Fractal Graph Contrastive Learning

2025-05-16

AI Summary

Graph contrastive learning (GCL) suffers from global structural inconsistency in positive sample pairs, as existing graph augmentation methods lack explicit modeling of topological consistency. To address this, we propose a fractal self-similarity–driven contrastive learning framework. First, we introduce fractal renormalization augmentation—based on box-counting—to explicitly preserve multi-scale topological self-similarity. Second, we design a fractal dimension–aware contrastive loss, theoretically proving its weak convergence with respect to fractal dimension discrepancy, and propose a single-shot estimator to reduce computational overhead. By unifying fractal geometry, graph renormalization, and contrastive learning, our method achieves state-of-the-art performance on standard graph benchmarks. On traffic network datasets, it improves average accuracy by 7% and reduces training time by 61%.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

While Graph Contrastive Learning (GCL) has attracted considerable attention in the field of graph self-supervised learning, its performance heavily relies on data augmentations that are expected to generate semantically consistent positive pairs. Existing strategies typically resort to random perturbations or local structure preservation, yet lack explicit control over global structural consistency between augmented views. To address this limitation, we propose Fractal Graph Contrastive Learning (FractalGCL), a theory-driven framework that leverages fractal self-similarity to enforce global topological coherence. FractalGCL introduces two key innovations: a renormalisation-based augmentation that generates structurally aligned positive views via box coverings; and a fractal-dimension-aware contrastive loss that aligns graph embeddings according to their fractal dimensions. While combining the two innovations markedly boosts graph-representation quality, it also adds non-trivial computational overhead. To mitigate the computational overhead of fractal dimension estimation, we derive a one-shot estimator by proving that the dimension discrepancy between original and renormalised graphs converges weakly to a centred Gaussian distribution. This theoretical insight enables a reduction in dimension computation cost by an order of magnitude, cutting overall training time by approximately 61%. The experiments show that FractalGCL not only delivers state-of-the-art results on standard benchmarks but also outperforms traditional baselines on traffic networks by an average margin of about remarkably 7%. Codes are available at (https://anonymous.4open.science/r/FractalGCL-0511).

Problem

• Enhance global structural consistency in graph contrastive learning
• Reduce computational overhead of fractal dimension estimation
• Improve graph-representation quality with fractal self-similarity

Innovation

• Leverages fractal self-similarity for global coherence
• Renormalisation-based augmentation aligns structural views
• One-shot estimator reduces computational overhead significantly