Multiplex Graph Contrastive Learning with Soft Negatives

Zhenhao Zhao, Minhong Zhu, Chen Wang, Sijia Wang, Jiqiang Zhang, Li Chen, Weiran Cai

Main figure for Multiplex Graph Contrastive Learning with Soft Negatives

Abstract

Graph Contrastive Learning (GCL) seeks to learn nodal or graph representations that contain maximal consistent information from graph-structured data. While node-level contrasting modes are dominating, some efforts commence to explore consistency across different scales. Yet, they tend to lose consistent information and be contaminated by disturbing features. Here, we introduce MUX-GCL, a novel cross-scale contrastive learning paradigm that utilizes multiplex representations as effective patches. While this learning mode minimizes contaminating noises, a commensurate contrasting strategy using positional affinities further avoids information loss by correcting false negative pairs across scales. Extensive downstream experiments demonstrate that MUX-GCL yields multiple state-of-the-art results on public datasets. Our theoretical analysis further guarantees the new objective function as a stricter lower bound of mutual information of raw input features and output embeddings, which rationalizes this paradigm. Code is available at https://github.com/MUX-GCL/Code.

Proposed method: MUX-GCL

Benchmark Results

Tested on 2 datasets 19 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
0.9669 ±0.0014
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
106
MUX-GCL
0.9390 ±0.0010
This paper
113
ProGCL
actual #113 vs paper #190 77 places worse
0.9381 ±0.0048
best reported
actual #113 vs paper #190 77 places worse
paper 0.9320 ±0.0010
paper 0.9320 ±0.0010 Δ at pub 0.0061
114
MA-GCL
actual #114 vs paper #164 50 places worse
0.9380 ±0.0010
best reported
actual #114 vs paper #164 50 places worse
paper 0.9340 ±0.0010
paper 0.9340 ±0.0010 Δ at pub 0.0040
172
BGRL
actual #172 vs paper #371 199 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #371 199 places worse
paper 0.9150 ±0.0040
paper 0.9150 ±0.0040 Δ at pub 0.0187
191
GCA
actual #191 vs paper #324 133 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #324 133 places worse
paper 0.9220 ±0.0020
194
SUGRL
0.9320 ±0.0040
This paper
203
GRACE
actual #203 vs paper #279 76 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #279 76 places worse
paper 0.9250 ±0.0020
paper 0.9250 ±0.0020 Δ at pub 0.0030 Δ today 0.0063
206
MVGRL
actual #206 vs paper #362 156 places worse
0.9310 ±0.0040
best reported
actual #206 vs paper #362 156 places worse
paper 0.9170 ±0.0010
paper 0.9170 ±0.0010 Δ at pub 0.0140
213
DGI
actual #213 vs paper #366 153 places worse
0.9309 ±0.0008
best reported
actual #213 vs paper #366 153 places worse
paper 0.9160 ±0.0020
222
HomoGCL
actual #222 vs paper #222
0.9300 ±0.0020
actual #222 vs paper #222
paper 0.9300 ±0.0020

Improvement within reported uncertainty; not highlighted.

paper 0.9300 ±0.0020 Δ at pub 0.0008
240
SFA
0.9280 ±0.0010
This paper
263
COSTA
actual #263 vs paper #269 6 places worse
0.9267 ±0.0016
best reported
actual #263 vs paper #269 6 places worse
paper 0.9260 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.9260 ±0.0050 Δ at pub 0.0007
267
G-BT
actual #267 vs paper #269 2 places worse
0.9263 ±0.0044
best reported
actual #267 vs paper #269 2 places worse
paper 0.9260 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.9260 ±0.0050 Δ at pub 0.0003 Δ today 0.0003
317
VGAE
actual #317 vs paper #324 7 places worse
0.9224
best reported
actual #317 vs paper #324 7 places worse
paper 0.9220 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.9220 ±0.0010 Δ at pub 0.0004
352
GAE
actual #352 vs paper #366 14 places worse
0.9185 ±0.0006
best reported
actual #352 vs paper #366 14 places worse
paper 0.9160 ±0.0010
paper 0.9160 ±0.0010 Δ at pub 0.0025
390
MLP
0.9128 ±0.0063
444
DeepWalk
actual #444 vs paper #465 21 places worse
0.9005 ±0.0008
best reported
actual #444 vs paper #465 21 places worse
paper 0.8940 ±0.0010
paper 0.8940 ±0.0010 Δ at pub 0.0065 Δ today 0.0065
457
Node2Vec
0.8970 ±0.0010
This paper
531
Raw features
actual #531 vs paper #540 9 places worse
0.7999 ±0.0090
best reported
actual #531 vs paper #540 9 places worse
paper 0.7850
paper 0.7850 Δ at pub 0.0003 Δ today 0.0149
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
0.9412 ±0.0008
3
GAT
0.9398 ±0.0022
8
SAGE
0.9351 ±0.0006
64
MUX-GCL
0.9070 ±0.0010
This paper
79
BGRL
actual #79 vs paper #243 164 places worse
0.9034 ±0.0019
best reported
actual #79 vs paper #243 164 places worse
paper 0.8730 ±0.0040
paper 0.8730 ±0.0040 Δ at pub 0.0304 Δ today 0.0304
135
ProGCL
actual #135 vs paper #171 36 places worse
0.8955 ±0.0016
best reported
actual #135 vs paper #171 36 places worse
paper 0.8870 ±0.0010
paper 0.8870 ±0.0010 Δ at pub 0.0058 Δ today 0.0085
139
GRACE
actual #139 vs paper #217 78 places worse
0.8953 ±0.0035
best reported
actual #139 vs paper #217 78 places worse
paper 0.8780 ±0.0020
paper 0.8780 ±0.0020 Δ at pub 0.0173 Δ today 0.0173
157
HomoGCL
actual #157 vs paper #157
0.8900 ±0.0010
actual #157 vs paper #157
paper 0.8900 ±0.0010
paper 0.8900 ±0.0010 Δ at pub 0.0054
158
MA-GCL
0.8900 ±0.0010
This paper
160
GCA
actual #160 vs paper #235 75 places worse
0.8894 ±0.0015
best reported
actual #160 vs paper #235 75 places worse
paper 0.8750 ±0.0050
paper 0.8750 ±0.0050 Δ at pub 0.0144 Δ today 0.0144
162
SUGRL
actual #162 vs paper #169 7 places worse
0.8893 ±0.0021
best reported
actual #162 vs paper #169 7 places worse
paper 0.8880 ±0.0020

Difference within reported uncertainty; not counted as underperformance.

paper 0.8880 ±0.0020 Δ at pub 0.0013
179
MVGRL
actual #179 vs paper #235 56 places worse
0.8861 ±0.0064
best reported
actual #179 vs paper #235 56 places worse
paper 0.8750 ±0.0010
192
COSTA
actual #192 vs paper #196 4 places worse
0.8837 ±0.0022
best reported
actual #192 vs paper #196 4 places worse
paper 0.8830 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.8830 ±0.0010 Δ at pub 0.0007
202
G-BT
actual #202 vs paper #260 58 places worse
0.8814 ±0.0033
best reported
actual #202 vs paper #260 58 places worse
paper 0.8680 ±0.0030
paper 0.8680 ±0.0030 Δ at pub 0.0134 Δ today 0.0134
207
SFA
0.8810 ±0.0010
This paper
210
DGI
actual #210 vs paper #350 140 places worse
0.8798 ±0.0081
best reported
actual #210 vs paper #350 140 places worse
paper 0.8400 ±0.0050
paper 0.8400 ±0.0050 Δ at pub 0.0398
246
VGAE
actual #246 vs paper #273 27 places worse
0.8721 ±0.0026
best reported
actual #246 vs paper #273 27 places worse
paper 0.8640 ±0.0020
paper 0.8640 ±0.0020 Δ at pub 0.0081
264
GAE
actual #264 vs paper #303 39 places worse
0.8666 ±0.0007
best reported
actual #264 vs paper #303 39 places worse
paper 0.8530 ±0.0020
paper 0.8530 ±0.0020 Δ at pub 0.0136
278
DeepWalk
actual #278 vs paper #295 17 places worse
0.8628 ±0.0007
best reported
actual #278 vs paper #295 17 places worse
paper 0.8570 ±0.0010
paper 0.8570 ±0.0010 Δ at pub 0.0058 Δ today 0.0058
320
MLP
0.8463
330
Node2Vec
0.8440 ±0.0010
This paper
456
Raw features
actual #456 vs paper #459 3 places worse
0.7381
best reported
actual #456 vs paper #459 3 places worse
paper 0.7380
paper 0.7380 Δ at pub 0.0001 Δ today 0.0001
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 Best today — OK at publication; today's leaderboard best is elsewhere