GIR Framework: Learning Graph Positional Embeddings with Anchor Indication and Path Encoding

The majority of existing graph neural networks (GNNs) following the message passing neural network (MPNN) pattern have limited power in capturing position information for a given node. To solve such problems, recent works exploit positioning nodes with selected anchors, mostly in a process that first explicitly assign distances information and then perform message passing encoding. However, this two-stage strategy may ignore potentially useful interaction between intermediate results of the distance computing and encoding stages. In this work, we propose a novel framework which follows the anchor-based idea and aims at conveying distance information implicitly along the MPNN message passing steps for encoding position information, node attributes, and graph structure in a more flexible way. Specifically, we first leverage a simple anchor indication strategy to enable the position-aware ability for well-designed MPNNs. Then, following this strategy, we propose the Graph Inference Representation (GIR) model, which acts as a generalization of MPNNs with a more specific propagation path design for position-aware scenarios.  Meanwhile, we theoretically and empirically explore the ability of the proposed framework to get position-aware embeddings, and experimental results show that our proposed method generally outperforms previous position-aware GNN methods.