# Deformable Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2112.14438 · HTML: https://mlsanity.com/paper/2112.14438/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 42 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [EDVR: Video Restoration with Enhanced Deformable Convolutional Networks](https://mlsanity.com/paper/1905.02716/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Deformable GANs for Pose-based Human Image Generation](https://mlsanity.com/paper/1801.00055/) (2017)

## Built on by (most cited first, 6 of 6)

- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [LLaMo: Large Language Model-based Molecular Graph Assistant](https://mlsanity.com/paper/2411.00871/) (2024)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Deformable Graph Transformer](https://mlsanity.com/paper/2206.14337/) (2022)
- [Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing](https://mlsanity.com/paper/2507.20127/) (2025)
- [GDLNN: Marriage of Programming Language and Neural Networks for Accurate and Easy-to-Explain Graph Classification](https://mlsanity.com/paper/2510.00374/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) have significantly improved the representation power for graph-structured data. Despite of the recent success of GNNs, the graph convolution in most GNNs have two limitations. Since the graph convolution is performed in a small local neighborhood on the input graph, it is inherently incapable to capture long-range dependencies between distance nodes. In addition, when a node has neighbors that belong to different classes, i.e., heterophily, the aggregated messages from them often negatively affect representation learning. To address the two common problems of graph convolution, in this paper, we propose Deformable Graph Convolutional Networks (Deformable GCNs) that adaptively perform convolution in multiple latent spaces and capture short/long-range dependencies between nodes. Separated from node representations (features), our framework simultaneously learns the node positional embeddings (coordinates) to determine the relations between nodes in an end-to-end fashion. Depending on node position, the convolution kernels are deformed by deformation vectors and apply different transformations to its neighbor nodes. Our extensive experiments demonstrate that Deformable GCNs flexibly handles the heterophily and achieve the best performance in node classification tasks on six heterophilic graph datasets.