# Graph Coarsening via Convolution Matching for Scalable Graph Neural Network Training

arXiv: https://arxiv.org/abs/2312.15520 · HTML: https://mlsanity.com/paper/2312.15520/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 24 Dec 2023.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Dataset Distillation](https://mlsanity.com/paper/1811.10959/) (2018)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [DistDGL: Distributed Graph Neural Network Training for Billion-Scale Graphs](https://mlsanity.com/paper/2010.05337/) (2020)
- [Soft-Label Dataset Distillation and Text Dataset Distillation](https://mlsanity.com/paper/1910.02551/) (2019)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [Flexible Dataset Distillation: Learn Labels Instead of Images](https://mlsanity.com/paper/2006.08572/) (2020)
- [Scaling Up Graph Neural Networks Via Graph Coarsening](https://mlsanity.com/paper/2106.05150/) (2021)
- [Graph Condensation via Receptive Field Distribution Matching](https://mlsanity.com/paper/2206.13697/) (2022)
- [GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding](https://mlsanity.com/paper/1910.02370/) (2019)
- [MILE: A Multi-Level Framework for Scalable Graph Embedding](https://mlsanity.com/paper/1802.09612/) (2018)
- [Learn Locally, Correct Globally: A Distributed Algorithm for Training Graph Neural Networks](https://mlsanity.com/paper/2111.08202/) (2021)
- [Graph Summarization Methods and Applications: A Survey](https://mlsanity.com/paper/1612.04883/) (2016)
- [Faster Graph Embeddings via Coarsening](https://mlsanity.com/paper/2007.02817/) (2020)
- [Communication-Efficient Sampling for Distributed Training of Graph Convolutional Networks](https://mlsanity.com/paper/2101.07706/) (2021)
- [Simplifying Distributed Neural Network Training on Massive Graphs: Randomized Partitions Improve Model Aggregation](https://mlsanity.com/paper/2305.09887/) (2023)
- [COSINE: Compressive Network Embedding on Large-scale Information Networks](https://mlsanity.com/paper/1812.08972/) (2018)
- [Network Embedding: on Compression and Learning](https://mlsanity.com/paper/1907.02811/) (2019)

## Built on by (most cited first, 12 of 12)

- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Graph Coarsening with Message-Passing Guarantees](https://mlsanity.com/paper/2405.18127/) (2024)
- [Taxonomy of reduction matrices for Graph Coarsening](https://mlsanity.com/paper/2506.11743/) (2025)
- [Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening](https://mlsanity.com/paper/2505.14033/) (2025)
- [FIT-GNN: Faster Inference Time for GNNs that 'FIT' in Memory Using Coarsening](https://mlsanity.com/paper/2410.15001/) (2024)
- [Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle](https://mlsanity.com/paper/2605.13021/) (2026)
- [Adaptive Graph Coarsening for Efficient GNN Training](https://mlsanity.com/paper/2509.25706/) (2025)
- [Improving LLM Reasoning with Homophily-aware Structural and Semantic Text-Attributed Graph Compression](https://mlsanity.com/paper/2601.08187/) (2026)
- [Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms](https://mlsanity.com/paper/2601.22943/) (2026)
- [Efficient and Scalable Granular-ball Graph Coarsening Method for Large-scale Graph Node Classification](https://mlsanity.com/paper/2603.29148/) (2026)
- [CoRe-GNN: Multilevel Message passing on Coarsened graphs](https://mlsanity.com/paper/2608.02128/) (2026)

## Abstract (arXiv)

Graph summarization as a preprocessing step is an effective and complementary technique for scalable graph neural network (GNN) training. In this work, we propose the Coarsening Via Convolution Matching (CONVMATCH) algorithm and a highly scalable variant, A-CONVMATCH, for creating summarized graphs that preserve the output of graph convolution. We evaluate CONVMATCH on six real-world link prediction and node classification graph datasets, and show it is efficient and preserves prediction performance while significantly reducing the graph size. Notably, CONVMATCH achieves up to 95% of the prediction performance of GNNs on node classification while trained on graphs summarized down to 1% the size of the original graph. Furthermore, on link prediction tasks, CONVMATCH consistently outperforms all baselines, achieving up to a 2x improvement.