# Graph Distillation with Eigenbasis Matching

arXiv: https://arxiv.org/abs/2310.09202 · HTML: https://mlsanity.com/paper/2310.09202/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 30 of 33)

- [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)
- [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)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Improved Distribution Matching for Dataset Condensation](https://mlsanity.com/paper/2307.09742/) (2023)
- [Towards Lossless Dataset Distillation via Difficulty-Aligned Trajectory Matching](https://mlsanity.com/paper/2310.05773/) (2023)
- [Dataset Distillation via Factorization](https://mlsanity.com/paper/2210.16774/) (2022)
- [A Comprehensive Survey of Dataset Distillation](https://mlsanity.com/paper/2301.05603/) (2023)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [Graph Condensation via Receptive Field Distribution Matching](https://mlsanity.com/paper/2206.13697/) (2022)
- [Graph Coarsening with Preserved Spectral Properties](https://mlsanity.com/paper/1802.04447/) (2018)
- [A Survey on Dataset Distillation: Approaches, Applications and Future Directions](https://mlsanity.com/paper/2305.01975/) (2023)
- [Graph Condensation for Inductive Node Representation Learning](https://mlsanity.com/paper/2307.15967/) (2023)

## Built on by (most cited first, 16 of 16)

- [FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preference](https://mlsanity.com/paper/2410.20105/) (2024)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [RobGC: Towards Robust Graph Condensation](https://mlsanity.com/paper/2406.13200/) (2024)
- [Beyond Modality Collapse: Representations Blending for Multimodal Dataset Distillation](https://mlsanity.com/paper/2505.14705/) (2025)
- [Contrastive Graph Condensation: Advancing Data Versatility through Self-Supervised Learning](https://mlsanity.com/paper/2411.17063/) (2024)
- [Understanding Dataset Distillation via Spectral Filtering](https://mlsanity.com/paper/2503.01212/) (2025)
- [DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation](https://mlsanity.com/paper/2604.03154/) (2026)
- [Bonsai: Gradient-free Graph Condensation for Node Classification](https://mlsanity.com/paper/2410.17579/) (2024)
- [Training-free Heterogeneous Graph Condensation via Data Selection](https://mlsanity.com/paper/2412.16250/) (2024)
- [Position: Graph Condensation Needs a Reset -- Move Beyond Full-dataset Training and Model-Dependence](https://mlsanity.com/paper/2605.18893/) (2026)
- [Efficient and Privacy-Preserved Link Prediction via Condensed Graphs](https://mlsanity.com/paper/2503.12156/) (2025)
- [Towards Pre-trained Graph Condensation via Optimal Transport](https://mlsanity.com/paper/2509.14722/) (2025)
- [Adaptive Graph Coarsening for Efficient GNN Training](https://mlsanity.com/paper/2509.25706/) (2025)
- [Model-to-Data Distillation for Graph Neural Networks](https://mlsanity.com/paper/2605.06814/) (2026)
- [Heterogeneous Graph Condensation via Role-Aware Clustering](https://mlsanity.com/paper/2607.03097/) (2026)
- [Semi-Supervised Text-Attributed Graph Distillation](https://mlsanity.com/paper/2607.20477/) (2026)

## Abstract (arXiv)

The increasing amount of graph data places requirements on the efficient training of graph neural networks (GNNs). The emerging graph distillation (GD) tackles this challenge by distilling a small synthetic graph to replace the real large graph, ensuring GNNs trained on real and synthetic graphs exhibit comparable performance. However, existing methods rely on GNN-related information as supervision, including gradients, representations, and trajectories, which have two limitations. First, GNNs can affect the spectrum (i.e., eigenvalues) of the real graph, causing spectrum bias in the synthetic graph. Second, the variety of GNN architectures leads to the creation of different synthetic graphs, requiring traversal to obtain optimal performance. To tackle these issues, we propose Graph Distillation with Eigenbasis Matching (GDEM), which aligns the eigenbasis and node features of real and synthetic graphs. Meanwhile, it directly replicates the spectrum of the real graph and thus prevents the influence of GNNs. Moreover, we design a discrimination constraint to balance the effectiveness and generalization of GDEM. Theoretically, the synthetic graphs distilled by GDEM are restricted spectral approximations of the real graphs. Extensive experiments demonstrate that GDEM outperforms state-of-the-art GD methods with powerful cross-architecture generalization ability and significant distillation efficiency. Our code is available at https://github.com/liuyang-tian/GDEM.