ICML 2025

Learn Beneficial Noise as Graph Augmentation

Siqi Huang, Yanchen Xu, Hongyuan Zhang, Xuelong Li

Main figure for Learn Beneficial Noise as Graph Augmentation

Abstract

Although graph contrastive learning (GCL) has been widely investigated, it is still a challenge to generate effective and stable graph augmentations. Existing methods often apply heuristic augmentation like random edge dropping, which may disrupt important graph structures and result in unstable GCL performance. In this paper, we propose Positive-incentive Noise driven Graph Data Augmentation (PiNGDA), where positive-incentive noise (pi-noise) scientifically analyzes the beneficial effect of noise under the information theory. To bridge the standard GCL and pi-noise framework, we design a Gaussian auxiliary variable to convert the loss function to information entropy. We prove that the standard GCL with pre-defined augmentations is equivalent to estimate the beneficial noise via the point estimation. Following our analysis, PiNGDA is derived from learning the beneficial noise on both topology and attributes through a trainable noise generator for graph augmentations, instead of the simple estimation. Since the generator learns how to produce beneficial perturbations on graph topology and node attributes, PiNGDA is more reliable compared with the existing methods. Extensive experimental results validate the effectiveness and stability of PiNGDA.

Proposed method: CL

Benchmark Results

Tested on 7 datasets 25 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 #287 285 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #287 285 places worse
paper 0.9248 ±0.0021
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #277 269 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #277 269 places worse
paper 0.9255 ±0.0025
103
SGRL
actual #103 vs paper #222 119 places worse
0.9395 ±0.0003
best reported
actual #103 vs paper #222 119 places worse
paper 0.9297 ±0.0032
132
GREET
actual #132 vs paper #132
0.9361 ±0.0035
actual #132 vs paper #132
paper 0.9361 ±0.0035
172
BGRL
actual #172 vs paper #195 23 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #195 23 places worse
paper 0.9319 ±0.0043

Difference within reported uncertainty; not counted as underperformance.

paper 0.9319 ±0.0043 Δ at pub 0.0018
183
CL
0.9329 ±0.0017
This paper
191
GCA
actual #191 vs paper #195 4 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #195 4 places worse
paper 0.9319 ±0.0024

Difference within reported uncertainty; not counted as underperformance.

paper 0.9319 ±0.0024 Δ at pub 0.0001 Δ today 0.0001
196
GRACE +PiNGDA
0.9319 ±0.0018
This paper
203
GRACE
actual #203 vs paper #203
0.9313 ±0.0017
actual #203 vs paper #203
paper 0.9313 ±0.0017

Improvement within reported uncertainty; not highlighted.

paper 0.9313 ±0.0017 Δ at pub 0.0033
205
Sp2GCL +PiNGDA
0.9311 ±0.0014
This paper
213
DGI
actual #213 vs paper #474 261 places worse
0.9309 ±0.0008
best reported
actual #213 vs paper #474 261 places worse
paper 0.8901 ±0.0098
217
Sp2GCL
0.9305 ±0.0023
This paper
327
GASSL
0.9214 ±0.0023
This paper
347
AD-GCL
actual #347 vs paper #347
0.9192 ±0.0037
actual #347 vs paper #347
paper 0.9192 ±0.0037
paper 0.9192 ±0.0037 Δ at pub 0.0317
390
MLP
0.9128 ±0.0063
392
GRACEIS
0.9126 ±0.0058
This paper
408
GMI
actual #408 vs paper #442 34 places worse
0.9081 ±0.0015
best reported
actual #408 vs paper #442 34 places worse
paper 0.9013 ±0.0139

Difference within reported uncertainty; not counted as underperformance.

paper 0.9013 ±0.0139 Δ at pub 0.0060 Δ today 0.0068
460
GOUDA
0.8961 ±0.0117
This paper
542
JOAO
0.7823 ±0.0263
This paper
#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 #125 119 places worse
0.9782 ±0.0028
best reported
actual #6 vs paper #125 119 places worse
paper 0.9540 ±0.0008
paper 0.9540 ±0.0008 Δ at pub 0.0242
9
GCN
actual #9 vs paper #76 67 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #76 67 places worse
paper 0.9575 ±0.0005
paper 0.9575 ±0.0005 Δ at pub 0.0199
17
SAGE
0.9739 ±0.0018
52
GREET
actual #52 vs paper #55 3 places worse
0.9613 ±0.0012
best reported
actual #52 vs paper #55 3 places worse
paper 0.9605 ±0.0012

Difference within reported uncertainty; not counted as underperformance.

paper 0.9605 ±0.0012 Δ at pub 0.0008
58
MLP
0.9597 ±0.0007
63
GCA
actual #63 vs paper #160 97 places worse
0.9590 ±0.0020
best reported
actual #63 vs paper #160 97 places worse
paper 0.9496 ±0.0025
paper 0.9496 ±0.0025 Δ at pub 0.0094
67
CL
0.9581 ±0.0006
This paper
68
GRACE +PiNGDA
0.9581 ±0.0005
This paper
69
BGRL
actual #69 vs paper #109 40 places worse
0.9580 ±0.0040
best reported
actual #69 vs paper #109 40 places worse
paper 0.9554 ±0.0006

Difference within reported uncertainty; not counted as underperformance.

paper 0.9554 ±0.0006 Δ at pub 0.0026
77
GRACE
actual #77 vs paper #77
0.9574 ±0.0006
actual #77 vs paper #77
paper 0.9574 ±0.0006

Improvement within reported uncertainty; not highlighted.

paper 0.9574 ±0.0006 Δ at pub 0.0011
80
Sp2GCL +PiNGDA
0.9574 ±0.0004
This paper
81
Sp2GCL
0.9573 ±0.0004
This paper
94
SGRL
0.9564 ±0.0010
This paper
97
AD-GCL
actual #97 vs paper #97
0.9563 ±0.0010
actual #97 vs paper #97
paper 0.9563 ±0.0010
paper 0.9563 ±0.0010 Δ at pub 0.0106
161
GASSL
0.9493 ±0.0021
This paper
173
GOUDA
0.9454 ±0.0059
This paper
184
JOAO
0.9430 ±0.0038
This paper
187
GRACEIS
0.9428 ±0.0043
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
178
AD-GCL
actual #178 vs paper #213 35 places worse
0.9028 ±0.0401
best reported
actual #178 vs paper #213 35 places worse
paper 0.8970 ±0.0103

Difference within reported uncertainty; not counted as underperformance.

paper 0.8970 ±0.0103 Δ at pub 0.0058
213
CL
0.8971 ±0.0073
This paper
356
RU-GIN
0.8761 ±0.0039
This paper
403
MLP
0.8660 ±0.0495
#ModelAccuracy ↑Paper
1
WL-MLP
0.9954
2
GIN
0.9934
3
GCN
0.9727
104
GraphCL
actual #104 vs paper #503 399 places worse
0.8250 ±0.0013
best reported
actual #104 vs paper #503 399 places worse
paper 0.6854 ±0.0055
paper 0.6854 ±0.0055 Δ at pub 0.1396
131
GraphSAGE
0.8200 ±0.0100
338
InfoGraph
actual #338 vs paper #505 167 places worse
0.7750 ±0.0074
best reported
actual #338 vs paper #505 167 places worse
paper 0.6813 ±0.0059
paper 0.6813 ±0.0059 Δ at pub 0.0937
409
AD-GCL
actual #409 vs paper #489 80 places worse
0.7518 ±0.0031
best reported
actual #409 vs paper #489 80 places worse
paper 0.6967 ±0.0051
paper 0.6967 ±0.0051 Δ at pub 0.0551 Δ today 0.0551
494
CL
0.6935 ±0.0063
This paper
523
RU-GIN
actual #523 vs paper #538 15 places worse
0.6540 ±0.0017
best reported
actual #523 vs paper #538 15 places worse
paper 0.6298 ±0.0010
paper 0.6298 ±0.0010 Δ at pub 0.0242
#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 #68 45 places worse
0.9169 ±0.0070
best reported
actual #23 vs paper #68 45 places worse
paper 0.8263 ±0.0099
paper 0.8263 ±0.0099 Δ at pub 0.0906
37
AD-GCL
actual #37 vs paper #62 25 places worse
0.9010 ±0.0015
best reported
actual #37 vs paper #62 25 places worse
paper 0.8552 ±0.0079
paper 0.8552 ±0.0079 Δ at pub 0.0458
46
InfoGraph
actual #46 vs paper #72 26 places worse
0.8939 ±0.0181
best reported
actual #46 vs paper #72 26 places worse
paper 0.7879 ±0.0214
paper 0.7879 ±0.0214 Δ at pub 0.1060
67
CL
0.8399 ±0.0034
This paper
78
RU-GIN
actual #78 vs paper #87 9 places worse
0.7686 ±0.0025
best reported
actual #78 vs paper #87 9 places worse
paper 0.5897 ±0.0013
paper 0.5897 ±0.0013 Δ at pub 0.1789

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
101
GREET
actual #101 vs paper #461 360 places worse
0.8703 ±0.0236
best reported
actual #101 vs paper #461 360 places worse
paper 0.6279 ±0.0257
211
GAT
actual #211 vs paper #559 348 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #559 348 places worse
paper 0.5619 ±0.0216
paper 0.5619 ±0.0216 Δ at pub 0.2463 Δ today 0.2543
257
GCN
actual #257 vs paper #546 289 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #546 289 places worse
paper 0.5769 ±0.0446
best at pub: Graph Wave Networks (WWW 2025)
paper 0.5769 ±0.0446 Δ at pub 0.2164
304
DGI
actual #304 vs paper #548 244 places worse
0.7581 ±0.0503
best reported
actual #304 vs paper #548 244 places worse
paper 0.5755 ±0.0294
409
BGRL
actual #409 vs paper #571 162 places worse
0.6841 ±0.0501
best reported
actual #409 vs paper #571 162 places worse
paper 0.5488 ±0.0335
439
CL
0.6531 ±0.0129
This paper
468
JOAO
actual #468 vs paper #468
0.6245 ±0.0296
actual #468 vs paper #468
paper 0.6245 ±0.0296

Improvement within reported uncertainty; not highlighted.

paper 0.6245 ±0.0296 Δ at pub 0.0539
479
GRACEIS
0.6190 ±0.0240
This paper
492
AD-GCL
0.6082 ±0.0249
This paper
500
SGRL
0.6000 ±0.0027
This paper
515
GCA
actual #515 vs paper #532 17 places worse
0.5946
best reported
actual #515 vs paper #532 17 places worse
paper 0.5857 ±0.0210

Difference within reported uncertainty; not counted as underperformance.

paper 0.5857 ±0.0210 Δ at pub 0.0089
579
GMI
actual #579 vs paper #586 7 places worse
0.5049
best reported
actual #579 vs paper #586 7 places worse
paper 0.4898 ±0.0360

Difference within reported uncertainty; not counted as underperformance.

paper 0.4898 ±0.0360 Δ at pub 0.0151
#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
88
GREET
actual #88 vs paper #467 379 places worse
0.8514 ±0.0487
best reported
actual #88 vs paper #467 379 places worse
paper 0.5190 ±0.0247
138
SAGE
0.8269
158
GAT
actual #158 vs paper #509 351 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #509 351 places worse
paper 0.4762 ±0.0406
paper 0.4762 ±0.0406 Δ at pub 0.3428
170
GCN
actual #170 vs paper #502 332 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #502 332 places worse
paper 0.4844 ±0.0482
paper 0.4844 ±0.0482 Δ at pub 0.3171 Δ today 0.3238
350
DGI
actual #350 vs paper #508 158 places worse
0.6335
best reported
actual #350 vs paper #508 158 places worse
paper 0.4789 ±0.0205
415
BGRL
actual #415 vs paper #563 148 places worse
0.5730
best reported
actual #415 vs paper #563 148 places worse
paper 0.3515 ±0.1043
427
GCA
actual #427 vs paper #509 82 places worse
0.5541
best reported
actual #427 vs paper #509 82 places worse
paper 0.4745 ±0.0088
429
GMI
actual #429 vs paper #550 121 places worse
0.5476
best reported
actual #429 vs paper #550 121 places worse
paper 0.4109 ±0.0524
455
CL
0.5306 ±0.0105
This paper
477
JOAO
actual #477 vs paper #477
0.5102 ±0.0096
actual #477 vs paper #477
paper 0.5102 ±0.0096

Improvement within reported uncertainty; not highlighted.

paper 0.5102 ±0.0096 Δ at pub 0.1089
488
SGRL
0.5007 ±0.0033
This paper
493
AD-GCL
0.4952 ±0.0293
This paper
502
GRACEIS
0.4857 ±0.0195
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 at pub — reported value improved over the best known when published Best today — OK at publication; today's leaderboard best is elsewhere