# Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching

arXiv: https://arxiv.org/abs/2402.05011 · HTML: https://mlsanity.com/paper/2402.05011/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 63 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 45)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [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)
- [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)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Dataset Distillation using Neural Feature Regression](https://mlsanity.com/paper/2206.00719/) (2022)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation](https://mlsanity.com/paper/2211.11004/) (2022)
- [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)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [DREAM: Efficient Dataset Distillation by Representative Matching](https://mlsanity.com/paper/2302.14416/) (2023)
- [Rethinking Architecture Selection in Differentiable NAS](https://mlsanity.com/paper/2108.04392/) (2021)
- [InfoBatch: Lossless Training Speed Up by Unbiased Dynamic Data Pruning](https://mlsanity.com/paper/2303.04947/) (2023)
- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [Accelerating Dataset Distillation via Model Augmentation](https://mlsanity.com/paper/2212.06152/) (2022)
- [Graph Condensation via Receptive Field Distribution Matching](https://mlsanity.com/paper/2206.13697/) (2022)

## Built on by (most cited first, 28 of 28)

- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [TD3: Tucker Decomposition Based Dataset Distillation Method for Sequential Recommendation](https://mlsanity.com/paper/2502.02854/) (2025)
- [GC-Bench: An Open and Unified Benchmark for Graph Condensation](https://mlsanity.com/paper/2407.00615/) (2024)
- [Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph](https://mlsanity.com/paper/2410.00049/) (2024)
- [RobGC: Towards Robust Graph Condensation](https://mlsanity.com/paper/2406.13200/) (2024)
- [GDeR: Safeguarding Efficiency, Balancing, and Robustness via Prototypical Graph Pruning](https://mlsanity.com/paper/2410.13761/) (2024)
- [GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights](https://mlsanity.com/paper/2406.16715/) (2024)
- [Beyond Modality Collapse: Representations Blending for Multimodal Dataset Distillation](https://mlsanity.com/paper/2505.14705/) (2025)
- [Scalable Graph Condensation with Evolving Capabilities](https://mlsanity.com/paper/2502.17614/) (2025)
- [GCondenser: Benchmarking Graph Condensation](https://mlsanity.com/paper/2405.14246/) (2024)
- [Backdoor Graph Condensation](https://mlsanity.com/paper/2407.11025/) (2024)
- [Mitigating Bias in Dataset Distillation](https://mlsanity.com/paper/2406.06609/) (2024)
- [Efficient Graph Condensation via Gaussian Process](https://mlsanity.com/paper/2501.02565/) (2025)
- [Effective Dataset Distillation for Spatio-Temporal Forecasting with Bi-dimensional Compression](https://mlsanity.com/paper/2603.10410/) (2026)
- [GSTAM: Efficient Graph Distillation with Structural Attention-Matching](https://mlsanity.com/paper/2408.16871/) (2024)
- [Bonsai: Gradient-free Graph Condensation for Node Classification](https://mlsanity.com/paper/2410.17579/) (2024)
- [Multi-view Graph Condensation via Tensor Decomposition](https://mlsanity.com/paper/2508.14330/) (2025)
- [Position: Graph Condensation Needs a Reset -- Move Beyond Full-dataset Training and Model-Dependence](https://mlsanity.com/paper/2605.18893/) (2026)
- [Extending Graph Condensation to Multi-Label Datasets: A Benchmark Study](https://mlsanity.com/paper/2412.17961/) (2024)
- [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)
- [PLGC: Pseudo-Labeled Graph Condensation](https://mlsanity.com/paper/2601.10358/) (2026)
- [Transferable Graph Condensation from the Causal Perspective](https://mlsanity.com/paper/2601.21309/) (2026)
- [Learning from Complexity: Exploring Dynamic Sample Pruning of Spatio-Temporal Training](https://mlsanity.com/paper/2602.19113/) (2026)
- [Anchor-guided Hypergraph Condensation with Dual-level Discrimination](https://mlsanity.com/paper/2605.10001/) (2026)
- [An Efficient and Scalable Graph Condensation with Structure-Preserving](https://mlsanity.com/paper/2605.31016/) (2026)
- [TaLK: Text-attributed Graph Dataset Distillation via Coupling Language Model with Graph-Aware Kernel](https://mlsanity.com/paper/2606.22975/) (2026)
- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)

## Abstract (arXiv)

Graph condensation aims to reduce the size of a large-scale graph dataset by synthesizing a compact counterpart without sacrificing the performance of Graph Neural Networks (GNNs) trained on it, which has shed light on reducing the computational cost for training GNNs. Nevertheless, existing methods often fall short of accurately replicating the original graph for certain datasets, thereby failing to achieve the objective of lossless condensation. To understand this phenomenon, we investigate the potential reasons and reveal that the previous state-of-the-art trajectory matching method provides biased and restricted supervision signals from the original graph when optimizing the condensed one. This significantly limits both the scale and efficacy of the condensed graph. In this paper, we make the first attempt toward textitlossless graph condensation by bridging the previously neglected supervision signals. Specifically, we employ a curriculum learning strategy to train expert trajectories with more diverse supervision signals from the original graph, and then effectively transfer the information into the condensed graph with expanding window matching. Moreover, we design a loss function to further extract knowledge from the expert trajectories. Theoretical analysis justifies the design of our method and extensive experiments verify its superiority across different datasets. Code is released at https://github.com/NUS-HPC-AI-Lab/GEOM.