Towards Pre-trained Graph Condensation via Optimal Transport

2025-09-18

AI Summary

Traditional graph compression methods rely on fixed GNN architectures and task-specific supervision, limiting their generalizability and reusability. To address this, we propose PreGC—a task-agnostic, architecture-agnostic graph distillation framework. First, leveraging optimal transport theory, PreGC jointly aligns the source and distilled graphs in both structural and representation spaces to preserve semantic consistency. Second, it introduces a hybrid interval-based graph diffusion mechanism to enhance node-state uncertainty modeling. Third, it incorporates a traceable semantic coordinator that enables seamless pretraining–distillation co-optimization across diverse tasks and GNN backbones. Extensive experiments demonstrate that PreGC significantly improves distillation performance and cross-task transferability on multiple GNN architectures (e.g., GCN, GAT, GIN) and downstream tasks (node/graph classification). To our knowledge, PreGC is the first framework to establish a truly universal graph distillation paradigm.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a dependency severely restricts their reusability and generalization across various tasks and architectures. In this work, we revisit the goal of ideal GC from the perspective of GNN optimization consistency, and then a generalized GC optimization objective is derived, by which those traditional GC methods can be viewed nicely as special cases of this optimization paradigm. Based on this, Pre-trained Graph Condensation (PreGC) via optimal transport is proposed to transcend the limitations of task- and architecture-dependent GC methods. Specifically, a hybrid-interval graph diffusion augmentation is presented to suppress the weak generalization ability of the condensed graph on particular architectures by enhancing the uncertainty of node states. Meanwhile, the matching between optimal graph transport plan and representation transport plan is tactfully established to maintain semantic consistencies across source graph and condensed graph spaces, thereby freeing graph condensation from task dependencies. To further facilitate the adaptation of condensed graphs to various downstream tasks, a traceable semantic harmonizer from source nodes to condensed nodes is proposed to bridge semantic associations through the optimized representation transport plan in pre-training. Extensive experiments verify the superiority and versatility of PreGC, demonstrating its task-independent nature and seamless compatibility with arbitrary GNNs.

Problem

• Overcoming task and architecture dependency in graph condensation methods
• Enhancing generalization of condensed graphs across diverse GNN architectures
• Maintaining semantic consistency between source and condensed graph spaces

Innovation

• Optimal transport for task-independent graph condensation
• Hybrid-interval diffusion enhances condensed graph generalization
• Semantic harmonizer bridges associations via transport plan