Beyond Message Passing: Neural Graph Pattern Machine
Abstract
Graph learning tasks often hinge on identifying key substructure patterns -- such as triadic closures in social networks or benzene rings in molecular graphs -- that underpin downstream performance. However, most existing graph neural networks (GNNs) rely on message passing, which aggregates local neighborhood information iteratively and struggles to explicitly capture such fundamental motifs, like triangles, k-cliques, and rings. This limitation hinders both expressiveness and long-range dependency modeling. In this paper, we introduce the Neural Graph Pattern Machine (GPM), a novel framework that bypasses message passing by learning directly from graph substructures. GPM efficiently extracts, encodes, and prioritizes task-relevant graph patterns, offering greater expressivity and improved ability to capture long-range dependencies. Empirical evaluations across four standard tasks -- node classification, link prediction, graph classification, and graph regression -- demonstrate that GPM outperforms state-of-the-art baselines. Further analysis reveals that GPM exhibits strong out-of-distribution generalization, desirable scalability, and enhanced interpretability. Code and datasets are available at: https://github.com/Zehong-Wang/GPM.
Benchmark Results
Tested on 6 datasets 10 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GCN | 0.9302
±0.0011 best reported | best at pub: Augmentation-Free Graph Contrastive Learning with Performance Guarantee (2022) |
| 2 | RSE + RGCN (70b) | 0.8852
±0.0019 | |
| 3 | LEMP+T | 0.8825 | |
| 9 | SAGE | 0.8771 | |
| 12 | APPNP | 0.8754 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 31 | GAT | 0.8533 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 37 | VCR-Graphormer | 0.8432
±0.0001 best reported | best today: Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025) |
| 48 | NAGphormer | 0.8341
±0.0034 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 58 | GPRGNN | 0.8258
±0.0089 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 74 | NodeFormer | 0.8103
±0.0094 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 91 | GPM | 0.8019
±0.0041 | This paper |
| 120 | GraphGPS | 0.7926
±0.0057 best reported | best at pub: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) Difference within reported uncertainty; not counted as underperformance. |
| 134 | OrderedGNN | 0.7901
±0.0068 | This paper |
| 159 | SAN | 0.7846
±0.0099 | This paper |
| 171 | RUM | 0.7820
±0.0029 | This paper |
| 172 | GCFormer | 0.7812
±0.0050 | This paper |
| 175 | RAW-GNN | 0.7801
±0.0058 | This paper |
| 176 | GOAT | 0.7796
±0.0063 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) best today: Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification (2026) Difference within reported uncertainty; not counted as underperformance. |
| 237 | MLP | 0.7469
±0.0085 |
| # | Model | MAE ↓ | Paper |
|---|---|---|---|
| 1 | TIGT | 0.0140
±0.0010 | |
| 2 | FloydNet | 0.0160 | |
| 3 | GSSC | 0.0190
±0.0010 | |
| 22 | Graphormer | 0.0250
±0.0040 | prev best: Enhancing Graph Neural Networks with Quantum Computed Encodings (2023) |
| 41 | GNN-AK+ | 0.0340
±0.0070 | This paper |
| 42 | Graph ViT | 0.0350
±0.0050 | This paper |
| 44 | CRaWl | 0.0360
±0.0050 | This paper |
| 45 | SAT | 0.0360
±0.0020 | This paper |
| 47 | AgentNet | 0.0400
±0.0060 | This paper |
| 59 | AWE | 0.0590
±0.0050 | This paper |
| 62 | GPM | 0.0640
±0.0040 | This paper |
| 63 | PNA | 0.0670
±0.0090 | prev best: Topology-Informed Graph Transformer (2024) |
| 69 | GIN | 0.0880
±0.0020 | This paper |
| 79 | GCN | 0.1130
±0.0020 |
TU Dortmund
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | WL-MLP | 0.9792 | |
| 2 | MSH-GNN | 0.9640
±0.0070 | |
| 3 | CoCN | 0.8722
±0.0013 | |
| 21 | SAN | 0.8273
±0.0192 best reported | best today: Explainable Graph Representation Learning via Graph Pattern Analysis (IJCAI 2025) |
| 23 | GCN | 0.8260
±0.0220 | |
| 30 | GIN | 0.8220
±0.0210 best reported | best at pub: Scalable Expressiveness through Preprocessed Graph Perturbations (2024) Difference within reported uncertainty; not counted as underperformance. |
| 38 | Graphormer | 0.8180
±0.0224 best reported | best at pub: SignGT: Signed Attention-based Graph Transformer for Graph Representation Learning (2023) Difference within reported uncertainty; not counted as underperformance. |
| 93 | GMT | 0.8074
±0.0054 best reported | best at pub: Structural Entropy Guided Graph Hierarchical Pooling (ICML 2022) best today: Cluster-wise Graph Transformer with Dual-granularity Kernelized Attention (NeurIPS 2024) |
| 101 | SAT | 0.8060
±0.0060 best reported | best at pub: Graph Classification via Reference Distribution Learning: Theory and Practice (NeurIPS 2024) |
| 151 | MLP | 0.7920
±0.0240 | |
| 165 | Graph ViT | 0.7879
±0.0074 | This paper |
| 195 | GPS | 0.7741
±0.0056 | This paper |
| 196 | GNN-AK+ | 0.7735
±0.0093 | This paper |
| 199 | AgentNet | 0.7730
±0.0198 | This paper |
| 203 | CRaWl | 0.7717
±0.0078 | This paper |
| 241 | RUM | 0.7550
±0.0058 | This paper |
| 254 | PNA | 0.7473
±0.0109 | prev best: OOD-GNN: Out-of-Distribution Generalized Graph Neural Network (2021) |
| 265 | AWE | 0.7393
±0.0194 | prev best: Wasserstein Embedding for Graph Learning (ICLR 2020) Improvement within reported uncertainty; not highlighted. |
| 274 | DGK | 0.7310
±0.0030 best reported | best at pub: Wasserstein Embedding for Graph Learning (ICLR 2020) best today: InfoGCL: Information-Aware Graph Contrastive Learning (NeurIPS 2021) Difference within reported uncertainty; not counted as underperformance. |
OGB
| # | Model | Hits@50 ↑ | Paper |
|---|---|---|---|
| 1 | PROXI | 0.7650
±0.0027 | |
| 2 | OGB Leader | 0.7129
±0.0018 | |
| 3 | GIDN | 0.7096
±0.0055 | |
| 9 | GCN | 0.6621
±0.0033 best reported | best at pub: On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024) |
| 28 | SAGE | 0.5944
±0.0137 | |
| 66 | GPM | 0.4970
±0.0059 | This paper |
| 73 | LLP | 0.4910
±0.0057 | This paper |
| 81 | RUM | 0.4819
±0.0094 | This paper |
| 84 | NAGphormer | 0.4756
±0.0052 | This paper |
| 87 | NodeFormer | 0.4656
±0.0062 | This paper |
| 94 | MLP | 0.4438
±0.0347 |
GNNBenchmark
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 32 | GPM | 1.0000 | This paper |
| 8 | GCN | 1.0000 best reported | best at pub: GNNBenchmark (JMLR 2023) |
| 31 | Graph ViT | 1.0000 | This paper |
| 19 | ESC-GNN | 1.0000 | This paper |
| 1 | PPGN | 1.0000 | |
| 2 | RW-AgentNet | 1.0000 | |
| 3 | AgentNet | 1.0000 | |
| 35 | GraphSAGE | 0.9993
±0.0047 | |
| 36 | GatedGCN | 0.9960
±0.0108 best reported | best at pub: GNNBenchmark (JMLR 2023) |
| 49 | 3-GNN | 0.9570 | This paper |
| 87 | GraphTrans | 0.1000 | This paper |
LINKX Benchmarks
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | GPM | 0.6726
±0.0022 | This paper |
| 2 | NodeFormer | 0.6640
±0.0070 | This paper |
| 3 | OrderedGNN | 0.6612
±0.0075 | This paper |
| 4 | APPNP | 0.6610
±0.0060 | This paper |
| 5 | NAGphormer | 0.6554
±0.0057 | This paper |
| 6 | GOAT | 0.6531
±0.0024 | This paper |
| 7 | VCR-Graphormer | 0.6528
±0.0051 | This paper |
| 8 | GCFormer | 0.6516
±0.0033 | This paper |
| 9 | RAW-GNN | 0.6511
±0.0064 | This paper |
| 10 | SAN | 0.6429
±0.0035 | This paper |
| 11 | RUM | 0.6425
±0.0062 | This paper |
| 12 | GPRGNN | 0.6320
±0.0084 | This paper |
| 13 | GCN | 0.6270
±0.0070 | This paper |
| 14 | GAT | 0.6170
±0.0080 | This paper |
| 15 | GraphGPS | 0.6056
±0.0062 | This paper |
