AAAI 2024

Graph Structure Refinement with Energy-based Contrastive Learning

Xianlin Zeng, Yufeng Wang, Yuqi Sun, Guodong Guo, Baochang Zhang, Wenrui Ding

Main figure for Graph Structure Refinement with Energy-based Contrastive Learning

Abstract

Graph Neural Networks (GNNs) have recently gained widespread attention as a successful tool for analyzing graph-structured data. However, imperfect graph structure with noisy links lacks enough robustness and may damage graph representations, therefore limiting the GNNs' performance in practical tasks. Moreover, existing generative architectures fail to fit discriminative graph-related tasks. To tackle these issues, we introduce an unsupervised method based on a joint of generative training and discriminative training to learn graph structure and representation, aiming to improve the discriminative performance of generative models. We propose an Energy-based Contrastive Learning (ECL) guided Graph Structure Refinement (GSR) framework, denoted as ECL-GSR. To our knowledge, this is the first work to combine energy-based models with contrastive learning for GSR. Specifically, we leverage ECL to approximate the joint distribution of sample pairs, which increases the similarity between representations of positive pairs while reducing the similarity between negative ones. Refined structure is produced by augmenting and removing edges according to the similarity metrics among node representations. Extensive experiments demonstrate that ECL-GSR outperforms the state-of-the-art on eight benchmark datasets in node classification. ECL-GSR achieves faster training with fewer samples and memories against the leading baseline, highlighting its simplicity and efficiency in downstream tasks.

Proposed method: ECL-GSR

Benchmark Results

Tested on 5 datasets 16 baseline values reported too low

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

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
51
PSCN
actual #51 vs paper #279 228 places worse
0.9263 ±0.0421
best reported
actual #51 vs paper #279 228 places worse
paper 0.8895 ±0.0437

Difference within reported uncertainty; not counted as underperformance.

paper 0.8895 ±0.0437 Δ at pub 0.0368 Δ today 0.0368
63
GCN
actual #63 vs paper #729 666 places worse
0.9220 ±0.0440
best reported
actual #63 vs paper #729 666 places worse
paper 0.7392 ±0.0884
paper 0.7392 ±0.0884 Δ at pub 0.1518 Δ today 0.1828
97
ECL-GSR
0.9145 ±0.0275
This paper
183
GAT
actual #183 vs paper #651 468 places worse
0.9010 ±0.0580
best reported
actual #183 vs paper #651 468 places worse
paper 0.7871 ±0.0751
paper 0.7871 ±0.0751 Δ at pub 0.1139 Δ today 0.1139
207
GFN-light
0.8989 ±0.0714
This paper
301
CapsGNN
actual #301 vs paper #402 101 places worse
0.8867 ±0.0688
best reported
actual #301 vs paper #402 101 places worse
paper 0.8667 ±0.0688

Difference within reported uncertainty; not counted as underperformance.

paper 0.8667 ±0.0688 Δ at pub 0.0200
403
MLP
0.8660 ±0.0495
425
DGCNN
0.8583 ±0.0116
This paper
661
HGP-SL
0.7807 ±0.1085
This paper
718
SAGE
actual #718 vs paper #763 45 places worse
0.7490 ±0.0870
best reported
actual #718 vs paper #763 45 places worse
paper 0.6865 ±0.0431

Difference within reported uncertainty; not counted as underperformance.

paper 0.6865 ±0.0431 Δ at pub 0.0625
764
VIB-GSL
0.6863 ±0.0515
This paper
#ModelAccuracy ↑Paper
1
WL-MLP
0.9792
2
MSH-GNN
0.9640 ±0.0070
3
CoCN
0.8722 ±0.0013
17
ECL-GSR
0.8300 ±0.0143
This paper
23
GCN
actual #23 vs paper #211 188 places worse
0.8260 ±0.0220
best reported
actual #23 vs paper #211 188 places worse
paper 0.7696 ±0.0228
paper 0.7696 ±0.0228 Δ at pub 0.0564
30
GIN
0.8220 ±0.0210
67
GFN-light
0.8134 ±0.0173
This paper
137
SAGE
actual #137 vs paper #236 99 places worse
0.7970 ±0.0170
best reported
actual #137 vs paper #236 99 places worse
paper 0.7558 ±0.0204
paper 0.7558 ±0.0204 Δ at pub 0.0412
140
CapsGNN
0.7962 ±0.0091
This paper
151
MLP
0.7920 ±0.0240
155
GAT
actual #155 vs paper #155
0.7908 ±0.0136
actual #155 vs paper #155
paper 0.7908 ±0.0136

Improvement within reported uncertainty; not highlighted.

paper 0.7908 ±0.0136 Δ at pub 0.0308
176
HGP-SL
0.7806 ±0.0217
This paper
191
DGCNN
actual #191 vs paper #269 78 places worse
0.7759 ±0.0224
best reported
actual #191 vs paper #269 78 places worse
paper 0.7376 ±0.0049
paper 0.7376 ±0.0049 Δ at pub 0.0369 Δ today 0.0383
205
VIB-GSL
0.7714 ±0.0159
This paper
281
PSCN
0.7260 ±0.0215
This paper

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
34
MLP
0.9230 ±0.0070
53
GraphSAGE
0.9000 ±0.0365
155
NodeFormer
actual #155 vs paper #527 372 places worse
0.8463 ±0.0347
best reported
actual #155 vs paper #527 372 places worse
paper 0.5892 ±0.0432
paper 0.5892 ±0.0432 Δ at pub 0.2571
211
GAT
actual #211 vs paper #574 363 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #574 363 places worse
paper 0.5405 ±0.0735
paper 0.5405 ±0.0735 Δ at pub 0.2677 Δ today 0.2757
257
GCN
actual #257 vs paper #544 287 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #544 287 places worse
paper 0.5783 ±0.0276
best today: Graph Wave Networks (WWW 2025)
paper 0.5783 ±0.0276 Δ at pub 0.2057 Δ today 0.2150
273
GEN
actual #273 vs paper #432 159 places worse
0.7830 ±0.0800
best reported
actual #273 vs paper #432 159 places worse
paper 0.6594 ±0.0413
paper 0.6594 ±0.0413 Δ at pub 0.1236
353
ECL-GSR
0.7297 ±0.0339
This paper
391
SUBLIME
0.7021 ±0.0232
This paper
470
IDGL
0.6243 ±0.0609
This paper
475
GRCN
0.6216 ±0.0705
This paper
493
SGSR
0.6081 ±0.0487
This paper
516
CoGSL
0.5946 ±0.0436
This paper
529
LDS
0.5892 ±0.0432
This paper
552
GAuG-O
0.5690 ±0.0360
This paper
567
STABLE
0.5524 ±0.0604
This paper
593
ProGNN
0.4837 ±0.0875
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
0.9480 ±0.0380
3
RF-GCN
0.9429
24
MLP
0.9136 ±0.0070
138
SAGE
0.8269
158
GAT
actual #158 vs paper #521 363 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #521 363 places worse
paper 0.4622 ±0.0633
paper 0.4622 ±0.0633 Δ at pub 0.3568
168
GEN
actual #168 vs paper #418 250 places worse
0.8100 ±0.0390
best reported
actual #168 vs paper #418 250 places worse
paper 0.5702 ±0.0719
paper 0.5702 ±0.0719 Δ at pub 0.2398
170
GCN
actual #170 vs paper #509 339 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #509 339 places worse
paper 0.4784 ±0.0555
paper 0.4784 ±0.0555 Δ at pub 0.3231 Δ today 0.3298
274
ECL-GSR
0.7127 ±0.0206
This paper
282
SUBLIME
0.7029 ±0.0351
This paper
323
NodeFormer
actual #323 vs paper #542 219 places worse
0.6577 ±0.0459
best reported
actual #323 vs paper #542 219 places worse
paper 0.4270 ±0.0551
paper 0.4270 ±0.0551 Δ today 0.2307
409
GAuG-O
0.5760 ±0.0380
This paper
435
GRCN
0.5432 ±0.0824
This paper
441
ProGNN
0.5405 ±0.0616
This paper
465
CoGSL
0.5216 ±0.0321
This paper
490
IDGL
0.5000 ±0.0898
This paper
509
LDS
0.4787 ±0.0714
This paper
532
SGSR
0.4432 ±0.0216
This paper
536
STABLE
0.4403 ±0.0405
This paper
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
42
MLP
0.4026 ±0.0108
68
GraphSAGE
0.3899 ±0.0085
119
GEN
actual #119 vs paper #409 290 places worse
0.3730 ±0.0140
best reported
actual #119 vs paper #409 290 places worse
paper 0.2721 ±0.0205
paper 0.2721 ±0.0205 Δ at pub 0.1009
135
GCN
actual #135 vs paper #352 217 places worse
0.3690
best reported
actual #135 vs paper #352 217 places worse
paper 0.3001 ±0.0077
paper 0.3001 ±0.0077 Δ at pub 0.0689
136
NodeFormer
actual #136 vs paper #423 287 places worse
0.3690 ±0.0100
best reported
actual #136 vs paper #423 287 places worse
paper 0.2551 ±0.0117
best at pub: Even Sparser Graph Transformers (NeurIPS 2024)
paper 0.2551 ±0.0117 Δ at pub 0.1139
182
GAT
actual #182 vs paper #376 194 places worse
0.3605 ±0.0035
best reported
actual #182 vs paper #376 194 places worse
paper 0.2891 ±0.0083
paper 0.2891 ±0.0083 Δ at pub 0.0714
276
ECL-GSR
0.3371 ±0.0096
This paper
290
CoGSL
0.3295 ±0.0120
This paper
326
LDS
0.3105 ±0.0131
This paper
331
SUBLIME
0.3079 ±0.0068
This paper
343
SGSR
0.3023 ±0.0038
This paper
347
STABLE
0.3018 ±0.0100
This paper
354
GRCN
0.2997 ±0.0071
This paper
392
IDGL
0.2816 ±0.0141
This paper
421
GAuG-O
0.2580 ±0.0100
This paper
465
ProGNN
0.2235 ±0.0088
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