IJCAI 2025

Negative Metric Learning for Graphs

Yiyang Zhao, Chengpei Wu, Lili Zhang, Ning Yang

Main figure for Negative Metric Learning for Graphs

Abstract

Graph contrastive learning (GCL) often suffers from false negatives, which degrades the performance on downstream tasks. The existing methods addressing the false negative issue usually rely on human prior knowledge, still leading GCL to suboptimal results. In this paper, we propose a novel Negative Metric Learning (NML) enhanced GCL (NML-GCL). NML-GCL employs a learnable Negative Metric Network (NMN) to build a negative metric space, in which false negatives can be distinguished better from true negatives based on their distance to anchor node. To overcome the lack of explicit supervision signals for NML, we propose a joint training scheme with bi-level optimization objective, which implicitly utilizes the self-supervision signals to iteratively optimize the encoder and the negative metric network. The solid theoretical analysis and the extensive experiments conducted on widely used benchmarks verify the superiority of the proposed method.

Proposed method: NML-GCL

Benchmark Results

Tested on 4 datasets 16 baseline values reported too low

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

Classic

#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
0.8033 ±0.0088
87
MVGRL
actual #87 vs paper #596 509 places worse
0.7808 ±0.0006
best reported
actual #87 vs paper #596 509 places worse
paper 0.7046 ±0.0023
136
BGRL
actual #136 vs paper #436 300 places worse
0.7600 ±0.0020
best reported
actual #136 vs paper #436 300 places worse
paper 0.7227 ±0.0026
paper 0.7227 ±0.0026 Δ at pub 0.0373
201
GRACE
actual #201 vs paper #587 386 places worse
0.7450 ±0.0010
best reported
actual #201 vs paper #587 386 places worse
paper 0.7057 ±0.0053
paper 0.7057 ±0.0053 Δ at pub 0.0393
291
NML-GCL
0.7337 ±0.0013
This paper
350
MLP
0.7289 ±0.0010
424
GRAPE
0.7234 ±0.0022
This paper
427
HomoGCL
actual #427 vs paper #616 189 places worse
0.7230 ±0.0070
best reported
actual #427 vs paper #616 189 places worse
paper 0.7011 ±0.0079
paper 0.7011 ±0.0079 Δ at pub 0.0219 Δ today 0.0219
477
Local-GCL
0.7178 ±0.0048
This paper
583
ProGCL
actual #583 vs paper #583
0.7063 ±0.0022
actual #583 vs paper #583
paper 0.7063 ±0.0022
paper 0.7063 ±0.0022 Δ at pub 0.0083
594
PHASES
0.7049 ±0.0040
This paper
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
18
GCN
0.9296 ±0.0015
144
BGRL
actual #144 vs paper #524 380 places worse
0.8830 ±0.0010
best reported
actual #144 vs paper #524 380 places worse
paper 0.7941 ±0.0023
paper 0.7941 ±0.0023 Δ at pub 0.0889
194
GRACE
actual #194 vs paper #363 169 places worse
0.8730 ±0.0010
best reported
actual #194 vs paper #363 169 places worse
paper 0.8113 ±0.0031
paper 0.8113 ±0.0031 Δ at pub 0.0617
196
MVGRL
actual #196 vs paper #628 432 places worse
0.8725 ±0.0012
best reported
actual #196 vs paper #628 432 places worse
paper 0.7863 ±0.0027
210
MLP
0.8690 ±0.0074
328
NML-GCL
0.8210 ±0.0030
This paper
365
HomoGCL
actual #365 vs paper #370 5 places worse
0.8110 ±0.0030
best reported
actual #365 vs paper #370 5 places worse
paper 0.8102 ±0.0068

Difference within reported uncertainty; not counted as underperformance.

paper 0.8102 ±0.0068 Δ at pub 0.0008 Δ today 0.0008
370
PHASES
0.8108 ±0.0062
This paper
376
Local-GCL
0.8095 ±0.0041
This paper
557
ProGCL
actual #557 vs paper #664 107 places worse
0.7920 ±0.0020
best reported
actual #557 vs paper #664 107 places worse
paper 0.7814 ±0.0043
paper 0.7814 ±0.0043 Δ at pub 0.0106
#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
113
ProGCL
actual #113 vs paper #254 141 places worse
0.9381 ±0.0048
best reported
actual #113 vs paper #254 141 places worse
paper 0.9271 ±0.0029
paper 0.9271 ±0.0029 Δ at pub 0.0110
172
BGRL
actual #172 vs paper #218 46 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #218 46 places worse
paper 0.9301 ±0.0027

Difference within reported uncertainty; not counted as underperformance.

paper 0.9301 ±0.0027 Δ at pub 0.0036
174
NML-GCL
0.9336 ±0.0021
This paper
188
Local-GCL
actual #188 vs paper #234 46 places worse
0.9325 ±0.0040
best reported
actual #188 vs paper #234 46 places worse
paper 0.9283 ±0.0028
paper 0.9283 ±0.0028 Δ at pub 0.0042
203
GRACE
actual #203 vs paper #253 50 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #253 50 places worse
paper 0.9273 ±0.0035

Difference within reported uncertainty; not counted as underperformance.

paper 0.9273 ±0.0035 Δ at pub 0.0007 Δ today 0.0040
206
MVGRL
actual #206 vs paper #272 66 places worse
0.9310 ±0.0040
best reported
actual #206 vs paper #272 66 places worse
paper 0.9259 ±0.0034

Difference within reported uncertainty; not counted as underperformance.

paper 0.9259 ±0.0034 Δ at pub 0.0051
222
HomoGCL
actual #222 vs paper #308 86 places worse
0.9300 ±0.0020
best reported
actual #222 vs paper #308 86 places worse
paper 0.9231 ±0.0036
paper 0.9231 ±0.0036 Δ at pub 0.0069
243
repl. cosine sim.
0.9280 ±0.0022
This paper
249
GRAPE
0.9276 ±0.0030
This paper
252
PHASES
0.9274 ±0.0037
This paper
390
MLP
0.9128 ±0.0063
#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
79
BGRL
actual #79 vs paper #198 119 places worse
0.9034 ±0.0019
best reported
actual #79 vs paper #198 119 places worse
paper 0.8825 ±0.0030
paper 0.8825 ±0.0030 Δ at pub 0.0209 Δ today 0.0209
135
ProGCL
actual #135 vs paper #212 77 places worse
0.8955 ±0.0016
best reported
actual #135 vs paper #212 77 places worse
paper 0.8790 ±0.0027
paper 0.8790 ±0.0027 Δ at pub 0.0138 Δ today 0.0165
138
Local-GCL
actual #138 vs paper #174 36 places worse
0.8954 ±0.0032
best reported
actual #138 vs paper #174 36 places worse
paper 0.8869 ±0.0050
paper 0.8869 ±0.0050 Δ at pub 0.0085
139
GRACE
actual #139 vs paper #180 41 places worse
0.8953 ±0.0035
best reported
actual #139 vs paper #180 41 places worse
paper 0.8856 ±0.0031
paper 0.8856 ±0.0031 Δ at pub 0.0097 Δ today 0.0097
142
NML-GCL
0.8943 ±0.0025
This paper
157
HomoGCL
actual #157 vs paper #215 58 places worse
0.8900 ±0.0010
best reported
actual #157 vs paper #215 58 places worse
paper 0.8782 ±0.0048
paper 0.8782 ±0.0048 Δ at pub 0.0118
179
MVGRL
actual #179 vs paper #228 49 places worse
0.8861 ±0.0064
best reported
actual #179 vs paper #228 49 places worse
paper 0.8766 ±0.0025

Difference within reported uncertainty; not counted as underperformance.

paper 0.8766 ±0.0025 Δ at pub 0.0095
211
GRAPE
0.8797 ±0.0033
This paper
220
PHASES
0.8780 ±0.0044
This paper
320
MLP
0.8463
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