Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks
Abstract
Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.
Benchmark Results
Tested on 6 datasets 28 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE+CNA | 0.9418
±0.0033 | |
| 2 | GCN+CNA | 0.9366
±0.0048 | |
| 3 | TransformerConv | 0.9350
±0.0058 | |
| 21 | GCN | 0.9004 best reported | best at pub: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 39 | SAGE | 0.8911
±0.0012 | |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 55 | JKNet | 0.8870 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 108 | APPNP | 0.8787 best reported | best at pub: Orthogonal Graph Neural Networks (AAAI 2021) best today: Feature Transportation Improves Graph Neural Networks (AAAI 2023) |
| 113 | MixHop | 0.8761
±0.0203 best reported | |
| 121 | SDRF | 0.8751
±0.0029 best reported | best today: Local Virtual Nodes for Alleviating Over-Squashing in Graph Neural Networks (2025) |
| 134 | GRACE | 0.8720
±0.0020 best reported | best at pub: Enhancing Graph Contrastive Learning with Node Similarity (2022) best today: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 177 | DGI | 0.8630
±0.0020 best reported | best at pub: Node Representation Learning in Graph via Node-to-Neighbourhood Mutual Information Maximization (2022) best today: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 334 | BAGCN-mul | 0.8370
±0.0020 | This paper |
| 397 | BAGCN-add | 0.8330
±0.0020 | This paper |
| 534 | BGCN | 0.8200
±0.0010 | This paper |
| 572 | GCN + FA | 0.8160
±0.0020 | This paper |
| 724 | MLP | 0.7768 best reported | best at pub: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 17 | APPNP | 0.9355
±0.0060 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 18 | GCN | 0.9296
±0.0015 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 20 | GAT | 0.9233
±0.0018 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 24 | JKNet | 0.9160 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 70 | MixHop | 0.9004
±0.0141 best reported | best at pub: Power up! Robust Graph Convolutional Network via Graph Powering (AAAI 2019) best today: Language is All a Graph Needs (2023) |
| 116 | SAGE | 0.8881
±0.0015 | |
| 194 | GRACE | 0.8730
±0.0010 best reported | best at pub: Enhancing Graph Contrastive Learning with Node Similarity (2022) best today: Oversmoothing: A Nightmare for Graph Contrastive Learning? (2023) |
| 204 | DGI | 0.8708
±0.0017 best reported | |
| 210 | MLP | 0.8690
±0.0074 best reported | best at pub: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) best today: On the Equivalence of Graph Convolution and Mixup (TMLR 2023) |
| 513 | GCN + FA | 0.7950
±0.0010 | This paper |
| 535 | BGCN | 0.7940
±0.0010 | This paper |
| 582 | SDRF | 0.7910
±0.0010 | This paper |
| 640 | BAGCN-mul | 0.7850
±0.0010 | This paper |
| 641 | BAGCN-add | 0.7850
±0.0010 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±0.0019 | |
| 2 | GAT | 0.9669
±0.0014 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) best today: Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification (2026) Difference within reported uncertainty; not counted as underperformance. |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 8 | GCN | 0.9632
±0.0008 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 87 | GCNII | 0.9430
±0.0020 best reported | best at pub: NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification (2020) best today: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 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) |
| 260 | DAGNN | 0.9269 best reported | best at pub: NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification (2020) Difference within reported uncertainty; not counted as underperformance. |
| 307 | BAGCN-add | 0.9235
±0.0090 | This paper |
| 378 | GraphSAGE-mean | 0.9143
±0.0130 | prev best: ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks (ICLR 2022) Improvement within reported uncertainty; not highlighted. |
| 390 | MLP | 0.9128
±0.0063 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) best today: Clarify Confused Nodes via Separated Learning (2023) |
| 393 | MoNet | 0.9124
±0.0130 | prev best: Beltrami Flow and Neural Diffusion on Graphs (NeurIPS 2021) Improvement within reported uncertainty; not highlighted. |
| 414 | GraphSAGE-meanpool | 0.9072
±0.0160 | This paper |
| 416 | BAGCN-mul | 0.9071
±0.0110 | This paper |
| 434 | GraphSAGE-maxpool | 0.9042
±0.0130 | 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: SelfGNN: Self-supervised Graph Neural Networks without explicit negative sampling (WWW 2021) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 9 | GCN | 0.9774
±0.0035 best reported | best at pub: SelfGNN: Self-supervised Graph Neural Networks without explicit negative sampling (WWW 2021) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 17 | SAGE | 0.9739
±0.0018 | |
| 54 | BAGCN-mul | 0.9608
±0.0050 | This paper |
| 58 | MLP | 0.9597
±0.0007 best reported | best at pub: Latent Graph Inference using Product Manifolds (ICLR 2022) |
| 59 | GCNII | 0.9394
±0.0040 | best today: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) Improvement within reported uncertainty; not highlighted. |
| 64 | BAGCN-add | 0.9588
±0.0080 | This paper |
| 77 | GRACE | 0.9563
±0.0010 | prev best: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Improvement within reported uncertainty; not highlighted. |
| 197 | DAGNN | 0.9401
±0.0060 | Improvement within reported uncertainty; not highlighted. |
| 239 | GraphSAGE-mean | 0.9306
±0.0080 | This paper |
| 247 | GraphSAGE-meanpool | 0.9265
±0.0100 | This paper |
| 253 | MoNet | 0.9250
±0.0090 best reported | best at pub: GraphMix: Improved Training of GNNs for Semi-Supervised Learning (2019) best today: Revisiting the Necessity of Graph Learning and Common Graph Benchmarks (2024) Difference within reported uncertainty; not counted as underperformance. |
| 273 | GraphSAGE-maxpool | 0.9026
±0.0120 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DoG | 0.9690
±0.0030 | |
| 2 | GWN-fa | 0.9667
±0.0026 | |
| 3 | GWN-sym | 0.9666
±0.0026 | |
| 6 | GraphSAGE | 0.9593
±0.0025 | |
| 12 | GCN | 0.9514
±0.0025 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 21 | GAT | 0.9437
±0.0028 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 69 | GRACE | 0.9301
±0.0003 best reported | best at pub: MA-GCL: Model Augmentation Tricks for Graph Contrastive Learning (AAAI 2022) best today: A Fused Gromov-Wasserstein Approach to Subgraph Contrastive Learning (TMLR 2025) |
| 88 | MLP | 0.9280
±0.0020 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Revisiting the Necessity of Graph Learning and Common Graph Benchmarks (2024) |
| 91 | DAGNN | 0.9278
±0.0090 | Improvement within reported uncertainty; not highlighted. |
| 104 | GCNII | 0.9241
±0.0050 | |
| 112 | BAGCN-add | 0.9227
±0.0050 | This paper |
| 137 | BAGCN-mul | 0.9148
±0.0090 | This paper |
| 139 | GraphSAGE-mean | 0.9132
±0.0290 | prev best: ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks (ICLR 2022) Improvement within reported uncertainty; not highlighted. |
| 155 | MoNet | 0.9082
±0.0160 | prev best: GraphMix: Improved Training of GNNs for Semi-Supervised Learning (2019) Improvement within reported uncertainty; not highlighted. |
| 166 | GraphSAGE-meanpool | 0.8966
±0.0090 | This paper |
| 185 | GraphSAGE-maxpool | 0.8504
±0.0110 | This paper |
