Bootstrap Latents of Nodes and Neighbors for Graph Self-Supervised Learning

Yunhui Liu, Huaisong Zhang, Tieke He, Tao Zheng, Jianhua Zhao

Main figure for Bootstrap Latents of Nodes and Neighbors for Graph Self-Supervised Learning

Abstract

Contrastive learning is a significant paradigm in graph self-supervised learning. However, it requires negative samples to prevent model collapse and learn discriminative representations. These negative samples inevitably lead to heavy computation, memory overhead and class collision, compromising the representation learning. Recent studies present that methods obviating negative samples can attain competitive performance and scalability enhancements, exemplified by bootstrapped graph latents (BGRL). However, BGRL neglects the inherent graph homophily, which provides valuable insights into underlying positive pairs. Our motivation arises from the observation that subtly introducing a few ground-truth positive pairs significantly improves BGRL. Although we can't obtain ground-truth positive pairs without labels under the self-supervised setting, edges in the graph can reflect noisy positive pairs, i.e., neighboring nodes often share the same label. Therefore, we propose to expand the positive pair set with node-neighbor pairs. Subsequently, we introduce a cross-attention module to predict the supportiveness score of a neighbor with respect to the anchor node. This score quantifies the positive support from each neighboring node, and is encoded into the training objective. Consequently, our method mitigates class collision from negative and noisy positive samples, concurrently enhancing intra-class compactness. Extensive experiments are conducted on five benchmark datasets and three downstream task node classification, node clustering, and node similarity search. The results demonstrate that our method generates node representations with enhanced intra-class compactness and achieves state-of-the-art performance. Our implementation code is available at.

Proposed method: BLNN

Benchmark Results

Tested on 4 datasets 18 baseline values reported too low

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

Classic

#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #275 273 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #275 273 places worse
paper 0.9256 ±0.0035
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #292 284 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #292 284 places worse
paper 0.9242 ±0.0022
113
ProGCL
actual #113 vs paper #176 63 places worse
0.9381 ±0.0048
best reported
actual #113 vs paper #176 63 places worse
paper 0.9330 ±0.0009
paper 0.9330 ±0.0009 Δ at pub 0.0051
130
AFGRL
actual #130 vs paper #189 59 places worse
0.9361 ±0.0020
best reported
actual #130 vs paper #189 59 places worse
paper 0.9322 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.9322 ±0.0028 Δ at pub 0.0039
144
BLNN
0.9354 ±0.0023
This paper
164
GraphMAE
actual #164 vs paper #222 58 places worse
0.9341 ±0.0010
best reported
actual #164 vs paper #222 58 places worse
paper 0.9298 ±0.0035

Difference within reported uncertainty; not counted as underperformance.

paper 0.9298 ±0.0035 Δ at pub 0.0043
172
BGRL
actual #172 vs paper #198 26 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #198 26 places worse
paper 0.9317 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.9317 ±0.0030 Δ at pub 0.0020
186
CCA-SSG
actual #186 vs paper #201 15 places worse
0.9325 ±0.0021
best reported
actual #186 vs paper #201 15 places worse
paper 0.9314 ±0.0014

Difference within reported uncertainty; not counted as underperformance.

paper 0.9314 ±0.0014 Δ at pub 0.0011
191
GCA
actual #191 vs paper #277 86 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #277 86 places worse
paper 0.9253 ±0.0016
198
gCooL
0.9318 ±0.0012
This paper
203
GRACE
actual #203 vs paper #288 85 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #288 85 places worse
paper 0.9246 ±0.0018
paper 0.9246 ±0.0018 Δ at pub 0.0034 Δ today 0.0067
206
MVGRL
actual #206 vs paper #337 131 places worse
0.9310 ±0.0040
best reported
actual #206 vs paper #337 131 places worse
paper 0.9204 ±0.0098

Difference within reported uncertainty; not counted as underperformance.

paper 0.9204 ±0.0098 Δ at pub 0.0106
213
DGI
actual #213 vs paper #363 150 places worse
0.9309 ±0.0008
best reported
actual #213 vs paper #363 150 places worse
paper 0.9169 ±0.0107

Difference within reported uncertainty; not counted as underperformance.

paper 0.9169 ±0.0107 Δ at pub 0.0140
228
FastGCL
0.9291 ±0.0007
This paper
263
COSTA
actual #263 vs paper #275 12 places worse
0.9267 ±0.0016
best reported
actual #263 vs paper #275 12 places worse
paper 0.9256 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9256 ±0.0045 Δ at pub 0.0011
267
G-BT
actual #267 vs paper #288 21 places worse
0.9263 ±0.0044
best reported
actual #267 vs paper #288 21 places worse
paper 0.9246 ±0.0035

Difference within reported uncertainty; not counted as underperformance.

paper 0.9246 ±0.0035 Δ at pub 0.0017 Δ today 0.0017
284
AF-GCL
0.9249 ±0.0031
This paper
297
CGKS
0.9240 ±0.0010
This paper
390
MLP
actual #390 vs paper #535 145 places worse
0.9128 ±0.0063
best reported
actual #390 vs paper #535 145 places worse
paper 0.7853
paper 0.7853 Δ at pub 0.1275
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #269 267 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #269 267 places worse
paper 0.8651 ±0.0054
paper 0.8651 ±0.0054 Δ at pub 0.0321 Δ today 0.0761
3
GAT
actual #3 vs paper #256 253 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #256 253 places worse
paper 0.8693 ±0.0029
8
SAGE
0.9351 ±0.0006
53
BLNN
0.9102 ±0.0023
This paper
79
BGRL
0.9034 ±0.0019
This paper
100
GraphMAE
actual #100 vs paper #111 11 places worse
0.9002 ±0.0024
best reported
actual #100 vs paper #111 11 places worse
paper 0.8988 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.8988 ±0.0010 Δ today 0.0014
112
AFGRL
0.8988 ±0.0033
This paper
127
AF-GCL
0.8968 ±0.0019
This paper
135
ProGCL
actual #135 vs paper #147 12 places worse
0.8928 ±0.0015
actual #135 vs paper #147 12 places worse
paper 0.8928 ±0.0015
paper 0.8928 ±0.0015 Δ at pub 0.0185 Δ today 0.0027
139
GRACE
actual #139 vs paper #197 58 places worse
0.8953 ±0.0035
best reported
actual #139 vs paper #197 58 places worse
paper 0.8829 ±0.0011
paper 0.8829 ±0.0011 Δ at pub 0.0124 Δ today 0.0124
145
FastGCL
0.8935 ±0.0009
This paper
159
CCA-SSG
actual #159 vs paper #171 12 places worse
0.8896 ±0.0013
best reported
actual #159 vs paper #171 12 places worse
paper 0.8874 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.8874 ±0.0028 Δ today 0.0022
160
GCA
actual #160 vs paper #213 53 places worse
0.8894 ±0.0015
best reported
actual #160 vs paper #213 53 places worse
paper 0.8785 ±0.0031
paper 0.8785 ±0.0031 Δ at pub 0.0109 Δ today 0.0109
166
gCooL
0.8885 ±0.0014
This paper
179
MVGRL
actual #179 vs paper #240 61 places worse
0.8861 ±0.0064
best reported
actual #179 vs paper #240 61 places worse
paper 0.8739 ±0.0092

Difference within reported uncertainty; not counted as underperformance.

paper 0.8739 ±0.0092 Δ at pub 0.0051 Δ today 0.0122
185
CGKS
0.8850 ±0.0020
This paper
192
COSTA
actual #192 vs paper #193 1 place worse
0.8837 ±0.0022
best reported
actual #192 vs paper #193 1 place worse
paper 0.8832 ±0.0003

Difference within reported uncertainty; not counted as underperformance.

paper 0.8832 ±0.0003 Δ at pub 0.0005
202
G-BT
actual #202 vs paper #212 10 places worse
0.8814 ±0.0033
best reported
actual #202 vs paper #212 10 places worse
paper 0.8793 ±0.0036

Difference within reported uncertainty; not counted as underperformance.

paper 0.8793 ±0.0036 Δ at pub 0.0021 Δ today 0.0021
210
DGI
actual #210 vs paper #210
0.8798 ±0.0081
actual #210 vs paper #210
paper 0.8798 ±0.0081

Improvement within reported uncertainty; not highlighted.

paper 0.8798 ±0.0081 Δ at pub 0.0058
320
MLP
actual #320 vs paper #455 135 places worse
0.8463
best reported
actual #320 vs paper #455 135 places worse
paper 0.7381
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
0.9796 ±0.0081
6
GAT
actual #6 vs paper #122 116 places worse
0.9782 ±0.0028
best reported
actual #6 vs paper #122 116 places worse
paper 0.9547 ±0.0015
paper 0.9547 ±0.0015 Δ at pub 0.0116 Δ today 0.0235
9
GCN
actual #9 vs paper #90 81 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #90 81 places worse
paper 0.9565 ±0.0016
paper 0.9565 ±0.0016 Δ at pub 0.0085 Δ today 0.0209
17
SAGE
0.9739 ±0.0018
58
MLP
actual #58 vs paper #210 152 places worse
0.9597 ±0.0007
best reported
actual #58 vs paper #210 152 places worse
paper 0.9358
63
GCA
actual #63 vs paper #88 25 places worse
0.9590 ±0.0020
best reported
actual #63 vs paper #88 25 places worse
paper 0.9568 ±0.0005

Difference within reported uncertainty; not counted as underperformance.

paper 0.9568 ±0.0005 Δ at pub 0.0022
65
BLNN
0.9586 ±0.0010
This paper
69
BGRL
actual #69 vs paper #80 11 places worse
0.9580 ±0.0040
best reported
actual #69 vs paper #80 11 places worse
paper 0.9573 ±0.0005

Difference within reported uncertainty; not counted as underperformance.

paper 0.9573 ±0.0005 Δ at pub 0.0007
77
GRACE
actual #77 vs paper #140 63 places worse
0.9574 ±0.0006
best reported
actual #77 vs paper #140 63 places worse
paper 0.9526 ±0.0022
paper 0.9526 ±0.0022 Δ at pub 0.0037 Δ today 0.0048
78
AFGRL
actual #78 vs paper #88 10 places worse
0.9574 ±0.0010
best reported
actual #78 vs paper #88 10 places worse
paper 0.9569 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9569 ±0.0010 Δ at pub 0.0005
100
COSTA
0.9560 ±0.0002
This paper
106
CCA-SSG
actual #106 vs paper #133 27 places worse
0.9559 ±0.0007
best reported
actual #106 vs paper #133 27 places worse
paper 0.9538 ±0.0006
paper 0.9538 ±0.0006 Δ at pub 0.0021
111
FastGCL
0.9553 ±0.0002
This paper
117
GraphMAE
actual #117 vs paper #125 8 places worse
0.9550 ±0.0010
best reported
actual #117 vs paper #125 8 places worse
paper 0.9540 ±0.0006

Difference within reported uncertainty; not counted as underperformance.

paper 0.9540 ±0.0006 Δ today 0.0010
125
MVGRL
actual #125 vs paper #134 9 places worse
0.9544 ±0.0027
best reported
actual #125 vs paper #134 9 places worse
paper 0.9533 ±0.0003

Difference within reported uncertainty; not counted as underperformance.

paper 0.9533 ±0.0003 Δ at pub 0.0011
141
G-BT
actual #141 vs paper #141
0.9525 ±0.0013
actual #141 vs paper #141
paper 0.9525 ±0.0013

Improvement within reported uncertainty; not highlighted.

paper 0.9525 ±0.0013 Δ at pub 0.0018
154
AF-GCL
0.9512 ±0.0015
This paper
167
DGI
actual #167 vs paper #174 7 places worse
0.9489 ±0.0009
best reported
actual #167 vs paper #174 7 places worse
paper 0.9451 ±0.0052

Difference within reported uncertainty; not counted as underperformance.

paper 0.9451 ±0.0052 Δ at pub 0.0006 Δ today 0.0038
#ModelAccuracy ↑Paper
1
GCN
actual #1 vs paper #202 201 places worse
0.9302 ±0.0011
best reported
actual #1 vs paper #202 201 places worse
paper 0.7719 ±0.0012
paper 0.7719 ±0.0012 Δ at pub 0.1583
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
31
GAT
actual #31 vs paper #187 156 places worse
0.8533
best reported
actual #31 vs paper #187 156 places worse
paper 0.7765 ±0.0011
84
GraphMAE
actual #84 vs paper #111 27 places worse
0.8052 ±0.0032
best reported
actual #84 vs paper #111 27 places worse
paper 0.7954 ±0.0058
paper 0.7954 ±0.0058 Δ at pub 0.0038 Δ today 0.0098
86
BLNN
0.8048 ±0.0052
This paper
94
GRACE
actual #94 vs paper #151 57 places worse
0.8014 ±0.0048
best reported
actual #94 vs paper #151 57 places worse
paper 0.7864 ±0.0033
paper 0.7864 ±0.0033 Δ at pub 0.0150 Δ today 0.0150
100
BGRL
actual #100 vs paper #100
0.8000 ±0.0010
best reported
actual #100 vs paper #100
paper 0.7998 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.7998 ±0.0010 Δ at pub 0.0002 Δ today 0.0002
125
FastGCL
0.7920 ±0.0007
This paper
126
CGKS
0.7920 ±0.0010
This paper
129
COSTA
0.7912 ±0.0002
This paper
130
CCA-SSG
0.7908 ±0.0053
This paper
133
AF-GCL
0.7901 ±0.0051
This paper
143
AFGRL
actual #143 vs paper #187 44 places worse
0.7890 ±0.0060
best reported
actual #143 vs paper #187 44 places worse
paper 0.7762 ±0.0049
paper 0.7762 ±0.0049 Δ today 0.0128
147
gCooL
0.7874 ±0.0004
This paper
150
ProGCL
0.7868 ±0.0012
This paper
151
DGI
actual #151 vs paper #167 16 places worse
0.7825 ±0.0056
actual #151 vs paper #167 16 places worse
paper 0.7825 ±0.0056
paper 0.7825 ±0.0056 Δ at pub 0.0285
162
GCA
actual #162 vs paper #163 1 place worse
0.7840 ±0.0013
best reported
actual #162 vs paper #163 1 place worse
paper 0.7835 ±0.0005

Difference within reported uncertainty; not counted as underperformance.

paper 0.7835 ±0.0005 Δ at pub 0.0005 Δ today 0.0005
190
MVGRL
actual #190 vs paper #190
0.7757 ±0.0046
actual #190 vs paper #190
paper 0.7757 ±0.0046

Improvement within reported uncertainty; not highlighted.

paper 0.7757 ±0.0046 Δ at pub 0.0005
211
G-BT
actual #211 vs paper #211
0.7683 ±0.0073
actual #211 vs paper #211
paper 0.7683 ±0.0073

Improvement within reported uncertainty; not highlighted.

paper 0.7683 ±0.0073 Δ at pub 0.0018
237
MLP
actual #237 vs paper #252 15 places worse
0.7469 ±0.0085
best reported
actual #237 vs paper #252 15 places worse
paper 0.7198
paper 0.7198 Δ at pub 0.0074 Δ today 0.0271
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