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