Fractal Graph Contrastive Learning

TL;DR

FractalGCL introduces a global augmentation framework for graph contrastive learning using fractal-dimension-aware loss, improving efficiency and performance on various graph tasks.

Contribution

It proposes a theory-driven global augmentation method with a novel contrastive loss and a Gaussian surrogate for efficient computation.

Findings

Achieves 61% runtime reduction with Gaussian surrogate.

Serves as effective frozen-pretraining on MalNet-Tiny.

Outperforms previous methods on TUDataset and urban traffic tasks.

Abstract

Graph Contrastive Learning (GCL) relies on semantically consistent graph augmentations, but common local perturbations provide limited control over global structural consistency, motivating a more principled global augmentation strategy. We therefore propose Fractal Graph Contrastive Learning (FractalGCL), a theory-motivated framework that constructs a renormalisation-based augmented graph and introduces a fractal-dimension-aware contrastive loss that penalises unreliable positive views and reweights negative-pair repulsion by finite-scale box-counting discrepancies. However, computing these discrepancies introduces substantial overhead, so we derive and justify a Gaussian surrogate that avoids repeated box-counting on renormalised graphs, yielding about a $61\%$ runtime reduction. Experiments show that FractalGCL serves as an effective frozen-pretraining tool on MalNet-Tiny, achieves strong performance on the standard TUDataset benchmarks, and outperforms the next-best method on real-world urban traffic tasks by $4.51$ percentage points in average accuracy. Code is available at https://anonymous.4open.science/r/FractalGCL-0511/.