Learn Beneficial Noise as Graph Augmentation
Abstract
Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.
Benchmark Results
Tested on 7 datasets 25 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±0.0019 | |
| 2 | GAT | 0.9669
±0.0014 best reported | |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 8 | GCN | 0.9632
±0.0008 best reported | |
| 103 | SGRL | 0.9395
±0.0003 best reported | |
| 132 | GREET | 0.9361
±0.0035 | |
| 172 | BGRL | 0.9337
±0.0021 best reported | best at pub: Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 183 | CL | 0.9329
±0.0017 | This paper |
| 191 | GCA | 0.9320
±0.0060 best reported | best at pub: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) best today: Decoupling Weighing and Selecting for Integrating Multiple Graph Pre-training Tasks (ICLR 2024) Difference within reported uncertainty; not counted as underperformance. |
| 196 | GRACE +PiNGDA | 0.9319
±0.0018 | This paper |
| 203 | GRACE | 0.9313
±0.0017 | prev best: Learning Graph Augmentations to Learn Graph Representations (2022) Improvement within reported uncertainty; not highlighted. |
| 205 | Sp2GCL +PiNGDA | 0.9311
±0.0014 | This paper |
| 213 | DGI | 0.9309
±0.0008 best reported | |
| 217 | Sp2GCL | 0.9305
±0.0023 | This paper |
| 327 | GASSL | 0.9214
±0.0023 | This paper |
| 347 | AD-GCL | 0.9192
±0.0037 | prev best: GIMM: InfoMin-Max for Automated Graph Contrastive Learning (2023) |
| 390 | MLP | 0.9128
±0.0063 | |
| 392 | GRACEIS | 0.9126
±0.0058 | This paper |
| 408 | GMI | 0.9081
±0.0015 best reported | best at pub: Localized Graph Contrastive Learning (2022) best today: Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion (2025) Difference within reported uncertainty; not counted as underperformance. |
| 460 | GOUDA | 0.8961
±0.0117 | This paper |
| 542 | JOAO | 0.7823
±0.0263 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GrokFormer | 0.9831
±0.0018 | |
| 2 | PolyFormer | 0.9808
±0.0027 | |
| 3 | SGFormer | 0.9796
±0.0081 | |
| 6 | GAT | 0.9782
±0.0028 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 9 | GCN | 0.9774
±0.0035 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 17 | SAGE | 0.9739
±0.0018 | |
| 52 | GREET | 0.9613
±0.0012 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 58 | MLP | 0.9597
±0.0007 | |
| 63 | GCA | 0.9590
±0.0020 best reported | best at pub: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) |
| 67 | CL | 0.9581
±0.0006 | This paper |
| 68 | GRACE +PiNGDA | 0.9581
±0.0005 | This paper |
| 69 | BGRL | 0.9580
±0.0040 best reported | best at pub: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) Difference within reported uncertainty; not counted as underperformance. |
| 77 | GRACE | 0.9574
±0.0006 | prev best: Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks (2023) Improvement within reported uncertainty; not highlighted. |
| 80 | Sp2GCL +PiNGDA | 0.9574
±0.0004 | This paper |
| 81 | Sp2GCL | 0.9573
±0.0004 | This paper |
| 94 | SGRL | 0.9564
±0.0010 | This paper |
| 97 | AD-GCL | 0.9563
±0.0010 | prev best: GIMM: InfoMin-Max for Automated Graph Contrastive Learning (2023) |
| 161 | GASSL | 0.9493
±0.0021 | This paper |
| 173 | GOUDA | 0.9454
±0.0059 | This paper |
| 184 | JOAO | 0.9430
±0.0038 | This paper |
| 187 | GRACEIS | 0.9428
±0.0043 | This paper |
TU Dortmund
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | MSH-GNN | 0.9910
±0.0030 | |
| 2 | ID-GNN+BEC | 0.9830
±0.0360 | |
| 3 | SupCosine | 0.9830
±0.0250 | |
| 39 | GIN | 0.9330
±0.0290 | |
| 178 | AD-GCL | 0.9028
±0.0401 best reported | best at pub: Unifying Graph Contrastive Learning via Graph Message Augmentation (2024) Difference within reported uncertainty; not counted as underperformance. |
| 213 | CL | 0.8971
±0.0073 | This paper |
| 356 | RU-GIN | 0.8761
±0.0039 | This paper |
| 403 | MLP | 0.8660
±0.0495 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | WL-MLP | 0.9954 | |
| 2 | GIN | 0.9934 | |
| 3 | GCN | 0.9727 | |
| 104 | GraphCL | 0.8250
±0.0013 best reported | best at pub: Label-invariant Augmentation for Semi-Supervised Graph Classification (NeurIPS 2022) |
| 131 | GraphSAGE | 0.8200
±0.0100 | |
| 338 | InfoGraph | 0.7750
±0.0074 best reported | best at pub: Graph Masked Autoencoders with Transformers (2022) |
| 409 | AD-GCL | 0.7518
±0.0031 best reported | best at pub: Graph Contrastive Learning with Personalized Augmentation (2022) best today: GIMM: InfoMin-Max for Automated Graph Contrastive Learning (2023) |
| 494 | CL | 0.6935
±0.0063 | This paper |
| 523 | RU-GIN | 0.6540
±0.0017 best reported | best at pub: Adversarial Graph Augmentation to Improve Graph Contrastive Learning (NeurIPS 2021) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | OEPG | 0.9630
±0.0090 | |
| 2 | MSH-GNN | 0.9580
±0.0090 | |
| 3 | GNN-AK+ | 0.9480
±0.0080 | |
| 13 | GIN | 0.9240
±0.0250 | |
| 23 | GraphCL | 0.9169
±0.0070 best reported | best at pub: Graph Contrastive Learning with Cohesive Subgraph Awareness (WWW 2024) |
| 37 | AD-GCL | 0.9010
±0.0015 best reported | best at pub: Graph Contrastive Learning with Personalized Augmentation (2022) |
| 46 | InfoGraph | 0.8939
±0.0181 best reported | best at pub: Graph Contrastive Learning with Cohesive Subgraph Awareness (WWW 2024) |
| 67 | CL | 0.8399
±0.0034 | This paper |
| 78 | RU-GIN | 0.7686
±0.0025 best reported | best at pub: Adversarial Graph Augmentation to Improve Graph Contrastive Learning (NeurIPS 2021) |
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9672
±0.0147 | |
| 2 | DoG | 0.9660
±0.0210 | |
| 3 | GPF-plus | 0.9583
±0.0419 | |
| 34 | MLP | 0.9230
±0.0070 | |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 101 | GREET | 0.8703
±0.0236 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) best today: Disentangled Generative Graph Representation Learning (2024) |
| 211 | GAT | 0.8162
±0.0645 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) best today: Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (2025) |
| 257 | GCN | 0.7933
±0.0447 best reported | best at pub: Graph Wave Networks (WWW 2025) |
| 304 | DGI | 0.7581
±0.0503 best reported | |
| 409 | BGRL | 0.6841
±0.0501 best reported | best at pub: Cross-Domain Graph Data Scaling: A Showcase with Diffusion Models (NeurIPS 2024) |
| 439 | CL | 0.6531
±0.0129 | This paper |
| 468 | JOAO | 0.6245
±0.0296 | prev best: Cross-Domain Graph Data Scaling: A Showcase with Diffusion Models (NeurIPS 2024) Improvement within reported uncertainty; not highlighted. |
| 479 | GRACEIS | 0.6190
±0.0240 | This paper |
| 492 | AD-GCL | 0.6082
±0.0249 | This paper |
| 500 | SGRL | 0.6000
±0.0027 | This paper |
| 515 | GCA | 0.5946 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 579 | GMI | 0.5049 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
