Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attention
Abstract
Recent years have witnessed the great potential of attention mechanism in graph representation learning. However, while variants of attention-based GNNs are setting new benchmarks for numerous real-world datasets, recent works have pointed out that their induced attentions are less robust and generalizable against noisy graphs due to lack of direct supervision. In this paper, we present a new framework which utilizes the tool of causality to provide a powerful supervision signal for the learning process of attention functions. Specifically, we estimate the direct causal effect of attention to the final prediction, and then maximize such effect to guide attention attending to more meaningful neighbors. Our method can serve as a plug-and-play module for any canonical attention-based GNNs in an end-to-end fashion. Extensive experiments on a wide range of benchmark datasets illustrated that, by directly supervising attention functions, the model is able to converge faster with a clearer decision boundary, and thus yields better performances.
Benchmark Results
Tested on 8 datasets 21 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 | |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 123 | UniMP+CSA-I | 0.8747
±0.0087 | This paper |
| 151 | UniMP | 0.8689
±0.0090 | This paper |
| 182 | GAT+CSA-I | 0.8616
±0.0095 | This paper |
| 724 | MLP | 0.7768 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 35 | GAT | 0.8080
±0.0026 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 | |
| 95 | GAT+CSA-I | 0.7772
±0.0125 | This paper |
| 98 | UniMP+CSA-I | 0.7761
±0.0082 | This paper |
| 174 | UniMP | 0.7514
±0.0068 | This paper |
| 350 | MLP | 0.7289
±0.0010 |
OGB
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Jacobi | 0.8968 | |
| 2 | GPR | 0.8953 | |
| 3 | LEMP4HG | 0.8939 | |
| 4 | SAGE | 0.8933 | |
| 9 | GAT | 0.8829 best reported | best at pub: PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm (WWW 2022) |
| 85 | UniMP | 0.8256
±0.0031 best reported | best at pub: Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification (IJCAI 2020) best today: Graph Attention MLP with Reliable Label Utilization (2021) |
| 92 | UniMP+CSA-I | 0.8224
±0.0063 | This paper |
| 214 | GAT+CSA-I | 0.7836
±0.0072 | This paper |
| 351 | MLP | 0.6605
±0.0020 |
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 | |
| 30 | GPR-GNN | 0.9291
±0.0132 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) |
| 34 | MLP | 0.9230
±0.0070 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 40 | H2GCN | 0.9189
±0.0393 best reported | best at pub: Graph-Coupled Oscillator Networks (ICML 2022) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) Difference within reported uncertainty; not counted as underperformance. |
| 46 | APPNP | 0.9131
±0.0197 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) best today: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 61 | FAGCN | 0.8961
±0.0152 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) Difference within reported uncertainty; not counted as underperformance. |
| 104 | WRGAT | 0.8698 best reported | best at pub: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) best today: Global-Local Graph Neural Networks for Node-Classification (2024) Difference within reported uncertainty; not counted as underperformance. |
| 148 | WRGAT+CSA-I | 0.8488
±0.0523 | This paper |
| 154 | FAGCN+CSA-I | 0.8472
±0.0671 | This paper |
| 211 | GAT | 0.8162
±0.0645 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) 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: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Graph Wave Networks (WWW 2025) |
| 469 | SGCN | 0.6243
±0.0443 best reported | best at pub: A Piece-wise Polynomial Filtering Approach for Graph Neural Networks (2021) Difference within reported uncertainty; not counted as underperformance. |
| 535 | CSA | 0.5821
±0.0479 | This paper |
| 541 | GAT+CSA-I | 0.5804
±0.0527 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9541
±0.0272 | |
| 2 | ACM-GCN | 0.9480
±0.0380 | |
| 3 | RF-GCN | 0.9429 | |
| 11 | GPR-GNN | 0.9279
±0.0312 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 21 | APPNP | 0.9181
±0.0196 best reported | best at pub: LON-GNN: Spectral GNNs with Learnable Orthonormal Basis (2023) |
| 24 | MLP | 0.9136
±0.0070 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) Difference within reported uncertainty; not counted as underperformance. |
| 38 | FAGCN | 0.8852
±0.0133 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) Difference within reported uncertainty; not counted as underperformance. |
| 68 | H2GCN | 0.8623
±0.0471 best reported | best at pub: Graph-Coupled Oscillator Networks (ICML 2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 138 | SAGE | 0.8269 | |
| 145 | WRGAT+CSA-I | 0.8243
±0.0400 | This paper |
| 158 | GAT | 0.8190
±0.0540 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 160 | WRGAT | 0.8162
±0.0390 | This paper |
| 169 | FAGCN+CSA-I | 0.8094
±0.0977 | This paper |
| 170 | GCN | 0.8082
±0.0360 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Bayesian Neighborhood Adaptation for Graph Neural Networks (TMLR 2025) |
| 341 | CSA | 0.6426
±0.0521 | This paper |
| 348 | GAT+CSA-I | 0.6358
±0.0603 | This paper |
| 356 | SGCN | 0.6252
±0.0510 | prev best: A Piece-wise Polynomial Filtering Approach for Graph Neural Networks (2021) Improvement within reported uncertainty; not highlighted. |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DiGGR | 0.4535
±0.0353 | |
| 2 | TRIGON | 0.4402
±0.0028 | |
| 3 | DoG | 0.4320
±0.0120 | |
| 41 | APPNP | 0.4046
±0.0064 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) best today: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) |
| 42 | MLP | 0.4026
±0.0108 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 53 | GPR-GNN | 0.3992
±0.0067 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) best today: Piecewise Constant Spectral Graph Neural Network (TMLR 2025) |
| 56 | FAGCN | 0.3970 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 68 | GraphSAGE | 0.3899
±0.0085 | |
| 71 | H2GCN | 0.3885
±0.0117 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 75 | WRGAT | 0.3860
±0.0110 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) |
| 135 | GCN | 0.3690 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 137 | WRGAT+CSA-I | 0.3689
±0.0072 | This paper |
| 228 | FAGCN+CSA-I | 0.3512
±0.0098 | This paper |
| 337 | SGCN | 0.3050
±0.0094 | This paper |
| 359 | GAT+CSA-I | 0.2972
±0.0086 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Hetero-S (GAT 8-layer) | 0.8693 | |
| 2 | Dir-GNN+CNA | 0.8586
±0.0180 | |
| 3 | GAT | 0.8560 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs (KDD 2024) |
| 24 | GPR-GNN | 0.7830
±0.0060 best reported | best at pub: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) best today: Efficient Learning on Large Graphs using a Densifying Regularity Lemma (2025) |
| 52 | GCN | 0.7033 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 79 | APPNP | 0.6670
±0.0270 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 86 | WRGAT+CSA-I | 0.6536
±0.0105 | This paper |
| 91 | WRGAT | 0.6524
±0.0087 | This paper |
| 107 | FAGCN | 0.6344
±0.0205 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. |
| 108 | SAGE | 0.6340
±0.0300 | |
| 117 | FAGCN+CSA-I | 0.6186
±0.0298 | This paper |
| 126 | SGCN | 0.6089
±0.0221 | This paper |
| 127 | GAT+CSA-I | 0.6073
±0.0135 | This paper |
| 133 | H2GCN | 0.6030
±0.0231 best reported | best at pub: Optimization-Induced Graph Implicit Nonlinear Diffusion (ICML 2022) Difference within reported uncertainty; not counted as underperformance. |
| 169 | MLP | 0.5429 best reported | best at pub: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | IBG-NN | 0.7763
±0.0179 | |
| 2 | Dir-GNN+CNA | 0.7747
±0.0128 | |
| 3 | DHGNN | 0.7684
±0.0161 | |
| 10 | GPR-GNN | 0.7480
±0.0050 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) best today: Efficient Learning on Large Graphs using a Densifying Regularity Lemma (2025) |
| 39 | H2GCN | 0.6190
±0.0140 best reported | best at pub: Optimization-Induced Graph Implicit Nonlinear Diffusion (ICML 2022) best today: Efficient Learning on Large Graphs using a Densifying Regularity Lemma (2025) |
| 46 | GCN | 0.6067 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 67 | GAT | 0.5630
±0.0220 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 68 | APPNP | 0.5590
±0.0290 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 79 | SGCN | 0.5274
±0.0158 | This paper |
| 94 | WRGAT+CSA-I | 0.4946
±0.0074 | This paper |
| 96 | WRGAT | 0.4885
±0.0078 | This paper |
| 120 | SAGE | 0.4460
±0.0130 | |
| 139 | FAGCN | 0.4259
±0.0069 best reported | best at pub: Gradient Gating for Deep Multi-Rate Learning on Graphs (ICLR 2022) best today: Graph Neural Reaction Diffusion Models Submitted to the editors June 2023. Accepted in March 2024. (2024) Difference within reported uncertainty; not counted as underperformance. |
| 140 | FAGCN+CSA-I | 0.4255
±0.0074 | This paper |
| 159 | GAT+CSA-I | 0.4051
±0.0098 | This paper |
| 172 | MLP | 0.3930
±0.0079 best reported | best at pub: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) |
