Title: Fractal Graph Contrastive Learning
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Representation Learning, Graph Contrastive Learning, Fractal Geometry, Graph Classification, Network Science

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 introducing 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, equipping the method with a fallback mechanism guaranteeing a performance lower bound even on non-fractal graphs. 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 and latest baselines on traffic networks by an average margin of about remarkably 4\%. Codes are available at (\url{https://anonymous.4open.science/r/FractalGCL-0511/}).

TL;DR: We were among the first to bring fractal concepts into graph representation learning and developed FractalGCL—a theory-driven yet practical framework that leverages fractal geometry to enhance GCL.