Many real‑world problems can be expressed as graphs. Conventional GNNs exchange messages only between first‑order neighbors, which brings over‑smoothing with depth, compresses long‑range dependencies, limits receptive fields with fixed neighborhoods, and turns topological neighbors into noise on heterophilous graphs. Existing works usually target a single issue, lacking a unified remedy. We therefore introduce a Position Encoding‑Based Deformable Spatial Aggregation Module (PEBDSAM) that adds a deformable mechanism in position space, dynamically selecting remote nodes relevant to the target node to supplement first‑order information, thus enabling GNNs to handle heterophily.
Diagnostic experiments show that current offsets have little effect; we analyze why offsets fail and why performance still improves, outlining future research directions. Guided by these findings we streamline the design into a Position Encoding‑Based Spatial Aggregation Module (PEBSAM) and propose a lightweight PEBSAM‑Speed for large‑scale datasets. The module is plug‑and‑play, integrated into GCN, GAT, GIN and GraphSAGE, and yields notable gains on three homophilous and six heterophilous benchmarks. Review