IJCAI 2023

Hierarchical Transformer for Scalable Graph Learning

Wenhao Zhu, Tianyu Wen, Guojie Song, Xiaojun Ma, Liang Wang

Main figure for 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.

Proposed method: HSGT

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

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
actual #21 vs paper #736 715 places worse
0.9004
best reported
actual #21 vs paper #736 715 places worse
paper 0.7720 ±0.0151
paper 0.7720 ±0.0151 Δ at pub 0.0997 Δ today 0.1284
39
SAGE
0.8911 ±0.0012
44
GAT
actual #44 vs paper #439 395 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #439 395 places worse
paper 0.8280 ±0.0047
paper 0.8280 ±0.0047 Δ at pub 0.0610 Δ today 0.0617
165
GIN
actual #165 vs paper #759 594 places worse
0.8660 ±0.0091
best reported
actual #165 vs paper #759 594 places worse
paper 0.7593 ±0.0099
paper 0.7593 ±0.0099 Δ at pub 0.0587 Δ today 0.1067
360
HSGT
0.8356 ±0.0177
This paper
456
Graphormer
actual #456 vs paper #849 393 places worse
0.8262 ±0.0012
best reported
actual #456 vs paper #849 393 places worse
paper 0.6635 ±0.0244
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
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
35
GAT
actual #35 vs paper #644 609 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #644 609 places worse
paper 0.6920 ±0.0045
paper 0.6920 ±0.0045 Δ at pub 0.1093 Δ today 0.1160
44
GCN
actual #44 vs paper #638 594 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #638 594 places worse
paper 0.6949 ±0.0058
paper 0.6949 ±0.0058 Δ at pub 0.0994 Δ today 0.1084
61
GraphSAGE
0.7923 ±0.0053
101
ANS-GT
actual #101 vs paper #784 683 places worse
0.7760 ±0.0051
best reported
actual #101 vs paper #784 683 places worse
paper 0.6452 ±0.0071
paper 0.6452 ±0.0071 Δ today 0.1308
350
MLP
0.7289 ±0.0010
389
GIN
actual #389 vs paper #796 407 places worse
0.7250 ±0.0080
best reported
actual #389 vs paper #796 407 places worse
paper 0.6383 ±0.0049
paper 0.6383 ±0.0049 Δ at pub 0.0867
548
GAS-GCN
0.7118 ±0.0097
This paper
582
SAN
actual #582 vs paper #882 300 places worse
0.7064 ±0.0097
best reported
actual #582 vs paper #882 300 places worse
paper 0.4435 ±0.0108
paper 0.4435 ±0.0108 Δ at pub 0.2629
704
HSGT
0.6741 ±0.0092
This paper
744
Graphormer
actual #744 vs paper #853 109 places worse
0.6621 ±0.0083
best reported
actual #744 vs paper #853 109 places worse
paper 0.5622 ±0.0327
paper 0.5622 ±0.0327 Δ at pub 0.0999
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
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
18
GCN
actual #18 vs paper #707 689 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #707 689 places worse
paper 0.7760 ±0.0096
20
GAT
actual #20 vs paper #743 723 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #743 723 places worse
paper 0.7690 ±0.0085
100
ANS-GT
actual #100 vs paper #694 594 places worse
0.8914 ±0.0026
best reported
actual #100 vs paper #694 594 places worse
paper 0.7780 ±0.0065
paper 0.7780 ±0.0065 Δ today 0.1134
116
SAGE
0.8881 ±0.0015
157
GIN
actual #157 vs paper #739 582 places worse
0.8810
best reported
actual #157 vs paper #739 582 places worse
paper 0.7703 ±0.0042
paper 0.7703 ±0.0042 Δ at pub 0.0373 Δ today 0.1107
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
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #231 229 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #231 229 places worse
paper 0.9288 ±0.0037
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #289 281 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #289 281 places worse
paper 0.9244 ±0.0022
59
HSGT
0.9501 ±0.0034
This paper
60
ANS-GT
actual #60 vs paper #528 468 places worse
0.9498 ±0.0043
best reported
actual #60 vs paper #528 468 places worse
paper 0.8041 ±0.0078
paper 0.8041 ±0.0078 Δ today 0.1457
250
Graphormer-SAMPLE
0.9276 ±0.0059
This paper
328
GIN
actual #328 vs paper #528 200 places worse
0.9211 ±0.0032
best reported
actual #328 vs paper #528 200 places worse
paper 0.8014 ±0.0146
best today: Union Subgraph Neural Networks (AAAI 2023)
paper 0.8014 ±0.0146 Δ at pub 0.1076 Δ today 0.1197
385
SAT-SAMPLE
0.9135 ±0.0042
This paper
390
MLP
0.9128 ±0.0063
428
GAS-GCN
0.9053 ±0.0140
This paper

Reddit

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is F1. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑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
actual #18 vs paper #114 96 places worse
0.9660 ±0.0010
best reported
actual #18 vs paper #114 96 places worse
paper 0.9092 ±0.0061
paper 0.9092 ±0.0061 Δ at pub 0.0568 Δ today 0.0568
21
GraphSAGE
actual #21 vs paper #21
0.9653 ±0.0011
actual #21 vs paper #21
paper 0.9653 ±0.0011

Improvement within reported uncertainty; not highlighted.

paper 0.9653 ±0.0011 Δ at pub 0.0006
22
GAT
0.9650 ±0.0014
This paper
23
SAGE
0.9650 ±0.0003
26
GCN
actual #26 vs paper #113 87 places worse
0.9648
best reported
actual #26 vs paper #113 87 places worse
paper 0.9101 ±0.0029
paper 0.9101 ±0.0029 Δ at pub 0.0547
38
Cluster-GCN
actual #38 vs paper #66 28 places worse
0.9623
best reported
actual #38 vs paper #66 28 places worse
paper 0.9512 ±0.0008
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

#ModelAccuracy ↑Paper
1
Jacobi
0.8968
2
GPR
0.8953
3
LEMP4HG
0.8939
4
SAGE
0.8933
9
GAT
actual #9 vs paper #164 155 places worse
0.8829
best reported
actual #9 vs paper #164 155 places worse
paper 0.7945 ±0.0059
96
ANS-GT
actual #96 vs paper #133 37 places worse
0.8215 ±0.0030
best reported
actual #96 vs paper #133 37 places worse
paper 0.8064 ±0.0029
paper 0.8064 ±0.0029 Δ at pub 0.0151
121
HSGT
0.8115 ±0.0013
This paper
182
Graphormer-SAMPLE
0.7910 ±0.0012
This paper
185
GIN
actual #185 vs paper #278 93 places worse
0.7907 ±0.0052
best reported
actual #185 vs paper #278 93 places worse
paper 0.7479 ±0.0081
paper 0.7479 ±0.0081 Δ today 0.0428
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
#ModelROC-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
actual #9 vs paper #63 54 places worse
0.8682 ±0.0021
best reported
actual #9 vs paper #63 54 places worse
paper 0.7202 ±0.0044
paper 0.7202 ±0.0044 Δ at pub 0.1480
16
GraphSAGE
0.8430
42
HSGT
0.7813 ±0.0025
This paper
51
GIN
actual #51 vs paper #65 14 places worse
0.7677 ±0.0020
best reported
actual #51 vs paper #65 14 places worse
paper 0.7076 ±0.0008
paper 0.7076 ±0.0008 Δ at pub 0.0601
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
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best today — OK at publication; today's leaderboard best is elsewhere