Hierarchical Transformer for Scalable Graph Learning
Abstract
Graph Transformer is gaining increasing attention in the field of machine learning and has demonstrated state-of-the-art performance on benchmarks for graph representation learning. However, as current implementations of Graph Transformer primarily focus on learning representations of small-scale graphs, the quadratic complexity of the global self-attention mechanism presents a challenge for full-batch training when applied to larger graphs. Additionally, conventional sampling-based methods fail to capture necessary high-level contextual information, resulting in a significant loss of performance. In this paper, we introduce the Hierarchical Scalable Graph Transformer (HSGT) as a solution to these challenges. HSGT successfully scales the Transformer architecture to node representation learning tasks on large-scale graphs, while maintaining high performance. By utilizing graph hierarchies constructed through coarsening techniques, HSGT efficiently updates and stores multi-scale information in node embeddings at different levels. Together with sampling-based training methods, HSGT effectively captures and aggregates multi-level information on the hierarchical graph using only Transformer blocks. Empirical evaluations demonstrate that HSGT achieves state-of-the-art performance on large-scale benchmarks with graphs containing millions of nodes with high efficiency.
Benchmark Results
Tested on 7 datasets 18 baseline values reported too low Non-standard metric on 1 dataset
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) |
| 165 | GIN | 0.8660
±0.0091 best reported | best at pub: Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings (TMLR 2022) best today: Large Language Model Meets Graph Neural Network in Knowledge Distillation (AAAI 2024) |
| 360 | HSGT | 0.8356
±0.0177 | This paper |
| 456 | Graphormer | 0.8262
±0.0012 best reported | best today: Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction (NeurIPS 2025) |
| 500 | GAS-GCN | 0.8229
±0.0076 | This paper |
| 684 | ANS-GT | 0.7935
±0.0090 | This paper |
| 724 | MLP | 0.7768 | |
| 774 | Graphormer-SAMPLE | 0.7514
±0.0131 | This paper |
| 779 | SAT-SAMPLE | 0.7455
±0.0124 | This paper |
| 800 | SAT | 0.7240
±0.0031 | This paper |
| 910 | SAN | 0.3661
±0.0349 | This paper |
| # | 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: Gophormer: Ego-Graph Transformer for Node Classification (2021) best today: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 best reported | best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) |
| 61 | GraphSAGE | 0.7923
±0.0053 | |
| 101 | ANS-GT | 0.7760
±0.0051 best reported | |
| 350 | MLP | 0.7289
±0.0010 | |
| 389 | GIN | 0.7250
±0.0080 best reported | best at pub: Towards Self-Explainable Graph Neural Network (2021) |
| 548 | GAS-GCN | 0.7118
±0.0097 | This paper |
| 582 | SAN | 0.7064
±0.0097 best reported | best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) |
| 704 | HSGT | 0.6741
±0.0092 | This paper |
| 744 | Graphormer | 0.6621
±0.0083 best reported | best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) |
| 819 | SAT-SAMPLE | 0.6158
±0.0087 | This paper |
| 821 | Graphormer-SAMPLE | 0.6146
±0.0190 | This paper |
| 824 | SAT | 0.6093
±0.0125 | 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 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) |
| 100 | ANS-GT | 0.8914
±0.0026 best reported | |
| 116 | SAGE | 0.8881
±0.0015 | |
| 157 | GIN | 0.8810 best reported | best at pub: Learning Conjoint Attentions for Graph Neural Nets (NeurIPS 2021) best today: UGSL: A Unified Framework for Benchmarking Graph Structure Learning (2023) |
| 210 | MLP | 0.8690
±0.0074 | |
| 485 | HSGT | 0.7965
±0.0052 | This paper |
| 555 | GAS-GCN | 0.7923
±0.0062 | This paper |
| 753 | SAT-SAMPLE | 0.7670
±0.0074 | This paper |
| 789 | Graphormer-SAMPLE | 0.7545
±0.0098 | 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) |
| 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) |
| 59 | HSGT | 0.9501
±0.0034 | This paper |
| 60 | ANS-GT | 0.9498
±0.0043 best reported | |
| 250 | Graphormer-SAMPLE | 0.9276
±0.0059 | This paper |
| 328 | GIN | 0.9211
±0.0032 best reported | best at pub: Learning Graph Augmentations to Learn Graph Representations (2022) best today: Union Subgraph Neural Networks (AAAI 2023) |
| 385 | SAT-SAMPLE | 0.9135
±0.0042 | This paper |
| 390 | MLP | 0.9128
±0.0063 | |
| 428 | GAS-GCN | 0.9053
±0.0140 | This paper |
Sorted by Accuracy. Highlighted rows are from other papers.
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GAP-EDP | 0.9870
±0.0003 | |
| 2 | NE-ASGCN | 0.9758
±0.0027 | |
| 3 | HSGT | 0.9730
±0.0024 | This paper |
| 11 | SIGN | 0.9680 | This paper |
| 18 | GraphSAINT | 0.9660
±0.0010 best reported | best at pub: ROD: Reception-aware Online Distillation for Sparse Graphs (KDD 2021) best today: PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm (WWW 2022) |
| 21 | GraphSAGE | 0.9653
±0.0011 | prev best: DropEdge: Towards Deep Graph Convolutional Networks on Node Classification (ICLR 2019) Improvement within reported uncertainty; not highlighted. |
| 22 | GAT | 0.9650
±0.0014 | This paper |
| 23 | SAGE | 0.9650
±0.0003 | |
| 26 | GCN | 0.9648 best reported | best at pub: DropEdge: Towards Deep Graph Convolutional Networks on Node Classification (ICLR 2019) |
| 38 | Cluster-GCN | 0.9623 best reported | |
| 51 | GAS-GCN | 0.9545 | This paper |
| 56 | ANS-GT | 0.9530
±0.0081 | This paper |
| 90 | SAT-SAMPLE | 0.9337
±0.0032 | This paper |
| 94 | Graphormer-SAMPLE | 0.9305
±0.0022 | This paper |
| 99 | GraphZoom | 0.9250 | This paper |
| 141 | GIN | 0.8637
±0.0062 | This paper |
| 147 | MLP | 0.8240
±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) |
| 96 | ANS-GT | 0.8215
±0.0030 best reported | best at pub: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) |
| 121 | HSGT | 0.8115
±0.0013 | This paper |
| 182 | Graphormer-SAMPLE | 0.7910
±0.0012 | This paper |
| 185 | GIN | 0.7907
±0.0052 best reported | best today: Automatic Graph Topology-Aware Transformer (2024) |
| 224 | SAT-SAMPLE | 0.7764
±0.0020 | This paper |
| 234 | GAS-GCN | 0.7666 | This paper |
| 295 | GraphZoom | 0.7406
±0.0026 | This paper |
| 351 | MLP | 0.6605
±0.0020 |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | LD | 0.8942
±0.0007 | |
| 2 | X_WO/LD | 0.8915
±0.0012 | |
| 3 | X_PNE | 0.8894
±0.0014 | |
| 9 | GAT | 0.8682
±0.0021 best reported | best at pub: Training Graph Neural Networks with 1000 Layers (ICML 2021) |
| 16 | GraphSAGE | 0.8430 | |
| 42 | HSGT | 0.7813
±0.0025 | This paper |
| 51 | GIN | 0.7677
±0.0020 best reported | best at pub: SoGCN: Second-Order Graph Convolutional Networks (2021) |
| 56 | Cluster-GCN | 0.7489
±0.0012 | This paper |
| 57 | ANS-GT | 0.7467
±0.0065 | This paper |
| 62 | Graphormer-SAMPLE | 0.7234
±0.0051 | This paper |
| 66 | SAT-SAMPLE | 0.7062
±0.0085 | This paper |
| 67 | GraphSAINT | 0.7022
±0.0084 | This paper |
