Negative Metric Learning for Graphs
Abstract
Graph contrastive learning (GCL) often suffers from false negatives, which degrades the performance on downstream tasks. The existing methods addressing the false negative issue usually rely on human prior knowledge, still leading GCL to suboptimal results. In this paper, we propose a novel Negative Metric Learning (NML) enhanced GCL (NML-GCL). NML-GCL employs a learnable Negative Metric Network (NMN) to build a negative metric space, in which false negatives can be distinguished better from true negatives based on their distance to anchor node. To overcome the lack of explicit supervision signals for NML, we propose a joint training scheme with bi-level optimization objective, which implicitly utilizes the self-supervision signals to iteratively optimize the encoder and the negative metric network. The solid theoretical analysis and the extensive experiments conducted on widely used benchmarks verify the superiority of the proposed method.
Benchmark Results
Tested on 4 datasets 16 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 44 | GCN | 0.8033
±0.0088 | |
| 87 | MVGRL | 0.7808
±0.0006 best reported | |
| 136 | BGRL | 0.7600
±0.0020 best reported | best at pub: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 201 | GRACE | 0.7450
±0.0010 best reported | best at pub: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 291 | NML-GCL | 0.7337
±0.0013 | This paper |
| 350 | MLP | 0.7289
±0.0010 | |
| 424 | GRAPE | 0.7234
±0.0022 | This paper |
| 427 | HomoGCL | 0.7230
±0.0070 best reported | best at pub: HomoGCL: Rethinking Homophily in Graph Contrastive Learning (KDD 2023) best today: Rethinking Graph Contrastive Learning through Relative Similarity Preservation (IJCAI 2025) |
| 477 | Local-GCL | 0.7178
±0.0048 | This paper |
| 583 | ProGCL | 0.7063
±0.0022 | prev best: HomoGCL: Rethinking Homophily in Graph Contrastive Learning (KDD 2023) |
| 594 | PHASES | 0.7049
±0.0040 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 18 | GCN | 0.9296
±0.0015 | |
| 144 | BGRL | 0.8830
±0.0010 best reported | best at pub: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 194 | GRACE | 0.8730
±0.0010 best reported | best at pub: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 196 | MVGRL | 0.8725
±0.0012 best reported | |
| 210 | MLP | 0.8690
±0.0074 | |
| 328 | NML-GCL | 0.8210
±0.0030 | This paper |
| 365 | HomoGCL | 0.8110
±0.0030 best reported | best at pub: HomoGCL: Rethinking Homophily in Graph Contrastive Learning (KDD 2023) best today: Rethinking Graph Contrastive Learning through Relative Similarity Preservation (IJCAI 2025) Difference within reported uncertainty; not counted as underperformance. |
| 370 | PHASES | 0.8108
±0.0062 | This paper |
| 376 | Local-GCL | 0.8095
±0.0041 | This paper |
| 557 | ProGCL | 0.7920
±0.0020 best reported | best at pub: HomoGCL: Rethinking Homophily in Graph Contrastive Learning (KDD 2023) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±0.0019 | |
| 2 | GAT | 0.9669
±0.0014 | |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 113 | ProGCL | 0.9381
±0.0048 best reported | best at pub: Architecture Matters: Uncovering Implicit Mechanisms in Graph Contrastive Learning (NeurIPS 2023) |
| 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. |
| 174 | NML-GCL | 0.9336
±0.0021 | This paper |
| 188 | Local-GCL | 0.9325
±0.0040 best reported | best at pub: Localized Graph Contrastive Learning (2022) |
| 203 | GRACE | 0.9313
±0.0017 best reported | best at pub: Learning Graph Augmentations to Learn Graph Representations (2022) best today: Learn Beneficial Noise as Graph Augmentation (ICML 2025) Difference within reported uncertainty; not counted as underperformance. |
| 206 | MVGRL | 0.9310
±0.0040 best reported | best at pub: Decoupling Weighing and Selecting for Integrating Multiple Graph Pre-training Tasks (ICLR 2024) Difference within reported uncertainty; not counted as underperformance. |
| 222 | HomoGCL | 0.9300
±0.0020 best reported | best at pub: Multiplex Graph Contrastive Learning with Soft Negatives (2024) |
| 243 | repl. cosine sim. | 0.9280
±0.0022 | This paper |
| 249 | GRAPE | 0.9276
±0.0030 | This paper |
| 252 | PHASES | 0.9274
±0.0037 | This paper |
| 390 | MLP | 0.9128
±0.0063 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9461
±0.0017 | |
| 2 | GCN | 0.9412
±0.0008 | |
| 3 | GAT | 0.9398
±0.0022 | |
| 8 | SAGE | 0.9351
±0.0006 | |
| 79 | BGRL | 0.9034
±0.0019 best reported | best at pub: Spectral Augmentation for Self-Supervised Learning on Graphs (ICLR 2022) best today: Adaptive Negative Scheduling for Graph Contrastive Learning (2026) |
| 135 | ProGCL | 0.8955
±0.0016 best reported | best at pub: Bootstrap Latents of Nodes and Neighbors for Graph Self-Supervised Learning (2024) best today: Adaptive Negative Scheduling for Graph Contrastive Learning (2026) |
| 138 | Local-GCL | 0.8954
±0.0032 best reported | best at pub: Str-GCL: Structural Commonsense Driven Graph Contrastive Learning (WWW 2025) |
| 139 | GRACE | 0.8953
±0.0035 best reported | best at pub: Spectral Augmentation for Self-Supervised Learning on Graphs (ICLR 2022) best today: Adaptive Negative Scheduling for Graph Contrastive Learning (2026) |
| 142 | NML-GCL | 0.8943
±0.0025 | This paper |
| 157 | HomoGCL | 0.8900
±0.0010 best reported | best at pub: Multiplex Graph Contrastive Learning with Soft Negatives (2024) |
| 179 | MVGRL | 0.8861
±0.0064 best reported | best at pub: Balancing Graph Embedding Smoothness in Self-Supervised Learning via Information-Theoretic Decomposition (WWW 2025) Difference within reported uncertainty; not counted as underperformance. |
| 211 | GRAPE | 0.8797
±0.0033 | This paper |
| 220 | PHASES | 0.8780
±0.0044 | This paper |
| 320 | MLP | 0.8463 |
