# Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching

arXiv: https://arxiv.org/abs/2402.04924 · HTML: https://mlsanity.com/paper/2402.04924/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 90 of its 160 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 90)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Dataset Distillation](https://mlsanity.com/paper/1811.10959/) (2018)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)

## Built on by (most cited first, 8 of 8)

- [Rethinking and Accelerating Graph Condensation: A Training-Free Approach with Class Partition](https://mlsanity.com/paper/2405.13707/) (2024)
- [GC-Bench: An Open and Unified Benchmark for Graph Condensation](https://mlsanity.com/paper/2407.00615/) (2024)
- [GDeR: Safeguarding Efficiency, Balancing, and Robustness via Prototypical Graph Pruning](https://mlsanity.com/paper/2410.13761/) (2024)
- [A Large-Scale Study on Video Action Dataset Condensation](https://mlsanity.com/paper/2412.21197/) (2024)
- [Backdoor Graph Condensation](https://mlsanity.com/paper/2407.11025/) (2024)
- [Position: Graph Condensation Needs a Reset -- Move Beyond Full-dataset Training and Model-Dependence](https://mlsanity.com/paper/2605.18893/) (2026)
- [TS-Inverse: A Gradient Inversion Attack Tailored for Federated Time Series Forecasting Models](https://mlsanity.com/paper/2503.20952/) (2025)
- [Model-to-Data Distillation for Graph Neural Networks](https://mlsanity.com/paper/2605.06814/) (2026)

## Abstract (arXiv)

Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have raised growing concerns. As one of the most promising directions, graph condensation methods address these issues by employing gradient matching, aiming to condense the full graph into a more concise yet information-rich synthetic set. Though encouraging, these strategies primarily emphasize matching directions of the gradients, which leads to deviations in the training trajectories. Such deviations are further magnified by the differences between the condensation and evaluation phases, culminating in accumulated errors, which detrimentally affect the performance of the condensed graphs. In light of this, we propose a novel graph condensation method named CrafTing RationaL trajectory (CTRL), which offers an optimized starting point closer to the original dataset's feature distribution and a more refined strategy for gradient matching. Theoretically, CTRL can effectively neutralize the impact of accumulated errors on the performance of condensed graphs. We provide extensive experiments on various graph datasets and downstream tasks to support the effectiveness of CTRL. Code is released at https://github.com/NUS-HPC-AI-Lab/CTRL.