Degraded but Not Entirely Ineffective: PE-Based Deformable Graph Neural Networks
| Source: arXiv AI
Tags: GNN, graph-neural-networks, heterophily, position-encoding, deep-learning
PEBSAM is a plug-and-play position encoding module for GNNs that simultaneously addresses over-smoothing, over-compression, and heterophily — finding that the deformable offset mechanism initially fails but the simplified position-encoding approach still improves performance on both homophilous and heterophilous graphs.
Details
Traditional GNNs transmit messages through fixed first-order neighborhoods, creating four compounding problems: over-smoothing with depth, over-compression of long-range dependencies, receptive field rigidity, and neighbor noise on heterophilous graphs. Most prior work fixes one problem at a time. PEBDSAM (Position Encoding-Based Deformable Spatial Aggregation Module) proposes a unified solution using deformable mechanisms in position space to identify relevant nodes beyond first-order neighbors. However, diagnostic experiments reveal that the offset mechanism fails — current offsets have no positive effect. The paper analyzes why offsets fail and why performance improves anyway, ultimately deriving PEBSAM as a simplified, working version. PEBSAM is designed as plug-and-play and tested on four GNN architectures: GCN, GAT, GIN, and GraphSAGE. Results across nine datasets — three homophilous and six heterophilous — are positive, though specific numbers are not given in the abstract. A PEBSAM-Speed variant handles large-scale graphs. The honest diagnosis of why the full deformable approach fails, combined with an explanation of why the simplified version still works, is the most valuable aspect of the paper. This kind of diagnostic transparency is rare and useful for practitioners trying to understand GNN augmentation boundaries.