AAAI 2024

Rethinking Graph Masked Autoencoders through Alignment and Uniformity

Liang Wang, Xiang Tao, Q. Liu, Shu Wu

Main figure for Rethinking Graph Masked Autoencoders through Alignment and Uniformity

Abstract

Self-supervised learning on graphs can be bifurcated into contrastive and generative methods. Contrastive methods, also known as graph contrastive learning (GCL), have dominated graph self-supervised learning in the past few years, but the recent advent of graph masked autoencoder (GraphMAE) rekindles the momentum behind generative methods. Despite the empirical success of GraphMAE, there is still a dearth of theoretical understanding regarding its efficacy. Moreover, while both generative and contrastive methods have been shown to be effective, their connections and differences have yet to be thoroughly investigated. Therefore, we theoretically build a bridge between GraphMAE and GCL, and prove that the node-level reconstruction objective in GraphMAE implicitly performs context-level GCL. Based on our theoretical analysis, we further identify the limitations of the GraphMAE from the perspectives of alignment and uniformity, which have been considered as two key properties of high-quality representations in GCL. We point out that GraphMAE's alignment performance is restricted by the masking strategy, and the uniformity is not strictly guaranteed. To remedy the aforementioned limitations, we propose an lignment- niformity enhanced raph asked uto ncoder, named AUG-MAE. Specifically, we propose an easy-to-hard adversarial masking strategy to provide hard-to-align samples, which improves the alignment performance. Meanwhile, we introduce an explicit uniformity regularizer to ensure the uniformity of the learned representations. Experimental results on benchmark datasets demonstrate the superiority of our model over existing state-of-the-art methods. The code is available at:.

Proposed method: AUG-MAE

Benchmark Results

Tested on 5 datasets 9 baseline values reported too low

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

Classic

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Global leaderboard →

Default metric is F1. The paper reports 7 values on F1 and 1 value on Accuracy (%) .

#ModelF1 ↑ defaultAccuracy (%) ↑Paper
1
EnGCN
0.9714 ± 0.0003
—
2
SAGN+SLE
0.9710 ± 0.0000
—
3
GAMLP(JK)
0.9704 ± 0.0001
—
14
GraphSAGE
0.9660
—
36
AUG-MAE
—
0.9610 ± 0.0010
Accuracy (%) 0.9610 ± 0.0010
This paper
38
GraphMAE
0.9601 ±0.0008
best reported
—
Accuracy (%) —
paper 0.9580 ±0.0040

Difference within reported uncertainty; not counted as underperformance.

paper 0.9580 ±0.0040 Δ at pub 0.0021
54
MaskGAE
0.9540 ± 0.0010
—
Accuracy (%) —
This paper
61
SEEGERA
0.9520 ± 0.0020
—
Accuracy (%) —
This paper
63
CCA-SSG
0.9511 ±0.0018
best reported
—
Accuracy (%) —
paper 0.9510 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9510 ±0.0010 Δ at pub 0.0001
68
GRACE
0.9501 ±0.0036
best reported
—
Accuracy (%) —
paper 0.9470 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9470 ±0.0010 Δ at pub 0.0031
74
BGRL
0.9490 ±0.0400
best reported
—
Accuracy (%) —
paper 0.9420 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9420 ±0.0010 Δ at pub 0.0070
82
DGI
0.9414 ±0.0003
best reported
—
Accuracy (%) —
paper 0.9400 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9400 ±0.0010 Δ at pub 0.0014
#ModelF1 ↑Paper
1
GAMLP(JK)
0.9982 ±0.0001
2
GraphCON-GCN
0.9960
3
GCNII
0.9953 ±0.0001
21
GCN
0.9850
114
GraphMAE
actual #114 vs paper #115 1 place worse
0.7450 ±0.0029
best reported
actual #114 vs paper #115 1 place worse
paper 0.7410 ±0.0040

Difference within reported uncertainty; not counted as underperformance.

paper 0.7410 ±0.0040 Δ at pub 0.0040 Δ today 0.0040
115
AUG-MAE
0.7430 ±0.0010
This paper
116
MaskGAE
0.7390 ±0.0030
This paper
117
BGRL
actual #117 vs paper #117
0.7363 ±0.0016
best reported
actual #117 vs paper #117
paper 0.7360 ±0.0020

Difference within reported uncertainty; not counted as underperformance.

paper 0.7360 ±0.0020 Δ at pub 0.0003 Δ today 0.0003
118
SEEGERA
0.7340 ±0.0030
This paper
119
CCA-SSG
actual #119 vs paper #119
0.7334 ±0.0017
best reported
actual #119 vs paper #119
paper 0.7330 ±0.0020

Difference within reported uncertainty; not counted as underperformance.

paper 0.7330 ±0.0020 Δ at pub 0.0004 Δ today 0.0004
126
GRACE
actual #126 vs paper #127 1 place worse
0.6971 ±0.0017
best reported
actual #126 vs paper #127 1 place worse
paper 0.6970 ±0.0020

Difference within reported uncertainty; not counted as underperformance.

paper 0.6970 ±0.0020 Δ at pub 0.0001 Δ today 0.0001
148
DGI
0.6380 ±0.0020
This paper
173
MLP
0.4620
#ModelAccuracy ↑Paper
1
GCN
0.9302 ±0.0011
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
83
AUG-MAE
actual #83 vs paper #260 177 places worse
0.8053 ±0.0034
best reported
actual #83 vs paper #260 177 places worse
paper 0.7170 ±0.0060
paper 0.7170 ±0.0060 Δ today 0.0883
84
GraphMAE
actual #84 vs paper #264 180 places worse
0.8052 ±0.0032
best reported
actual #84 vs paper #264 180 places worse
paper 0.7060 ±0.0090
paper 0.7060 ±0.0090 Δ at pub 0.0932 Δ today 0.0992
94
GRACE
actual #94 vs paper #276 182 places worse
0.8014 ±0.0048
best reported
actual #94 vs paper #276 182 places worse
paper 0.6800 ±0.0070
paper 0.6800 ±0.0070 Δ at pub 0.1214 Δ today 0.1214
100
BGRL
actual #100 vs paper #292 192 places worse
0.8000 ±0.0010
best reported
actual #100 vs paper #292 192 places worse
paper 0.6550 ±0.0150
paper 0.6550 ±0.0150 Δ at pub 0.1450 Δ today 0.1450
122
SEEGERA
actual #122 vs paper #290 168 places worse
0.7923 ±0.0045
best reported
actual #122 vs paper #290 168 places worse
paper 0.6580 ±0.0020
paper 0.6580 ±0.0020 Δ today 0.1343
130
CCA-SSG
actual #130 vs paper #277 147 places worse
0.7908 ±0.0053
best reported
actual #130 vs paper #277 147 places worse
paper 0.6740 ±0.0090
paper 0.6740 ±0.0090 Δ at pub 0.1168 Δ today 0.1168
151
DGI
actual #151 vs paper #294 143 places worse
0.7865 ±0.0690
best reported
actual #151 vs paper #294 143 places worse
paper 0.6480 ±0.0060
paper 0.6480 ±0.0060 Δ at pub 0.1060 Δ today 0.1385
190
MVGRL
actual #190 vs paper #294 104 places worse
0.7757 ±0.0046
best reported
actual #190 vs paper #294 104 places worse
paper 0.6480 ±0.0070
237
MLP
0.7469 ±0.0085
290
MaskGAE
0.6600 ±0.0020
This paper

TU Dortmund

#ModelAccuracy ↑Paper
1
MSH-GNN
0.9910 ±0.0030
2
ID-GNN+BEC
0.9830 ±0.0360
3
SupCosine
0.9830 ±0.0250
39
GIN
0.9330 ±0.0290
105
InfoGCL
0.9120 ±0.0130
This paper
199
MVGRL
actual #199 vs paper #213 14 places worse
0.8993 ±0.0616
best reported
actual #199 vs paper #213 14 places worse
paper 0.8970 ±0.0110

Difference within reported uncertainty; not counted as underperformance.

paper 0.8970 ±0.0110 Δ at pub 0.0023
210
AUG-MAE
actual #210 vs paper #322 112 places worse
0.8980 ±0.0130
best reported
actual #210 vs paper #322 112 places worse
paper 0.8828 ±0.0098
paper 0.8828 ±0.0098 Δ today 0.0152
257
InfoGraph
actual #257 vs paper #272 15 places worse
0.8930 ±0.0514
best reported
actual #257 vs paper #272 15 places worse
paper 0.8901 ±0.0113

Difference within reported uncertainty; not counted as underperformance.

paper 0.8901 ±0.0113 Δ at pub 0.0029
258
GraphMAE
actual #258 vs paper #326 68 places worse
0.8930 ±0.0110
best reported
actual #258 vs paper #326 68 places worse
paper 0.8819 ±0.0126

Difference within reported uncertainty; not counted as underperformance.

paper 0.8819 ±0.0126 Δ today 0.0111
351
JOAO
actual #351 vs paper #370 19 places worse
0.8770 ±0.0080
best reported
actual #351 vs paper #370 19 places worse
paper 0.8735 ±0.0102

Difference within reported uncertainty; not counted as underperformance.

paper 0.8735 ±0.0102 Δ at pub 0.0035 Δ today 0.0035
354
GraphCL
actual #354 vs paper #396 42 places worse
0.8766 ±0.0103
best reported
actual #354 vs paper #396 42 places worse
paper 0.8680 ±0.0134

Difference within reported uncertainty; not counted as underperformance.

paper 0.8680 ±0.0134 Δ at pub 0.0086
403
MLP
0.8660 ±0.0495
407
graph2vec
actual #407 vs paper #517 110 places worse
0.8644 ±0.0125
best reported
actual #407 vs paper #517 110 places worse
paper 0.8315 ±0.0925

Difference within reported uncertainty; not counted as underperformance.

paper 0.8315 ±0.0925 Δ at pub 0.0329
#ModelAccuracy ↑Paper
1
WL-MLP
0.9792
2
MSH-GNN
0.9640 ±0.0070
3
CoCN
0.8722 ±0.0013
22
GraphMAE
actual #22 vs paper #109 87 places worse
0.8270 ±0.0100
best reported
actual #22 vs paper #109 87 places worse
paper 0.8032 ±0.0042
paper 0.8032 ±0.0042 Δ today 0.0238
23
GCN
0.8260 ±0.0220
75
GCC
actual #75 vs paper #161 86 places worse
0.8110
best reported
actual #75 vs paper #161 86 places worse
paper 0.7890
paper 0.7890 Δ at pub 0.0220
80
GraphCL
actual #80 vs paper #290 210 places worse
0.8108 ±0.0017
best reported
actual #80 vs paper #290 210 places worse
paper 0.7136 ±0.0115
paper 0.7136 ±0.0115 Δ at pub 0.0972
103
AUG-MAE
actual #103 vs paper #103
0.8050 ±0.0050
best reported
actual #103 vs paper #103
paper 0.8048 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.8048 ±0.0050 Δ today 0.0002
126
InfoGCL
actual #126 vs paper #126
0.8001 ±0.0132
best reported
actual #126 vs paper #126
paper 0.8000 ±0.0130

Difference within reported uncertainty; not counted as underperformance.

paper 0.8000 ±0.0130 Δ today 0.0001
146
InfoGraph
actual #146 vs paper #295 149 places worse
0.7940
best reported
actual #146 vs paper #295 149 places worse
paper 0.7065 ±0.0113
paper 0.7065 ±0.0113 Δ at pub 0.0875
151
MLP
0.7920 ±0.0240
248
JOAO
actual #248 vs paper #305 57 places worse
0.7535 ±0.0093
best reported
actual #248 vs paper #305 57 places worse
paper 0.6950 ±0.0036
paper 0.6950 ±0.0036 Δ at pub 0.0585
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