WWW 2026

VecFormer: Towards Efficient and Generalizable Graph Transformer with Graph Token Attention

Jingbo Zhou, Jun Xia, Siyuan Li, Yunfan Liu, Wenjun Wang, Yufei Huang, Changxi Chi, Mutian Hong, Zhuoli Ouyang, S. Wang, Zhongqi Wang, Xingyu Wu, Chang Yu, Stan Z. Li

Main figure for VecFormer: Towards Efficient and Generalizable Graph Transformer with Graph Token Attention

Abstract

Graph Transformer has demonstrated impressive capabilities in the field of graph representation learning. However, existing approaches face two critical challenges: (1) most models suffer from exponentially increasing computational complexity, making it difficult to scale to large graphs; (2) attention mechanisms based on node-level operations limit the flexibility of the model and result in poor generalization performance in out-of-distribution (OOD) scenarios. To address these issues, we propose VecFormer (the Vector Quantized Graph Transformer), an efficient and highly generalizable model for node classification, particularly under OOD settings. VecFormer adopts a two-stage training paradigm. In the first stage, two codebooks are used to reconstruct the node features and the graph structure, aiming to learn the rich semantic Graph Codes. In the second stage, attention mechanisms are performed at the Graph Token level based on the transformed cross codebook, reducing computational complexity while enhancing the model's generalization capability. Extensive experiments on datasets of various sizes demonstrate that VecFormer outperforms the existing Graph Transformer in both performance and speed.

Proposed method: VecFormer

Benchmark Results

Tested on 4 datasets 23 baseline values reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

Classic

#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
7
NodeFormer
actual #7 vs paper #334 327 places worse
0.9490 ±0.0019
best reported
actual #7 vs paper #334 327 places worse
paper 0.8187 ±0.0224
18
GCN
actual #18 vs paper #192 174 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #192 174 places worse
paper 0.8736 ±0.0035
20
GAT
actual #20 vs paper #228 208 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #228 208 places worse
paper 0.8612 ±0.0044
53
Polynormer
0.9044 ±0.0021
This paper
56
SGFormer
actual #56 vs paper #56
0.9037 ±0.0020
actual #56 vs paper #56
paper 0.9037 ±0.0020
paper 0.9037 ±0.0020 Δ at pub 0.0115
91
NAGphormer
actual #91 vs paper #123 32 places worse
0.8939 ±0.0013
best reported
actual #91 vs paper #123 32 places worse
paper 0.8865 ±0.0042
paper 0.8865 ±0.0042 Δ at pub 0.0074
99
GOAT
0.8915 ±0.0039
This paper
105
Exphormer
actual #105 vs paper #105
0.8906 ±0.0024
actual #105 vs paper #105
paper 0.8906 ±0.0024
paper 0.8906 ±0.0024 Δ at pub 0.0586
106
VQGraph
actual #106 vs paper #106
0.8905 ±0.0032
actual #106 vs paper #106
paper 0.8905 ±0.0032
paper 0.8905 ±0.0032 Δ at pub 0.0102
116
SAGE
actual #116 vs paper #162 46 places worse
0.8881 ±0.0015
best reported
actual #116 vs paper #162 46 places worse
paper 0.8783 ±0.0034
paper 0.8783 ±0.0034 Δ at pub 0.0098
125
GraphSAGE
0.8864 ±0.0030
172
GraphGPS
0.8772 ±0.0030
This paper
210
MLP
0.8690 ±0.0074
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #78 76 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #78 76 places worse
paper 0.9446 ±0.0069
3
GAT+T
0.9660 ±0.0007
4
Polynormer
actual #4 vs paper #34 30 places worse
0.9657 ±0.0023
best reported
actual #4 vs paper #34 30 places worse
paper 0.9544 ±0.0024
7
SAGE
actual #7 vs paper #99 92 places worse
0.9403 ±0.0069
actual #7 vs paper #99 92 places worse
paper 0.9403 ±0.0069

Improvement within reported uncertainty; not highlighted.

paper 0.9403 ±0.0069 Δ at pub 0.0023 Δ today 0.0240
8
GCN
actual #8 vs paper #79 71 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #79 71 places worse
paper 0.9444 ±0.0057
11
NAGphormer
actual #11 vs paper #58 47 places worse
0.9614 ±0.0016
best reported
actual #11 vs paper #58 47 places worse
paper 0.9503 ±0.0077

Difference within reported uncertainty; not counted as underperformance.

paper 0.9503 ±0.0077 Δ at pub 0.0091 Δ today 0.0111
16
VecFormer
0.9584 ±0.0041
This paper
23
Exphormer
actual #23 vs paper #91 68 places worse
0.9569 ±0.0039
best reported
actual #23 vs paper #91 68 places worse
paper 0.9410 ±0.0031
best at pub: Even Sparser Graph Transformers (NeurIPS 2024)
paper 0.9410 ±0.0031 Δ at pub 0.0126 Δ today 0.0159
29
SGFormer
actual #29 vs paper #68 39 places worse
0.9481 ±0.0043
actual #29 vs paper #68 39 places worse
paper 0.9481 ±0.0043

Improvement within reported uncertainty; not highlighted.

paper 0.9481 ±0.0043 Δ at pub 0.0047 Δ today 0.0077
44
NodeFormer
actual #44 vs paper #112 68 places worse
0.9527 ±0.0022
best reported
actual #44 vs paper #112 68 places worse
paper 0.9382 ±0.0097

Difference within reported uncertainty; not counted as underperformance.

paper 0.9382 ±0.0097 Δ at pub 0.0145 Δ today 0.0145
56
GraphSAGE
0.9508 ±0.0026
57
GraphGPS
actual #57 vs paper #91 34 places worse
0.9506 ±0.0013
best reported
actual #57 vs paper #91 34 places worse
paper 0.9418 ±0.0064

Difference within reported uncertainty; not counted as underperformance.

paper 0.9418 ±0.0064 Δ at pub 0.0088 Δ today 0.0088
86
GOAT
actual #86 vs paper #327 241 places worse
0.9433 ±0.0021
best reported
actual #86 vs paper #327 241 places worse
paper 0.9211 ±0.0095
107
VQGraph
actual #107 vs paper #500 393 places worse
0.9390 ±0.0030
best reported
actual #107 vs paper #500 393 places worse
paper 0.8656 ±0.0239
paper 0.8656 ±0.0239 Δ at pub 0.0734
390
MLP
0.9128 ±0.0063
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #50 48 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #50 48 places worse
paper 0.9108 ±0.0062
3
GAT
actual #3 vs paper #44 41 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #44 41 places worse
paper 0.9131 ±0.0045
6
Polynormer
actual #6 vs paper #27 21 places worse
0.9378 ±0.0010
best reported
actual #6 vs paper #27 21 places worse
paper 0.9192 ±0.0025
8
SAGE
actual #8 vs paper #81 73 places worse
0.9351 ±0.0006
best reported
actual #8 vs paper #81 73 places worse
paper 0.9029 ±0.0068
paper 0.9029 ±0.0068 Δ at pub 0.0023 Δ today 0.0322
16
VecFormer
0.9251 ±0.0054
This paper
18
SGFormer
actual #18 vs paper #61 43 places worse
0.9075 ±0.0034
actual #18 vs paper #61 43 places worse
paper 0.9075 ±0.0034
20
GOAT
actual #20 vs paper #159 139 places worse
0.9229 ±0.0037
best reported
actual #20 vs paper #159 139 places worse
paper 0.8895 ±0.0100
33
Exphormer
actual #33 vs paper #164 131 places worse
0.9180 ±0.0035
best reported
actual #33 vs paper #164 131 places worse
paper 0.8885 ±0.0026
34
GraphGPS
actual #34 vs paper #228 194 places worse
0.9179 ±0.0063
best reported
actual #34 vs paper #228 194 places worse
paper 0.8762 ±0.0068
38
NAGphormer
actual #38 vs paper #122 84 places worse
0.9169 ±0.0030
best reported
actual #38 vs paper #122 84 places worse
paper 0.8971 ±0.0060
46
GraphSAGE
0.9120 ±0.0029
48
NodeFormer
actual #48 vs paper #296 248 places worse
0.9112 ±0.0043
best reported
actual #48 vs paper #296 248 places worse
paper 0.8569 ±0.0125
paper 0.8569 ±0.0125 Δ at pub 0.0543
237
VQGraph
actual #237 vs paper #312 75 places worse
0.8750 ±0.0070
best reported
actual #237 vs paper #312 75 places worse
paper 0.8500 ±0.0104
paper 0.8500 ±0.0104 Δ at pub 0.0250
320
MLP
0.8463
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
actual #3 vs paper #38 35 places worse
0.9796 ±0.0081
best reported
actual #3 vs paper #38 35 places worse
paper 0.9663 ±0.0014
paper 0.9663 ±0.0014 Δ at pub 0.0133
5
NAGphormer
actual #5 vs paper #33 28 places worse
0.9785 ±0.0026
best reported
actual #5 vs paper #33 28 places worse
paper 0.9686 ±0.0021
paper 0.9686 ±0.0021 Δ at pub 0.0099
6
GAT
actual #6 vs paper #43 37 places worse
0.9782 ±0.0028
best reported
actual #6 vs paper #43 37 places worse
paper 0.9647 ±0.0019
paper 0.9647 ±0.0019 Δ at pub 0.0135
9
GCN
actual #9 vs paper #42 33 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #42 33 places worse
paper 0.9653 ±0.0014
paper 0.9653 ±0.0014 Δ at pub 0.0121
13
GraphGPS
actual #13 vs paper #31 18 places worse
0.9760 ±0.0005
best reported
actual #13 vs paper #31 18 places worse
paper 0.9705 ±0.0018
paper 0.9705 ±0.0018 Δ at pub 0.0055
17
SAGE
actual #17 vs paper #47 30 places worse
0.9739 ±0.0018
best reported
actual #17 vs paper #47 30 places worse
paper 0.9629 ±0.0017
paper 0.9629 ±0.0017 Δ at pub 0.0110
26
Polynormer
actual #26 vs paper #33 7 places worse
0.9722 ±0.0006
best reported
actual #26 vs paper #33 7 places worse
paper 0.9689 ±0.0006
paper 0.9689 ±0.0006 Δ at pub 0.0033
27
Exphormer
actual #27 vs paper #33 6 places worse
0.9720 ±0.0010
best reported
actual #27 vs paper #33 6 places worse
paper 0.9693 ±0.0007
paper 0.9693 ±0.0007 Δ at pub 0.0027
28
VecFormer
0.9717 ±0.0024
This paper
34
NodeFormer
actual #34 vs paper #34
0.9680 ±0.0063
actual #34 vs paper #34
paper 0.9680 ±0.0063

Improvement within reported uncertainty; not highlighted.

paper 0.9680 ±0.0063 Δ at pub 0.0035
43
GraphSAGE
0.9649 ±0.0006
44
GOAT
actual #44 vs paper #47 3 places worse
0.9627 ±0.0030
actual #44 vs paper #47 3 places worse
paper 0.9627 ±0.0030

Improvement within reported uncertainty; not highlighted.

paper 0.9627 ±0.0030 Δ at pub 0.0003
45
VQGraph
0.9646 ±0.0020
This paper
58
MLP
0.9597 ±0.0007
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 at pub — reported value improved over the best known when published Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere