# Degraded but Not Entirely Ineffective: PE-Based Deformable Graph Neural Networks

arXiv: https://arxiv.org/abs/2609.13712 · HTML: https://mlsanity.com/paper/2609.13712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Graph-Bert: Only Attention is Needed for Learning Graph Representations](https://mlsanity.com/paper/2001.05140/) (2020)
- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)

## Abstract (arXiv)

Many real-world scenarios can be represented using graph-structured data. However, traditional GNNs that transmit messages based on first-order neighbors have long faced several fundamental contradictions: increasing depth leads to over-smoothing, long-range dependencies cause over-compression, fixed neighborhoods restrict the receptive field, and on heterophilous graphs, topological neighbors become a source of noise. Although many works have addressed these issues individually, few mechanisms can simultaneously alleviate all of these challenges. To address the aforementioned problems, we propose a Position Encoding-Based Deformable Spatial Aggregation Module (PEBDSAM) that solves them all in one step. Specifically, we utilize a deformable mechanism in the position space to identify relevant nodes to supplement the original first-order neighbor information of GNNs, allowing traditional GNNs to adapt to heterophilous scenarios. Through diagnostic experiments, we obtained several major findings: current offsets fail to have any effect; subsequently, we analyzed the causes of offset failure and why model performance still improves even after offset failure, pointing out future research directions. Based on these diagnostic experiments, we streamlined the original PEBDSAM, resulting in a simplified version, which we call the Position Encoding-Based Spatial Aggregation Module (PEBSAM). In addition, we propose a PEBSAM-Speed to adapt to large datasets. Finally, we designed the module to be plug-and-play and applied it to GCN, GAT, GIN, and GraphSAGE, achieving desirable results on three homophilous datasets and six heterophilous graph datasets.