abstract (English)
The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two promising approaches to mitigate this issue. PE schemes endow GNNs with location-aware features, while PH methods enhance GNNs with multiresolution topological features. However, a rigorous theoretical characterization of the relative merits and shortcomings of PE and PH has remained elusive. We bridge this gap by establishing that neither paradigm is more expressive than the other, providing novel constructions where one approach fails but the other succeeds. Our insights inform the design of a novel learnable method, PiPE (Persistence-informed Positional Encoding), which is provably more expressive than both PH and PE. PiPE demonstrates strong performance across a variety of tasks (e.g., molecule property prediction, graph classification, and out-of-distribution generalization), thereby advancing the frontiers of graph representation learning. Code is available at https://github.com/Aalto-QuML/PIPE.
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