Fractal Graph Contrastive Learning

Nero Li, Xuehao Zhai, Zhichao Shi, B. Shi, Xuhui Jiang

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\ 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.

Benchmark Results

Tested on 4 datasets 8 baseline values reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

TU Dortmund

MUTAG

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	MSH-GNN GNN global	0.9910 ±0.0030	Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing
2	ID-GNN+BEC Hyb global	0.9830 ±0.0360	Depth-Adaptive Graph Neural Networks via Learnable Bakry-Émery Curvature
3	SupCosine Hyb global	0.9830 ±0.0250	Supervised Contrastive Learning with Structure Inference for Graph Classification
39	GIN GNN global	0.9330 ±0.0290	ProtGNN: Towards Self-Explaining Graph Neural Networks
79	FractalGCL Hyb ★ proposed	0.9171 ±0.0023	This paper
222	JOAOv2 GNN baseline actual #222 vs paper #353 131 places worse	0.8967 ±0.0524 best reported	actual #222 vs paper #353 131 places worse paper 0.8767 ±0.0079 best at pub: Unifying Graph Contrastive Learning via Graph Message Augmentation (2024) Difference within reported uncertainty; not counted as underperformance. paper 0.8767 ±0.0079 Δ at pub 0.0200
227	MGCL GNN baseline	0.8955 ±0.0108	This paper
228	GAE GNN baseline actual #228 vs paper #742 514 places worse	0.8950 ±0.0150 best reported	actual #228 vs paper #742 514 places worse paper 0.7287 ±0.0684 best at pub: Revisiting Graph Autoencoders as Implicit Contrastive Learners (KDD 2024) paper 0.7287 ±0.0684 Δ at pub 0.1663
229	DRGCL GNN baseline	0.8950 ±0.0060	This paper
257	InfoGraph GNN baseline actual #257 vs paper #272 15 places worse	0.8930 ±0.0514 best reported	actual #257 vs paper #272 15 places worse paper 0.8901 ±0.0113 best at pub: Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalization (KDD 2023) Difference within reported uncertainty; not counted as underperformance. paper 0.8901 ±0.0113 Δ at pub 0.0029
272	SimGRACE GNN baseline actual #272 vs paper #272	0.8910 ±0.0140 best reported	actual #272 vs paper #272 paper 0.8901 ±0.0131 best at pub: GPS: graph contrastive learning via multi-scale augmented views from adversarial pooling (2024) Difference within reported uncertainty; not counted as underperformance. paper 0.8901 ±0.0131 Δ at pub 0.0009
311	GradGCL GNN baseline	0.8846 ±0.0098	This paper
351	JOAO GNN baseline actual #351 vs paper #370 19 places worse	0.8770 ±0.0080 best reported	actual #351 vs paper #370 19 places worse paper 0.8735 ±0.0102 best at pub: Graph Self-Supervised Learning: A Survey (2021) best today: Learning Graph Augmentations to Learn Graph Representations (2022) Difference within reported uncertainty; not counted as underperformance. paper 0.8735 ±0.0102 Δ at pub 0.0035 Δ today 0.0035
354	GraphCL GNN baseline actual #354 vs paper #396 42 places worse	0.8766 ±0.0103 best reported	actual #354 vs paper #396 42 places worse paper 0.8680 ±0.0134 best at pub: Graph Masked Autoencoders with Transformers (2022) Difference within reported uncertainty; not counted as underperformance. paper 0.8680 ±0.0134 Δ at pub 0.0086
355	RGCL GNN baseline	0.8766 ±0.0101	This paper
403	MLP code ↗ Trad global	0.8660 ±0.0495	Breaking the Limits of Message Passing Graph Neural Networks code ↗
407	graph2vec Walk baseline actual #407 vs paper #517 110 places worse	0.8644 ±0.0125 best reported	actual #407 vs paper #517 110 places worse paper 0.8315 ±0.0925 best at pub: Graph Masked Autoencoders with Transformers (2022) Difference within reported uncertainty; not counted as underperformance. paper 0.8315 ±0.0925 Δ at pub 0.0329
517	DGI GNN baseline actual #517 vs paper #772 255 places worse	0.8320 ±0.0130 best reported	actual #517 vs paper #772 255 places worse paper 0.6649 ±0.0228 best at pub: Revisiting Graph Autoencoders as Implicit Contrastive Learners (KDD 2024) paper 0.6649 ±0.0228 Δ at pub 0.1671
753	ContextPred GNN baseline	0.7175 ±0.0734	This paper

NCI1

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	WL-MLP GT global	0.9954	1-WL Expressiveness Is (Almost) All You Need
2	GIN GNN global	0.9934	1-WL Expressiveness Is (Almost) All You Need
3	GCN GNN global	0.9727	1-WL Expressiveness Is (Almost) All You Need
104	GraphCL GNN baseline actual #104 vs paper #325 221 places worse	0.8250 ±0.0013 best reported	actual #104 vs paper #325 221 places worse paper 0.7787 ±0.0041 best at pub: Label-invariant Augmentation for Semi-Supervised Graph Classification (NeurIPS 2022) paper 0.7787 ±0.0041 Δ at pub 0.0463
131	GraphSAGE code ↗ GNN global	0.8200 ±0.0100	Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings code ↗
141	SimGRACE GNN baseline actual #141 vs paper #258 117 places worse	0.8180 ±0.0015 best reported	actual #141 vs paper #258 117 places worse paper 0.7912 ±0.0044 best at pub: Label-invariant Augmentation for Semi-Supervised Graph Classification (NeurIPS 2022) paper 0.7912 ±0.0044 Δ at pub 0.0268
146	JOAOv2 GNN baseline actual #146 vs paper #303 157 places worse	0.8170 ±0.0026 best reported	actual #146 vs paper #303 157 places worse paper 0.7836 ±0.0053 best at pub: Label-invariant Augmentation for Semi-Supervised Graph Classification (NeurIPS 2022) paper 0.7836 ±0.0053 Δ at pub 0.0334
192	FractalGCL Hyb ★ proposed	0.8050 ±0.0016	This paper
236	GAE GNN baseline actual #236 vs paper #426 190 places worse	0.7978 ±0.0017 best reported	actual #236 vs paper #426 190 places worse paper 0.7436 ±0.0024 best at pub: Label-invariant Augmentation for Semi-Supervised Graph Classification (NeurIPS 2022) paper 0.7436 ±0.0024 Δ at pub 0.0542
239	GradGCL GNN baseline	0.7972 ±0.0053	This paper
277	DRGCL GNN baseline	0.7870 ±0.0040	This paper
283	MGCL GNN baseline	0.7866 ±0.0034	This paper
301	JOAO GNN baseline actual #301 vs paper #317 16 places worse	0.7840 ±0.0050 best reported	actual #301 vs paper #317 16 places worse paper 0.7807 ±0.0047 best at pub: Omni-Granular Ego-Semantic Propagation for Self-Supervised Graph Representation Learning (ICML 2022) Difference within reported uncertainty; not counted as underperformance. paper 0.7807 ±0.0047 Δ at pub 0.0033
315	RGCL GNN baseline	0.7814 ±0.0108	This paper
338	InfoGraph GNN baseline actual #338 vs paper #386 48 places worse	0.7750 ±0.0074 best reported	actual #338 vs paper #386 48 places worse paper 0.7620 ±0.0106 best at pub: Graph Masked Autoencoders with Transformers (2022) Difference within reported uncertainty; not counted as underperformance. paper 0.7620 ±0.0106 Δ at pub 0.0130
388	DGI GNN baseline actual #388 vs paper #417 29 places worse	0.7620 ±0.0180 best reported	actual #388 vs paper #417 29 places worse paper 0.7486 ±0.0026 best at pub: Revisiting Graph Autoencoders as Implicit Contrastive Learners (KDD 2024) paper 0.7486 ±0.0026 Δ at pub 0.0134
406	graph2vec Walk baseline actual #406 vs paper #446 40 places worse	0.7540 ±0.0120 best reported	actual #406 vs paper #446 40 places worse paper 0.7322 ±0.0181 best at pub: InfoGCL: Information-Aware Graph Contrastive Learning (NeurIPS 2021) Difference within reported uncertainty; not counted as underperformance. paper 0.7322 ±0.0181 Δ at pub 0.0218
450	ContextPred GNN baseline actual #450 vs paper #450	0.7300 ±0.0030	actual #450 vs paper #450 paper 0.7300 ±0.0030 prev best: Pre-training Graph Neural Networks on Molecules by Using Subgraph-Conditioned Graph Information Bottleneck (AAAI 2024) paper 0.7300 ±0.0030 Δ at pub 0.2353

PROTEINS

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	MSH-GNN GNN global	0.9410 ±0.0330	Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing
2	GRDL GNN global	0.8260 ±0.0120	Graph Classification via Reference Distribution Learning: Theory and Practice
3	GMN code ↗ Hyb global	0.8225	Memory-Based Graph Networks code ↗
32	GIN GNN global	0.7880 ±0.0410	Permutation-Invariant graph partitioning: How graph neural networks capture structural …
149	MLP Trad global	0.7600 ±0.0320	Simplifying Graph Convolutional Networks with Redundancy-Free Neighbors
162	FractalGCL Hyb ★ proposed	0.7585 ±0.0040	This paper
209	SimGRACE GNN baseline actual #209 vs paper #309 100 places worse	0.7535 ±0.0009 best reported	actual #209 vs paper #309 100 places worse paper 0.7403 ±0.0009 best at pub: SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation (WWW 2022) best today: Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networks (2025) paper 0.7403 ±0.0009 Δ at pub 0.0132 Δ today 0.0132
226	DRGCL GNN baseline	0.7520 ±0.0060	This paper
242	RGCL GNN baseline	0.7503 ±0.0043	This paper
265	GraphCL GNN baseline actual #265 vs paper #296 31 places worse	0.7489 ±0.0065 best reported	actual #265 vs paper #296 31 places worse paper 0.7439 ±0.0045 best at pub: Graph Masked Autoencoders with Transformers (2022) Difference within reported uncertainty; not counted as underperformance. paper 0.7439 ±0.0045 Δ at pub 0.0050
266	GradGCL GNN baseline	0.7489 ±0.0039	This paper
269	MGCL GNN baseline	0.7485 ±0.0071	This paper
283	JOAO GNN baseline actual #283 vs paper #288 5 places worse	0.7460 ±0.0040 best reported	actual #283 vs paper #288 5 places worse paper 0.7455 ±0.0041 best at pub: GPS: graph contrastive learning via multi-scale augmented views from adversarial pooling (2024) best today: Balancing Graph Embedding Smoothness in Self-Supervised Learning via Information-Theoretic Decomposition (WWW 2025) Difference within reported uncertainty; not counted as underperformance. paper 0.7455 ±0.0041 Δ at pub 0.0005 Δ today 0.0005
294	InfoGraph GNN baseline	0.7444 ±0.0031	This paper
309	JOAOv2 GNN baseline	0.7407 ±0.0110	This paper
350	graph2vec Walk baseline	0.7330 ±0.0205	This paper
400	DGI GNN baseline	0.7227 ±0.0040	This paper
451	GAE GNN baseline	0.7051 ±0.0017	This paper
455	ContextPred GNN baseline	0.7023 ±0.0063	This paper

D&D

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	GC-GNN (GCN) GNN global	0.9210 ±0.0810	Rethinking the Power of Graph Canonization in Graph Representation Learning with Stability
2	SUGAR code ↗ Hyb global	0.8403 ±0.0133	SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information … code ↗
3	Ortho-g-U-Nets global	0.8387	Orthogonal Graph Neural Networks
15	SAGE GNN global	0.8088 ±0.0233	Semi-Supervised Hierarchical Graph Classification
22	FractalGCL Hyb ★ proposed	0.8014 ±0.0012	This paper
47	GradGCL GNN baseline	0.7895 ±0.0047	This paper
49	MGCL GNN baseline	0.7888 ±0.0038	This paper
50	RGCL GNN baseline	0.7886 ±0.0048	This paper
58	GraphCL GNN baseline	0.7862 ±0.0040	This paper
65	DRGCL GNN baseline	0.7840 ±0.0070	This paper
93	SimGRACE GNN baseline	0.7744 ±0.0111	This paper
94	JOAOv2 GNN baseline	0.7740 ±0.0115	This paper
98	JOAO GNN baseline	0.7732 ±0.0054	This paper
124	DGI GNN baseline	0.7578 ±0.0034	This paper
141	ContextPred GNN baseline	0.7466 ±0.0051	This paper
145	GAE GNN baseline	0.7454 ±0.0068	This paper
148	InfoGraph GNN baseline actual #148 vs paper #157 9 places worse	0.7424 ±0.0086 best reported	actual #148 vs paper #157 9 places worse paper 0.7285 ±0.0178 best at pub: Contrastive Self-supervised Learning for Graph Classification (AAAI 2020) Difference within reported uncertainty; not counted as underperformance. paper 0.7285 ±0.0178 Δ at pub 0.0139
169	graph2vec Walk baseline	0.7032 ±0.0232	This paper

SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best at pub — reported value improved over the best known when published