ICML 2022

Self-Supervised Representation Learning via Latent Graph Prediction

Yaochen Xie, Zhao Xu, Shuiwang Ji

Main figure for Self-Supervised Representation Learning via Latent Graph Prediction

Abstract

Self-supervised learning (SSL) of graph neural networks is emerging as a promising way of leveraging unlabeled data. Currently, most methods are based on contrastive learning adapted from the image domain, which requires view generation and a sufficient number of negative samples. In contrast, existing predictive models do not require negative sampling, but lack theoretical guidance on the design of pretext training tasks. In this work, we propose the LaGraph, a theoretically grounded predictive SSL framework based on latent graph prediction. Learning objectives of LaGraph are derived as self-supervised upper bounds to objectives for predicting unobserved latent graphs. In addition to its improved performance, LaGraph provides explanations for recent successes of predictive models that include invariance-based objectives. We provide theoretical analysis comparing LaGraph to related methods in different domains. Our experimental results demonstrate the superiority of LaGraph in performance and the robustness to decreasing of training sample size on both graph-level and node-level tasks.

Proposed method: LaGraph

Benchmark Results

Tested on 6 datasets 9 baseline values reported too low

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

Classic

Reddit

Global leaderboard →

Default metric is F1. The paper reports 3 values on F1 and 1 value on F1-micro .

#ModelF1 ↑ defaultF1-micro ↑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
best reported
—
F1-micro —
paper 0.9080 ±0.0110
paper 0.9080 ±0.0110 Δ at pub 0.0580
58
GCN
0.9530 ± 0.0010
—
61
LaGraph
—
0.9520 ± 0.0000
F1-micro 0.9520 ± 0.0000
This paper
103
Super-GCN
0.9330 ± 0.0010
—
F1-micro —
This paper
133
Raw Feat.
0.5850 ± 0.0010
—
F1-micro —
This paper

PPI

Global leaderboard →

Default metric is F1. The paper reports 8 values on F1 and 1 value on F1-micro .

#ModelF1 ↑ defaultF1-micro ↑Paper
1
GAMLP(JK)
0.9982 ± 0.0001
—
2
GraphCON-GCN
0.9960
—
3
GCNII
0.9953 ± 0.0001
—
21
GCN
0.9850
—
59
Super-GAT
0.9730 ± 0.0020
—
F1-micro —
This paper
101
GraphSAGE
0.7860
best reported
—
F1-micro —
paper 0.4650 ±0.0070
paper 0.4650 ±0.0070 Δ at pub 0.2350 Δ today 0.3210
108
VGAE
0.7580 ± 0.0000
—
F1-micro —
This paper
109
GAE
0.7570 ± 0.0000
—
F1-micro —
This paper
113
LaGraph
—
0.7460 ± 0.0000
F1-micro 0.7460 ± 0.0000
This paper
123
BGRL-GAT
0.7050 ± 0.0010
—
F1-micro —
This paper
129
BGRL-GCN
0.6960 ± 0.0020
—
F1-micro —
This paper
165
Super-GCN
0.5150 ± 0.0060
—
F1-micro —
This paper
173
MLP
0.4620
—
177
Raw Feat.
0.4250 ± 0.0030
—
F1-micro —
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
159
WL
actual #159 vs paper #597 438 places worse
0.9040 ±0.0570
best reported
actual #159 vs paper #597 438 places worse
paper 0.8070 ±0.0300
paper 0.8070 ±0.0300 Δ at pub 0.0550 Δ today 0.0970
180
LaGraph
0.9020 ±0.0110
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 today 0.0023
228
GAE
actual #228 vs paper #484 256 places worse
0.8950 ±0.0150
best reported
actual #228 vs paper #484 256 places worse
paper 0.8400 ±0.0060
paper 0.8400 ±0.0060 Δ today 0.0550
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 0.8900 ±0.0110
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8900 ±0.0110 Δ at pub 0.0001 Δ today 0.0030
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 ±0.0130
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8680 ±0.0130 Δ today 0.0086
365
DGK
actual #365 vs paper #366 1 place worse
0.8744 ±0.0272
best reported
actual #365 vs paper #366 1 place worse
paper 0.8740 ±0.0270
best at pub: Provably Powerful Graph Networks (NeurIPS 2019)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8740 ±0.0270 Δ at pub 0.0004 Δ today 0.0004
403
MLP
0.8660 ±0.0495
407
graph2vec
actual #407 vs paper #515 108 places worse
0.8644 ±0.0125
best reported
actual #407 vs paper #515 108 places worse
paper 0.8320 ±0.0930

Difference within reported uncertainty; not counted as underperformance.

paper 0.8320 ±0.0930 Δ at pub 0.0048 Δ today 0.0324
444
GL
actual #444 vs paper #575 131 places worse
0.8520 ±0.0090
best reported
actual #444 vs paper #575 131 places worse
paper 0.8170 ±0.0210
paper 0.8170 ±0.0210 Δ at pub 0.0350
472
Sub2Vec
actual #472 vs paper #786 314 places worse
0.8447 ±0.0037
best reported
actual #472 vs paper #786 314 places worse
paper 0.6110 ±0.1580

Difference within reported uncertainty; not counted as underperformance.

paper 0.6110 ±0.1580 Δ at pub 0.0050 Δ today 0.2337
475
VGAE
0.8440 ±0.0060
This paper
746
Node2Vec
actual #746 vs paper #746
0.7263 ±0.1020
best reported
actual #746 vs paper #746
paper 0.7260 ±0.1020
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7260 ±0.1020 Δ at pub 0.0003 Δ today 0.0003
#ModelAccuracy ↑Paper
1
WL-MLP
0.9954
2
GIN
0.9934
3
GCN
0.9727
12
WL
actual #12 vs paper #223 211 places worse
0.8590 ±0.0010
best reported
actual #12 vs paper #223 211 places worse
paper 0.8000 ±0.0050
best at pub: Propagation Kernels (2014)
paper 0.8000 ±0.0050 Δ at pub 0.0590
104
GraphCL
actual #104 vs paper #325 221 places worse
0.8250 ±0.0013
best reported
actual #104 vs paper #325 221 places worse
paper 0.7790 ±0.0040
131
GraphSAGE
0.8200 ±0.0100
210
DGK
actual #210 vs paper #211 1 place worse
0.8031 ±0.0046
best reported
actual #210 vs paper #211 1 place worse
paper 0.8030 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.8030 ±0.0050 Δ at pub 0.0001 Δ today 0.0001
227
LaGraph
0.7990 ±0.0050
This paper
236
GAE
actual #236 vs paper #446 210 places worse
0.7978 ±0.0017
best reported
actual #236 vs paper #446 210 places worse
paper 0.7330 ±0.0060
paper 0.7330 ±0.0060 Δ today 0.0648
338
InfoGraph
actual #338 vs paper #386 48 places worse
0.7750 ±0.0074
best reported
actual #338 vs paper #386 48 places worse
paper 0.7620 ±0.0110

Difference within reported uncertainty; not counted as underperformance.

paper 0.7620 ±0.0110 Δ at pub 0.0044 Δ today 0.0130
356
MVGRL
actual #356 vs paper #410 54 places worse
0.7700 ±0.0080
best reported
actual #356 vs paper #410 54 places worse
paper 0.7510 ±0.0050
paper 0.7510 ±0.0050 Δ at pub 0.0190 Δ today 0.0190
406
graph2vec
actual #406 vs paper #446 40 places worse
0.7540 ±0.0120
best reported
actual #406 vs paper #446 40 places worse
paper 0.7320 ±0.0180

Difference within reported uncertainty; not counted as underperformance.

paper 0.7320 ±0.0180 Δ at pub 0.0220
441
VGAE
0.7370 ±0.0030
This paper
557
Sub2Vec
actual #557 vs paper #575 18 places worse
0.5976 ±0.0035
best reported
actual #557 vs paper #575 18 places worse
paper 0.5280 ±0.0150
best at pub: Graph Contrastive Learning Automated (ICML 2021)
paper 0.5280 ±0.0150 Δ at pub 0.0004 Δ today 0.0696
571
Node2Vec
0.5490 ±0.0160
This paper
#ModelAccuracy ↑Paper
1
WL-MLP
0.9792
2
MSH-GNN
0.9640 ±0.0070
3
CoCN
0.8722 ±0.0013
6
graph2vec
actual #6 vs paper #328 322 places worse
0.8558
best reported
actual #6 vs paper #328 322 places worse
paper 0.5990
paper 0.5990 Δ at pub 0.2568
23
GCN
0.8260 ±0.0220
80
GraphCL
actual #80 vs paper #289 209 places worse
0.8108 ±0.0017
best reported
actual #80 vs paper #289 209 places worse
paper 0.7140 ±0.0120
paper 0.7140 ±0.0120 Δ today 0.0968
91
GAE
actual #91 vs paper #338 247 places worse
0.8078 ±0.0012
best reported
actual #91 vs paper #338 247 places worse
paper 0.5630 ±0.0010
paper 0.5630 ±0.0010 Δ today 0.2448
146
InfoGraph
actual #146 vs paper #294 148 places worse
0.7940
best reported
actual #146 vs paper #294 148 places worse
paper 0.7070 ±0.0110
paper 0.7070 ±0.0110 Δ at pub 0.0870
151
MLP
0.7920 ±0.0240
189
LaGraph
0.7760 ±0.0020
This paper
325
Sub2Vec
0.6210 ±0.0140
This paper
339
VGAE
0.5630
This paper
341
Node2Vec
actual #341 vs paper #341
0.5610 ±0.0020
best reported
actual #341 vs paper #341
paper 0.5570 ±0.0020
paper 0.5570 ±0.0020 Δ at pub 0.0040 Δ today 0.0040
#ModelAccuracy ↑Paper
1
OEPG
0.9630 ±0.0090
2
MSH-GNN
0.9580 ±0.0090
3
GNN-AK+
0.9480 ±0.0080
13
GIN
0.9240 ±0.0250
23
GraphCL
actual #23 vs paper #44 21 places worse
0.9169 ±0.0070
best reported
actual #23 vs paper #44 21 places worse
paper 0.8950 ±0.0080
best at pub: Graph Contrastive Learning Automated (ICML 2021)
paper 0.8950 ±0.0080 Δ at pub 0.0003 Δ today 0.0219
33
LaGraph
0.9040 ±0.0080
This paper
46
InfoGraph
actual #46 vs paper #68 22 places worse
0.8939 ±0.0181
best reported
actual #46 vs paper #68 22 places worse
paper 0.8250 ±0.0140
paper 0.8250 ±0.0140 Δ today 0.0689
55
GAE
actual #55 vs paper #80 25 places worse
0.8769 ±0.0040
best reported
actual #55 vs paper #80 25 places worse
paper 0.7480 ±0.0020
paper 0.7480 ±0.0020 Δ today 0.1289
65
MVGRL
0.8450 ±0.0060
This paper
73
DGK
actual #73 vs paper #73
0.7804 ±0.0039
best reported
actual #73 vs paper #73
paper 0.7800 ±0.0040
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7800 ±0.0040 Δ at pub 0.0004 Δ today 0.0004
75
GL
actual #75 vs paper #76 1 place worse
0.7734 ±0.0018
best reported
actual #75 vs paper #76 1 place worse
paper 0.7730 ±0.0020
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7730 ±0.0020 Δ at pub 0.0004 Δ today 0.0004
80
graph2vec
0.7580 ±0.0100
This paper
81
VGAE
0.7480 ±0.0020
This paper
82
Node2Vec
0.7380 ±0.0050
This paper
83
Sub2Vec
actual #83 vs paper #83
0.7150 ±0.0040
actual #83 vs paper #83
paper 0.7150 ±0.0040

Improvement within reported uncertainty; not highlighted.

paper 0.7150 ±0.0040 Δ at pub 0.0002
85
WL
actual #85 vs paper #85
0.6882 ±0.0041
best reported
actual #85 vs paper #85
paper 0.6880 ±0.0040
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.6880 ±0.0040 Δ at pub 0.0002 Δ today 0.0002
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