# Graph Condensation via Receptive Field Distribution Matching

arXiv: https://arxiv.org/abs/2206.13697 · HTML: https://mlsanity.com/paper/2206.13697/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [Graph Learning based Recommender Systems: A Review](https://mlsanity.com/paper/2105.06339/) (2021)
- [Automated Scalable Bayesian Inference via Hilbert Coresets](https://mlsanity.com/paper/1710.05053/) (2017)
- [ScaIL: Classifier Weights Scaling for Class Incremental Learning](https://mlsanity.com/paper/2001.05755/) (2020)
- [Building a PubMed knowledge graph](https://mlsanity.com/paper/2005.04308/) (2020)
- [Survey of Image Based Graph Neural Networks](https://mlsanity.com/paper/2106.06307/) (2021)
- [Generative Invertible Networks (GIN): Pathophysiology-Interpretable Feature Mapping and Virtual Patient Generation](https://mlsanity.com/paper/1808.04495/) (2018)

## Built on by (most cited first, 30 of 60)

- [Dataset Distillation: A Comprehensive Review](https://mlsanity.com/paper/2301.07014/) (2023)
- [A Comprehensive Survey of Dataset Distillation](https://mlsanity.com/paper/2301.05603/) (2023)
- [Data Distillation: A Survey](https://mlsanity.com/paper/2301.04272/) (2023)
- [Accelerating Dataset Distillation via Model Augmentation](https://mlsanity.com/paper/2212.06152/) (2022)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [CaT: Balanced Continual Graph Learning with Graph Condensation](https://mlsanity.com/paper/2309.09455/) (2023)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Fast Graph Condensation with Structure-based Neural Tangent Kernel](https://mlsanity.com/paper/2310.11046/) (2023)
- [A Survey on Dataset Distillation: Approaches, Applications and Future Directions](https://mlsanity.com/paper/2305.01975/) (2023)
- [Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching](https://mlsanity.com/paper/2402.05011/) (2024)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Dataset Distillation via Vision-Language Category Prototype](https://mlsanity.com/paper/2506.23580/) (2025)
- [Graph Distillation with Eigenbasis Matching](https://mlsanity.com/paper/2310.09202/) (2023)
- [Graph Coarsening via Convolution Matching for Scalable Graph Neural Network Training](https://mlsanity.com/paper/2312.15520/) (2023)
- [GC-Bench: An Open and Unified Benchmark for Graph Condensation](https://mlsanity.com/paper/2407.00615/) (2024)
- [Disentangled Condensation for Large-scale Graphs](https://mlsanity.com/paper/2401.12231/) (2024)
- [PUMA: Efficient Continual Graph Learning for Node Classification with Graph Condensation](https://mlsanity.com/paper/2312.14439/) (2023)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Dataset Condensation for Time Series Classification via Dual Domain Matching](https://mlsanity.com/paper/2403.07245/) (2024)
- [Graph Continual Learning with Debiased Lossless Memory Replay](https://mlsanity.com/paper/2404.10984/) (2024)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [Simple Graph Condensation](https://mlsanity.com/paper/2403.14951/) (2024)
- [Federated Graph Condensation with Information Bottleneck Principles](https://mlsanity.com/paper/2405.03911/) (2024)
- [GCAL: Adapting Graph Models to Evolving Domain Shifts](https://mlsanity.com/paper/2505.16860/) (2025)
- [GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights](https://mlsanity.com/paper/2406.16715/) (2024)
- [Recent Advances in Malware Detection: Graph Learning and Explainability](https://mlsanity.com/paper/2502.10556/) (2025)
- [CondTSF: One-line Plugin of Dataset Condensation for Time Series Forecasting](https://mlsanity.com/paper/2406.02131/) (2024)
- [Contrastive Graph Condensation: Advancing Data Versatility through Self-Supervised Learning](https://mlsanity.com/paper/2411.17063/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) enable the analysis of graphs using deep learning, with promising results in capturing structured information in graphs. This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution. Thus, we propose Graph Condesation via Receptive Field Distribution Matching (GCDM), which is accomplished by optimizing the synthetic graph through the use of a distribution matching loss quantified by maximum mean discrepancy (MMD). Additionally, we demonstrate that the synthetic graph generated by GCDM is highly generalizable to a variety of models in evaluation phase and that the condensing speed is significantly improved using this framework.