Heterophily-informed Message Passing
Abstract
Graph neural networks (GNNs) are known to be vulnerable to oversmoothing due to their implicit homophily assumption. We mitigate this problem with a novel scheme that regulates the aggregation of messages, modulating the type and extent of message passing locally thereby preserving both the low and high-frequency components of information. Our approach relies solely on learnt embeddings, obviating the need for auxiliary labels, thus extending the benefits of heterophily-aware embeddings to broader applications,, generative modelling. Our experiments, conducted across various data sets and GNN architectures, demonstrate performance enhancements and reveal heterophily patterns across standard classification benchmarks. Furthermore, application to molecular generation showcases notable performance improvements on chemoinformatics benchmarks.
Benchmark Results
Tested on 11 datasets 34 baseline values reported too low Non-standard metric on 2 datasets
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | 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 best reported | best at pub: Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning (ICLR 2024) |
| 20 | GAT | 0.9233
±0.0018 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 95 | GraphSAGE+mix. | 0.8930
±0.0040 | This paper |
| 114 | GraphSAGE+hom. | 0.8890
±0.0040 | This paper |
| 116 | SAGE | 0.8881
±0.0015 | |
| 122 | GCN+hom. | 0.8870
±0.0050 | This paper |
| 125 | GraphSAGE | 0.8864
±0.0030 best reported | best at pub: Non-backtracking Graph Neural Networks (TMLR 2023) |
| 127 | GCN+mix. | 0.8860
±0.0050 | This paper |
| 155 | GAT+hom. | 0.8820
±0.0050 | This paper |
| 157 | GIN | 0.8810 best reported | best at pub: UGSL: A Unified Framework for Benchmarking Graph Structure Learning (2023) |
| 167 | GAT+mix. | 0.8780
±0.0070 | This paper |
| 190 | GIN+hom. | 0.8740
±0.0080 | This paper |
| 210 | MLP | 0.8690
±0.0074 | |
| 222 | GIN+mix. | 0.8660
±0.0090 | This paper |
| 282 | GCN+het. | 0.8390
±0.0050 | This paper |
| 368 | GIN+het. | 0.8110
±0.1490 | This paper |
| 496 | GAT+het. | 0.7960
±0.0090 | This paper |
Amazon-Photo
Global leaderboard →Sorted by ROC-AUC. Highlighted rows are from other papers.
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE | 0.9550
±0.0040 | This paper |
| 2 | GraphSAGE+hom. | 0.9550
±0.0040 | This paper |
| 3 | GraphSAGE+mix. | 0.9520
±0.0050 | This paper |
| 4 | GraphSAGE+het. | 0.9500
±0.0060 | This paper |
| 5 | GCN+mix. | 0.9460
±0.0060 | This paper |
| 6 | GCN | 0.9440
±0.0050 | This paper |
| 7 | GCN+hom. | 0.9440
±0.0040 | This paper |
| 8 | GAT | 0.9410
±0.0050 | This paper |
| 9 | GAT+mix. | 0.9410
±0.0030 | This paper |
| 10 | GAT+hom. | 0.9360
±0.0060 | This paper |
| 11 | GAT+het. | 0.8730
±0.0130 | This paper |
| 12 | GCN+het. | 0.8540
±0.0160 | This paper |
| 13 | GIN+mix. | 0.7820
±0.1360 | This paper |
| 14 | GIN+het. | 0.3840
±0.1570 | This paper |
| 15 | GIN+hom. | 0.3770
±0.0800 | This paper |
| 16 | GIN | 0.3530
±0.0710 | This paper |
Amazon-Computers
Global leaderboard →Sorted by ROC-AUC. Highlighted rows are from other papers.
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | GCN | 0.9160
±0.0050 | This paper |
| 2 | GCN+hom. | 0.9150
±0.0050 | This paper |
| 3 | GCN+mix. | 0.9120
±0.0060 | This paper |
| 4 | GAT | 0.9120
±0.0030 | This paper |
| 5 | GAT+mix. | 0.9110
±0.0030 | This paper |
| 6 | GAT+hom. | 0.9090
±0.0030 | This paper |
| 7 | GraphSAGE | 0.9090
±0.0030 | This paper |
| 8 | GraphSAGE+hom. | 0.9060
±0.0040 | This paper |
| 9 | GraphSAGE+mix. | 0.9030
±0.0050 | This paper |
| 10 | GraphSAGE+het. | 0.8940
±0.0060 | This paper |
| 11 | GAT+het. | 0.8400
±0.0200 | This paper |
| 12 | GCN+het. | 0.7830
±0.0140 | This paper |
| 13 | GIN+mix. | 0.5730
±0.1470 | This paper |
| 14 | GIN+het. | 0.4310
±0.0930 | This paper |
| 15 | GIN+hom. | 0.4280
±0.0380 | This paper |
| 16 | GIN | 0.4120
±0.0310 | This paper |
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 best reported | best at pub: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) best today: Graph Neural Networks Need Cluster-Normalize-Activate Modules (NeurIPS 2024) |
| 189 | SAGE | 0.8269 | |
| 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) |
| 249 | GraphSAGE+mix. | 0.7970
±0.0590 | This paper |
| 257 | GCN | 0.7933
±0.0447 best reported | best at pub: Graph Wave Networks (WWW 2025) |
| 303 | GraphSAGE+het. | 0.7590
±0.0680 | This paper |
| 326 | GIN | 0.7460
±0.0080 best reported | |
| 384 | GraphSAGE+hom. | 0.7050
±0.0550 | This paper |
| 501 | GCN+het. | 0.6000
±0.0770 | This paper |
| 509 | GAT+het. | 0.5970
±0.0550 | This paper |
| 511 | GAT+hom. | 0.5950
±0.0490 | This paper |
| 512 | GIN+het. | 0.5950
±0.0800 | This paper |
| 525 | GAT+mix. | 0.5920
±0.0470 | This paper |
| 531 | GCN+hom. | 0.5860
±0.0510 | This paper |
| 533 | GIN+mix. | 0.5840
±0.0680 | This paper |
| 538 | GIN+hom. | 0.5810
±0.0680 | This paper |
| 554 | GCN+mix. | 0.5680
±0.0530 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9541
±0.0272 | |
| 2 | ACM-GCN | 0.9480
±0.0380 | prev best: Simplifying Graph Convolutional Networks with Redundancy-Free Neighbors (2025) |
| 3 | RF-GCN | 0.9429 | |
| 22 | GPRGNN | 0.9157
±0.0196 best reported | best at pub: Simplified PCNet with Robustness (2024) Difference within reported uncertainty; not counted as underperformance. |
| 24 | MLP | 0.9136
±0.0070 | |
| 68 | H2GCN | 0.8620
±0.0470 | prev best: Design your own universe: a physics-informed agnostic method for enhancing graph neural networks (2024) Improvement within reported uncertainty; not highlighted. |
| 84 | ACMP | 0.8540
±0.0700 | This paper |
| 138 | SAGE | 0.8269 | |
| 157 | GraphSAGE | 0.8196
±0.0739 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 158 | GAT | 0.8190
±0.0540 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 170 | GCN | 0.8082
±0.0360 best reported | best at pub: Differentiable Cluster Graph Neural Network (2024) best today: Bayesian Neighborhood Adaptation for Graph Neural Networks (TMLR 2025) |
| 201 | GIN | 0.7800
±0.0190 best reported | |
| 266 | GraphSAGE+het. | 0.7220
±0.0760 | This paper |
| 300 | GraphSAGE+mix. | 0.6810
±0.0650 | This paper |
| 307 | GraphSAGE+hom. | 0.6730
±0.0410 | This paper |
| 342 | Geom-GCN | 0.6412 best reported | best at pub: Steering Graph Neural Networks with Pinning Control (2023) |
| 390 | GAT+het. | 0.5890
±0.0940 | This paper |
| 484 | GAT+mix. | 0.5050
±0.0750 | This paper |
| 486 | GIN+het. | 0.5030
±0.1070 | This paper |
| 491 | GCN+het. | 0.5000
±0.0820 | This paper |
| 494 | GIN+mix. | 0.4950
±0.0670 | This paper |
| 499 | GCN+mix. | 0.4890
±0.0620 | This paper |
| 515 | GAT+hom. | 0.4700
±0.0750 | This paper |
| 518 | GIN+hom. | 0.4680
±0.0660 | This paper |
| 549 | GCN+hom. | 0.4140
±0.0540 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DMD++ | 0.9190
±0.0260 | |
| 2 | F-GREAD-BS | 0.9059
±0.0380 | |
| 3 | APPNP | 0.9010
±0.0350 | |
| 37 | MLP | 0.8629
±0.0450 | |
| 49 | GraphSAGE+mix. | 0.8450
±0.0110 | This paper |
| 53 | GAT | 0.8430
±0.0370 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 63 | GCN | 0.8310
±0.0320 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 69 | GraphSAGE | 0.8118
±0.0556 best reported | best at pub: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) best today: Graph Navier–Stokes Networks (2026) Difference within reported uncertainty; not counted as underperformance. |
| 77 | GraphSAGE+hom. | 0.8020
±0.0520 | This paper |
| 78 | GraphSAGE+het. | 0.8000
±0.0430 | This paper |
| 86 | GIN | 0.7900
±0.0060 best reported | best at pub: Unleashing the Potential of Text-attributed Graphs: Automatic Relation Decomposition via Large Language Models (2024) best today: What Can We Learn From MIMO Graph Convolutions? (IJCAI 2025) |
| 149 | SAGE | 0.6480
±0.0520 | |
| 187 | GAT+mix. | 0.5530
±0.0630 | This paper |
| 188 | GAT+hom. | 0.5490
±0.0580 | This paper |
| 190 | GCN+hom. | 0.5450
±0.0330 | This paper |
| 192 | GCN+het. | 0.5390
±0.0380 | This paper |
| 195 | GAT+het. | 0.5330
±0.0680 | This paper |
| 203 | GCN+mix. | 0.5200
±0.0610 | This paper |
| 204 | GIN+het. | 0.5200
±0.0380 | This paper |
| 209 | GIN+mix. | 0.5060
±0.0780 | This paper |
| 214 | GIN+hom. | 0.4900
±0.0630 | This paper |
Heterophily Benchmark
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Dir-Poly | 0.9451
±0.0022 | |
| 2 | D-CDE | 0.9387
±0.0041 | |
| 3 | LargeScaleNet | 0.9358
±0.0024 | |
| 26 | GraphSAGE | 0.9106
±0.0027 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 64 | SAGE | 0.8574
±0.0067 | |
| 77 | GCN | 0.8272
±0.0082 best reported | best at pub: HyperAggregation: Aggregating over Graph Edges with Hypernetworks (2024) |
| 83 | GAT | 0.8145
±0.0009 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) best today: Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax (2025) |
| 98 | GraphSAGE+mix. | 0.7870
±0.0070 | This paper |
| 99 | GraphSAGE+hom. | 0.7860
±0.0060 | This paper |
| 103 | GraphSAGE+het. | 0.7810
±0.0070 | This paper |
| 118 | GCN+mix. | 0.7150
±0.0050 | This paper |
| 128 | GAT+mix. | 0.6890
±0.0090 | This paper |
| 135 | MLP | 0.6665
±0.0047 | |
| 140 | GIN+hom. | 0.6590
±0.0080 | This paper |
| 151 | GIN+mix. | 0.6400
±0.0100 | This paper |
| 164 | GCN+het. | 0.6020
±0.0050 | This paper |
| 170 | GIN+het. | 0.5860
±0.0110 | This paper |
| 174 | GAT+hom. | 0.5760
±0.0100 | This paper |
| 177 | GIN | 0.5680
±0.0100 best reported | best at pub: Diss-l-ECT: Dissecting Graph Data with local Euler Characteristic Transforms (ICML 2024) |
| 178 | GCN+hom. | 0.5660
±0.0060 | This paper |
| 193 | GAT+het. | 0.4800
±0.0130 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | UniGAP | 0.6375
±0.0110 | |
| 2 | H2GCN + HalfHop | 0.5961
±0.0100 | |
| 3 | GraphSAGE + HalfHop | 0.5897
±0.0150 | |
| 12 | SAGE | 0.5569
±0.0023 | |
| 14 | GAT | 0.5559
±0.0027 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) |
| 15 | GraphSAGE | 0.5540
±0.0020 best reported | |
| 24 | GCN | 0.5411
±0.0034 best reported | |
| 34 | GraphSAGE+mix. | 0.5350
±0.0070 | This paper |
| 61 | GraphSAGE+het. | 0.5220
±0.0060 | This paper |
| 67 | GraphSAGE+hom. | 0.5160
±0.0050 | This paper |
| 84 | MLP | 0.5058 | |
| 89 | GAT+mix. | 0.5020
±0.0050 | This paper |
| 88 | GIN | 0.5020
±0.0070 | prev best: Diss-l-ECT: Dissecting Graph Data with local Euler Characteristic Transforms (ICML 2024) |
| 98 | GCN+mix. | 0.4970
±0.0080 | This paper |
| 104 | GIN+hom. | 0.4920
±0.0070 | This paper |
| 119 | GIN+het. | 0.4820
±0.0120 | This paper |
| 120 | GIN+mix. | 0.4820
±0.0150 | This paper |
| 130 | GAT+hom. | 0.4720
±0.0070 | This paper |
| 131 | GCN+hom. | 0.4710
±0.0050 | This paper |
| 136 | GCN+het. | 0.4640
±0.0060 | This paper |
| 157 | GAT+het. | 0.4410
±0.0060 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | BuNN | 0.9899
±0.0016 | |
| 2 | DC-GNN | 0.9850
±0.0021 | |
| 3 | Tango -GPS | 0.9839
±0.0054 | |
| 36 | GAT | 0.9391
±0.0035 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) best today: Relieving the Over-Aggregating Effect in Graph Transformers (NeurIPS 2025) |
| 42 | GraphSAGE | 0.9358
±0.0005 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) best today: Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax (2025) |
| 46 | SAGE | 0.9351
±0.0057 | |
| 68 | GCN | 0.9150
±0.0006 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) best today: Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax (2025) |
| 104 | GIN | 0.8782
±0.0034 best reported | best at pub: TopoBench: A Framework for Benchmarking Topological Deep Learning (2024) |
| 127 | GAT+mix. | 0.7510
±0.0240 | This paper |
| 128 | GCN+mix. | 0.7450
±0.0230 | This paper |
| 131 | GraphSAGE+mix. | 0.7310
±0.0190 | This paper |
| 136 | GCN+het. | 0.7150
±0.0180 | This paper |
| 138 | GraphSAGE+het. | 0.7100
±0.0190 | This paper |
| 142 | GraphSAGE+hom. | 0.6840
±0.0140 | This paper |
| 146 | GIN+het. | 0.6570
±0.0980 | This paper |
| 151 | GIN+mix. | 0.6050
±0.0700 | This paper |
| 152 | GIN+hom. | 0.5820
±0.0460 | This paper |
| 153 | GCN+hom. | 0.5730
±0.0100 | This paper |
| 154 | GAT+hom. | 0.5550
±0.0320 | This paper |
| 155 | GAT+het. | 0.5270
±0.0380 | This paper |
| 156 | MLP | 0.5099
±0.0147 |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | Polynormer-r | 0.8591
±0.0074 | |
| 2 | DC-GNN | 0.8588
±0.0081 | |
| 3 | TANGO-GPS | 0.8566
±0.0101 | |
| 28 | GAT | 0.8443
±0.0100 best reported | best at pub: TopoBench: A Framework for Benchmarking Topological Deep Learning (2024) |
| 50 | GCN | 0.8364
±0.0067 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) |
| 77 | GraphSAGE | 0.8243
±0.0044 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) best today: Relieving the Over-Aggregating Effect in Graph Transformers (NeurIPS 2025) |
| 76 | SAGE | 0.8243
±0.0044 | |
| 89 | GIN | 0.8072
±0.0119 best reported | best at pub: TopoBench: A Framework for Benchmarking Topological Deep Learning (2024) |
| 139 | MLP | 0.7362
±0.0020 | |
| 156 | GAT+mix. | 0.6240
±0.0270 | This paper |
| 157 | GraphSAGE+hom. | 0.5970
±0.0150 | This paper |
| 158 | GraphSAGE+mix. | 0.5920
±0.0200 | This paper |
| 159 | GCN+mix. | 0.5870
±0.0160 | This paper |
| 160 | GCN+hom. | 0.5770
±0.0320 | This paper |
| 161 | GraphSAGE+het. | 0.5770
±0.0140 | This paper |
| 162 | GIN+mix. | 0.5630
±0.0700 | This paper |
| 163 | GAT+hom. | 0.5570
±0.0320 | This paper |
| 164 | GCN+het. | 0.5510
±0.0110 | This paper |
| 165 | GIN+het. | 0.5370
±0.0580 | This paper |
| 167 | GIN+hom. | 0.5300
±0.0640 | This paper |
| 168 | GAT+het. | 0.5050
±0.0050 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | NID_GAT | 0.9703
±0.0002 | |
| 2 | NID_GCN | 0.9685
±0.0010 | |
| 3 | UniGAP | 0.8421
±0.0080 | |
| 16 | GCN | 0.7902
±0.0060 best reported | |
| 26 | GAT | 0.7835
±0.0116 best reported | best at pub: Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning (ICLR 2024) |
| 46 | GraphSAGE | 0.7721
±0.0130 best reported | |
| 58 | SAGE | 0.7644
±0.0062 | |
| 96 | MLP | 0.7082
±0.0010 | |
| 118 | GIN | 0.6776 best reported | best at pub: Data Augmentation for Supervised Graph Outlier Detection via Latent Diffusion Models (LoG 2023) |
| 138 | GIN+mix. | 0.5930
±0.0390 | This paper |
| 142 | GraphSAGE+mix. | 0.5720
±0.0120 | This paper |
| 145 | GraphSAGE+het. | 0.5610
±0.0070 | This paper |
| 148 | GraphSAGE+hom. | 0.5570
±0.0070 | This paper |
| 149 | GIN+hom. | 0.5570
±0.0460 | This paper |
| 151 | GAT+mix. | 0.5480
±0.0090 | This paper |
| 155 | GCN+mix. | 0.5310
±0.0060 | This paper |
| 156 | GAT+hom. | 0.5300
±0.0070 | This paper |
| 157 | GCN+hom. | 0.5280
±0.0020 | This paper |
| 159 | GCN+het. | 0.5210
±0.0090 | This paper |
| 160 | GAT+het. | 0.5130
±0.0080 | This paper |
| 162 | GIN+het. | 0.5080
±0.0260 | This paper |
