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Graph Condensation via Receptive Field Distribution Matching

Mengyang Liu, Shanchuan Li, Xinshi Chen, Le Song

TL;DR

The paper tackles the computational burden of training on large graphs by proposing Graph Condensation via Receptive Field Distribution Matching (GCDM). It recasts histogram-like graph data into distributions of receptive fields and uses a kernel-based MMD loss to synthesize a small graph whose receptive-field statistics align with the original, independent of a specific GNN training objective. GCDM demonstrates strong, architecture-agnostic generalization, achieving high accuracy at extreme condensation rates and significantly faster condensation than prior gradient-based methods. The approach also offers a graphless variant (GCDM-X) and shows favorable generalization across diverse GNN models, enabling efficient model selection and hyperparameter tuning on condensed data.

Abstract

Graph neural networks (GNNs) enable the analysis of graphs using deep learning, with promising results in capturing structured information in graphs. This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution. Thus, we propose Graph Condesation via Receptive Field Distribution Matching (GCDM), which is accomplished by optimizing the synthetic graph through the use of a distribution matching loss quantified by maximum mean discrepancy (MMD). Additionally, we demonstrate that the synthetic graph generated by GCDM is highly generalizable to a variety of models in evaluation phase and that the condensing speed is significantly improved using this framework.

Graph Condensation via Receptive Field Distribution Matching

TL;DR

The paper tackles the computational burden of training on large graphs by proposing Graph Condensation via Receptive Field Distribution Matching (GCDM). It recasts histogram-like graph data into distributions of receptive fields and uses a kernel-based MMD loss to synthesize a small graph whose receptive-field statistics align with the original, independent of a specific GNN training objective. GCDM demonstrates strong, architecture-agnostic generalization, achieving high accuracy at extreme condensation rates and significantly faster condensation than prior gradient-based methods. The approach also offers a graphless variant (GCDM-X) and shows favorable generalization across diverse GNN models, enabling efficient model selection and hyperparameter tuning on condensed data.

Abstract

Graph neural networks (GNNs) enable the analysis of graphs using deep learning, with promising results in capturing structured information in graphs. This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution. Thus, we propose Graph Condesation via Receptive Field Distribution Matching (GCDM), which is accomplished by optimizing the synthetic graph through the use of a distribution matching loss quantified by maximum mean discrepancy (MMD). Additionally, we demonstrate that the synthetic graph generated by GCDM is highly generalizable to a variety of models in evaluation phase and that the condensing speed is significantly improved using this framework.
Paper Structure (29 sections, 15 equations, 2 figures, 7 tables, 1 algorithm)

This paper contains 29 sections, 15 equations, 2 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Neural Networks.
  4. Coreset & Data Condensation
  5. Graph Coarsening & Graph Sparsification.
  6. Data Condensation & Graph Condensation.
  7. Methodology
  8. Graph Condensation Problem
  9. Viewing a Graph as a Distribution
  10. Node classification by GNN
  11. Receptive Fields of GNN
  12. Viewing a Graph as a Distribution of Receptive Fields
  13. Some Remarks.
  14. GCDM: Graph Condensation via Receptive Field Distribution Matching
  15. Synthesize the Labels Y'
  16. ...and 14 more sections

Figures (2)

  • Figure 1: The overall framework of graph condensation via receptive field distribution matching (GCDM) and the test performance on Flickr dataset with 99.5% size reduction.
  • Figure 2: Receptive field $R(i, L)$ of GNNs for a node $i$ (red-colored) with $L=0, 1,2$.