# Efficient Graph Condensation via Gaussian Process

arXiv: https://arxiv.org/abs/2501.02565 · HTML: https://mlsanity.com/paper/2501.02565/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 65 references that are in the map.
- First posted on arXiv 5 Jan 2025.

## Builds on (most cited first, 30 of 42)

- [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)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (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)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [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)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [Dataset Condensation with Contrastive Signals](https://mlsanity.com/paper/2202.02916/) (2022)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)

## Built on by (most cited first, 4 of 4)

- [Simple yet Effective Graph Distillation via Clustering](https://mlsanity.com/paper/2505.20807/) (2025)
- [Position: Graph Condensation Needs a Reset -- Move Beyond Full-dataset Training and Model-Dependence](https://mlsanity.com/paper/2605.18893/) (2026)
- [FairGC: Fairness-aware Graph Condensation](https://mlsanity.com/paper/2603.28321/) (2026)
- [Heterogeneous Graph Condensation via Role-Aware Clustering](https://mlsanity.com/paper/2607.03097/) (2026)

## Abstract (arXiv)

Graph condensation reduces the size of large graphs while preserving performance, addressing the scalability challenges of Graph Neural Networks caused by computational inefficiencies on large datasets. Existing methods often rely on bi-level optimization, requiring extensive GNN training and limiting their scalability. To address these issues, this paper proposes Graph Condensation via Gaussian Process (GCGP), a novel and computationally efficient approach to graph condensation. GCGP utilizes a Gaussian Process (GP), with the condensed graph serving as observations, to estimate the posterior distribution of predictions. This approach eliminates the need for the iterative and resource-intensive training typically required by GNNs. To enhance the capability of the GCGP in capturing dependencies between function values, we derive a specialized covariance function that incorporates structural information. This covariance function broadens the receptive field of input nodes by local neighborhood aggregation, thereby facilitating the representation of intricate dependencies within the nodes. To address the challenge of optimizing binary structural information in condensed graphs, Concrete random variables are utilized to approximate the binary adjacency matrix in a continuous counterpart. This relaxation process allows the adjacency matrix to be represented in a differentiable form, enabling the application of gradient-based optimization techniques to discrete graph structures. Experimental results show that the proposed GCGP method efficiently condenses large-scale graph data while preserving predictive performance, addressing the scalability and efficiency challenges. The implementation of our method is publicly available at https://github.com/WANGLin0126/GCGP.