Adaptive Negative Scheduling for Graph Contrastive Learning

Adnan Ali, Jinlong Li, Syed Muhammad Israr, Ali Kashif Bashir

Main figure for Adaptive Negative Scheduling for Graph Contrastive Learning

Abstract

Graph contrastive learning (GCL) has become a central paradigm for self-supervised representation learning in computational intelligence, with applications spanning recommendation, anomaly detection, and personalization. A key limitation of existing methods is their reliance on static negative sampling, which fails to account for the dynamic informativeness and computational cost of negatives during training. We propose AdNGCL, an adaptive negative scheduling framework with a hardness-aware scheduler (HANS) that formulates negative selection as a loss-gated, budget-constrained process across hard, intermediate, and easy strata. The scheduler dynamically adjusts step sizes based on contrastive loss trends under both global and per-category budgets, while periodically refreshing samples to maintain diversity without exceeding compute constraints. Experiments on nine benchmark graph datasets demonstrate that AdNGCL consistently advances state-of-the-art performance—achieving the best accuracy on seven datasets and second-best on the remaining two—while offering explicit control over computational cost. These results highlight the value of budget-aware, loss-sensitive scheduling as a general strategy for improving the robustness and efficiency of representation learning in emerging computational intelligence applications. Code:.

Proposed method: AdNGCL

Benchmark Results

Tested on 9 datasets 24 baseline values reported too low Non-standard metric on 1 dataset

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

Classic

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
0.9004
92
AdNGCL
0.8805 ±0.0093
This paper
126
NegAmp.
0.8743 ±0.0032
This paper
130
BGRL
actual #130 vs paper #314 184 places worse
0.8730 ±0.0010
best reported
actual #130 vs paper #314 184 places worse
paper 0.8383 ±0.0161
paper 0.8383 ±0.0161 Δ at pub 0.0347
134
GRACE
actual #134 vs paper #389 255 places worse
0.8720 ±0.0020
best reported
actual #134 vs paper #389 255 places worse
paper 0.8330 ±0.0040
paper 0.8330 ±0.0040 Δ at pub 0.0390
156
MVGRL
0.8680 ±0.0050
This paper
177
DGI
actual #177 vs paper #456 279 places worse
0.8630 ±0.0020
best reported
actual #177 vs paper #456 279 places worse
paper 0.8260 ±0.0040
paper 0.8260 ±0.0040 Δ at pub 0.0370
190
USGCL
0.8590 ±0.0040
This paper
231
GRAM
0.8490 ±0.0050
This paper
271
COSTA
actual #271 vs paper #271
0.8430 ±0.0020
actual #271 vs paper #271
paper 0.8430 ±0.0020
paper 0.8430 ±0.0020 Δ at pub 0.0100
365
AdaS
0.8351 ±0.0118
This paper
414
AF-GCL
0.8316 ±0.0013
This paper
450
LG2AR
0.8270 ±0.0070
This paper
724
MLP
0.7768
#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
66
DGI
actual #66 vs paper #658 592 places worse
0.7890 ±0.0020
best reported
actual #66 vs paper #658 592 places worse
paper 0.6880 ±0.0070
paper 0.6880 ±0.0070 Δ at pub 0.1010
87
MVGRL
actual #87 vs paper #292 205 places worse
0.7808 ±0.0006
best reported
actual #87 vs paper #292 205 places worse
paper 0.7330 ±0.0050
123
AdNGCL
0.7650 ±0.0105
This paper
136
BGRL
actual #136 vs paper #425 289 places worse
0.7600 ±0.0020
best reported
actual #136 vs paper #425 289 places worse
paper 0.7232 ±0.0089
paper 0.7232 ±0.0089 Δ at pub 0.0368
140
NegAmp.
0.7592 ±0.0088
This paper
141
USGCL
0.7590 ±0.0060
This paper
201
GRACE
actual #201 vs paper #446 245 places worse
0.7450 ±0.0010
best reported
actual #201 vs paper #446 245 places worse
paper 0.7210 ±0.0050
paper 0.7210 ±0.0050 Δ at pub 0.0240
314
AdaS
0.7316 ±0.0078
This paper
337
COSTA
actual #337 vs paper #337
0.7290 ±0.0030
actual #337 vs paper #337
paper 0.7290 ±0.0030
paper 0.7290 ±0.0030 Δ at pub 0.0080
343
GRAM
0.7290 ±0.0050
This paper
350
MLP
0.7289 ±0.0010
461
AF-GCL
0.7196 ±0.0042
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 #229 85 places worse
0.8830 ±0.0010
best reported
actual #144 vs paper #229 85 places worse
paper 0.8603 ±0.0033
paper 0.8603 ±0.0033 Δ at pub 0.0227
165
AdNGCL
0.8781 ±0.0041
This paper
194
GRACE
actual #194 vs paper #219 25 places worse
0.8730 ±0.0010
best reported
actual #194 vs paper #219 25 places worse
paper 0.8670 ±0.0010
paper 0.8670 ±0.0010 Δ at pub 0.0060
196
MVGRL
actual #196 vs paper #439 243 places worse
0.8725 ±0.0012
best reported
actual #196 vs paper #439 243 places worse
paper 0.8010 ±0.0070
203
NegAmp.
0.8709 ±0.0005
This paper
204
DGI
actual #204 vs paper #230 26 places worse
0.8708 ±0.0017
best reported
actual #204 vs paper #230 26 places worse
paper 0.8600 ±0.0010
208
COSTA
actual #208 vs paper #226 18 places worse
0.8698 ±0.0033
best reported
actual #208 vs paper #226 18 places worse
paper 0.8620 ±0.0010
210
MLP
0.8690 ±0.0074
260
GRAM
0.8490 ±0.0020
This paper
312
USGCL
0.8270 ±0.0030
This paper
347
LG2AR
0.8150 ±0.0070
This paper
346
AF-GCL
actual #346 vs paper #346
0.8150 ±0.0070
actual #346 vs paper #346
paper 0.8150 ±0.0070
paper 0.8150 ±0.0070 Δ at pub 0.0245
409
AdaS
0.8047 ±0.0194
This paper
#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
51
AdNGCL
0.9511
This paper
91
USGCL
0.9420 ±0.0070
This paper
92
LG2AR
0.9410 ±0.0040
This paper
96
NegAmp.
0.9409 ±0.0039
This paper
113
ProGCL
actual #113 vs paper #128 15 places worse
0.9381 ±0.0048
best reported
actual #113 vs paper #128 15 places worse
paper 0.9364 ±0.0013

Difference within reported uncertainty; not counted as underperformance.

paper 0.9364 ±0.0013 Δ at pub 0.0017
130
AFGRL
actual #130 vs paper #189 59 places worse
0.9361 ±0.0020
best reported
actual #130 vs paper #189 59 places worse
paper 0.9322 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.9322 ±0.0028 Δ at pub 0.0039
149
ABGML
actual #149 vs paper #156 7 places worse
0.9350 ±0.0040
best reported
actual #149 vs paper #156 7 places worse
paper 0.9346 ±0.0036

Difference within reported uncertainty; not counted as underperformance.

paper 0.9346 ±0.0036 Δ at pub 0.0004
172
BGRL
actual #172 vs paper #198 26 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #198 26 places worse
paper 0.9317 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.9317 ±0.0030 Δ at pub 0.0020
191
GCA
actual #191 vs paper #277 86 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #277 86 places worse
paper 0.9253 ±0.0016
203
GRACE
actual #203 vs paper #244 41 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #244 41 places worse
paper 0.9278 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9278 ±0.0045 Δ at pub 0.0035
206
MVGRL
actual #206 vs paper #359 153 places worse
0.9310 ±0.0040
best reported
actual #206 vs paper #359 153 places worse
paper 0.9174 ±0.0007
paper 0.9174 ±0.0007 Δ at pub 0.0136
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 0.9161 ±0.0022
263
COSTA
actual #263 vs paper #275 12 places worse
0.9267 ±0.0016
best reported
actual #263 vs paper #275 12 places worse
paper 0.9256 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9256 ±0.0045 Δ at pub 0.0011
284
AF-GCL
0.9249 ±0.0031
This paper
390
MLP
0.9128 ±0.0063
420
AdaS
0.9063 ±0.0113
This paper
#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
36
AdNGCL
0.9176 ±0.0029
This paper
55
USGCL
0.9100 ±0.0040
This paper
75
NegAmp.
0.9043 ±0.0025
This paper
79
BGRL
0.9034 ±0.0019
This paper
84
ABGML
actual #84 vs paper #86 2 places worse
0.9020 ±0.0030
best reported
actual #84 vs paper #86 2 places worse
paper 0.9017 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.9017 ±0.0030 Δ at pub 0.0003
112
AFGRL
0.8988 ±0.0033
This paper
127
AF-GCL
0.8968 ±0.0019
This paper
131
LG2AR
0.8960 ±0.0030
This paper
135
ProGCL
actual #135 vs paper #135
0.8955 ±0.0016
actual #135 vs paper #135
paper 0.8955 ±0.0016
paper 0.8955 ±0.0016 Δ at pub 0.0027
139
GRACE
0.8953 ±0.0035
This paper
160
GCA
0.8894 ±0.0015
This paper
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 0.8752 ±0.0011
192
COSTA
actual #192 vs paper #193 1 place worse
0.8837 ±0.0022
best reported
actual #192 vs paper #193 1 place worse
paper 0.8832 ±0.0003

Difference within reported uncertainty; not counted as underperformance.

paper 0.8832 ±0.0003 Δ at pub 0.0005
210
DGI
actual #210 vs paper #354 144 places worse
0.8798 ±0.0081
best reported
actual #210 vs paper #354 144 places worse
paper 0.8395 ±0.0047
paper 0.8395 ±0.0047 Δ at pub 0.0403
320
MLP
0.8463
435
AdaS
0.7910 ±0.0165
This paper
#ModelAccuracy ↑Paper
1
GCN
0.9302 ±0.0011
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
56
AdNGCL
0.8293 ±0.0055
This paper
62
NegAmp.
0.8204 ±0.0010
This paper
94
GRACE
0.8014 ±0.0048
This paper
100
BGRL
actual #100 vs paper #100
0.8000 ±0.0010
best reported
actual #100 vs paper #100
paper 0.7998 ±0.0010

Difference within reported uncertainty; not counted as underperformance.

paper 0.7998 ±0.0010 Δ at pub 0.0002 Δ today 0.0002
129
COSTA
0.7912 ±0.0002
This paper
133
AF-GCL
0.7901 ±0.0051
This paper
143
AFGRL
actual #143 vs paper #187 44 places worse
0.7890 ±0.0060
best reported
actual #143 vs paper #187 44 places worse
paper 0.7762 ±0.0049
paper 0.7762 ±0.0049 Δ at pub 0.0128
149
ABGML
0.7870 ±0.0056
This paper
150
ProGCL
0.7868 ±0.0012
This paper
151
DGI
actual #151 vs paper #228 77 places worse
0.7865 ±0.0690
best reported
actual #151 vs paper #228 77 places worse
paper 0.7535 ±0.0014

Difference within reported uncertainty; not counted as underperformance.

paper 0.7535 ±0.0014 Δ at pub 0.0330
162
GCA
actual #162 vs paper #163 1 place worse
0.7840 ±0.0013
best reported
actual #162 vs paper #163 1 place worse
paper 0.7835 ±0.0005

Difference within reported uncertainty; not counted as underperformance.

paper 0.7835 ±0.0005 Δ at pub 0.0005 Δ today 0.0005
184
LG2AR
0.7780 ±0.0050
This paper
190
MVGRL
actual #190 vs paper #191 1 place worse
0.7757 ±0.0046
best reported
actual #190 vs paper #191 1 place worse
paper 0.7752 ±0.0008

Difference within reported uncertainty; not counted as underperformance.

paper 0.7752 ±0.0008 Δ at pub 0.0005 Δ today 0.0005
237
MLP
0.7469 ±0.0085
#ModelAccuracy ↑Paper
1
DoG
0.9690 ±0.0030
2
GWN-fa
0.9667 ±0.0026
3
GWN-sym
0.9666 ±0.0026
6
GraphSAGE
0.9593 ±0.0025
17
USGCL
0.9480 ±0.0050
This paper
22
AdNGCL
0.9430 ±0.0023
This paper
35
ProGCL
0.9367 ±0.0012
This paper
37
LG2AR
0.9360 ±0.0030
This paper
38
ABGML
actual #38 vs paper #40 2 places worse
0.9360 ±0.0020
best reported
actual #38 vs paper #40 2 places worse
paper 0.9356 ±0.0019

Difference within reported uncertainty; not counted as underperformance.

paper 0.9356 ±0.0019 Δ at pub 0.0004
43
DGI
actual #43 vs paper #114 71 places worse
0.9350 ±0.0030
best reported
actual #43 vs paper #114 71 places worse
paper 0.9215 ±0.0063
paper 0.9215 ±0.0063 Δ at pub 0.0135
51
GCA
actual #51 vs paper #63 12 places worse
0.9332 ±0.0012
best reported
actual #51 vs paper #63 12 places worse
paper 0.9310 ±0.0001
53
BGRL
0.9331 ±0.0013
This paper
56
AFGRL
actual #56 vs paper #58 2 places worse
0.9330 ±0.0020
best reported
actual #56 vs paper #58 2 places worse
paper 0.9327 ±0.0017

Difference within reported uncertainty; not counted as underperformance.

paper 0.9327 ±0.0017 Δ at pub 0.0003
59
NegAmp.
0.9326 ±0.0008
This paper
69
GRACE
actual #69 vs paper #148 79 places worse
0.9301 ±0.0003
best reported
actual #69 vs paper #148 79 places worse
paper 0.9112 ±0.0020
paper 0.9112 ±0.0020 Δ at pub 0.0189
76
COSTA
0.9295 ±0.0012
This paper
88
MLP
0.9280 ±0.0020
116
MVGRL
0.9211 ±0.0012
This paper
126
AF-GCL
0.9192 ±0.0010
This paper
133
AdaS
0.9163 ±0.0057
This paper

Heterophilic Graphs

#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
251
GRACE
actual #251 vs paper #340 89 places worse
0.3450 ±0.0110
best reported
actual #251 vs paper #340 89 places worse
paper 0.3033 ±0.0077
paper 0.3033 ±0.0077 Δ at pub 0.0417
324
NegAmp.
0.3114 ±0.0066
This paper
332
AdNGCL
0.3078 ±0.0054
This paper
356
BGRL
actual #356 vs paper #404 48 places worse
0.2986
best reported
actual #356 vs paper #404 48 places worse
paper 0.2764 ±0.0003

Heterogeneous Graph Benchmarks

DBLP

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is Micro-F1. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑Paper
1
HG-SCM
0.9490 ±0.0015
2
SeHGNN
0.9489 ±0.0018
3
AdvSynGNN
0.9486 ±0.0012
34
DGI
actual #34 vs paper #55 21 places worse
0.8800 ±0.0020
best reported
actual #34 vs paper #55 21 places worse
paper 0.8320 ±0.0010
paper 0.8320 ±0.0010 Δ at pub 0.0480
36
GCN
0.8758 ±0.0020
40
AdNGCL
0.8628 ±0.0052
This paper
42
NegAmplify
0.8587 ±0.0005
This paper
50
GRAM
0.8470 ±0.0010
This paper
51
COSTA
0.8450 ±0.0010
This paper
54
GRACE
0.8420 ±0.0010
This paper
55
BGRL
0.8407 ±0.0023
This paper
65
MLP
0.8118 ±0.0020
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