IJCAI 2023

Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attention

Hongjun Wang, Jiyuan Chen, Lun Du, Qiang Fu, Shi Han, Xuan Song

Main figure for Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attention

Abstract

Recent years have witnessed the great potential of attention mechanism in graph representation learning. However, while variants of attention-based GNNs are setting new benchmarks for numerous real-world datasets, recent works have pointed out that their induced attentions are less robust and generalizable against noisy graphs due to lack of direct supervision. In this paper, we present a new framework which utilizes the tool of causality to provide a powerful supervision signal for the learning process of attention functions. Specifically, we estimate the direct causal effect of attention to the final prediction, and then maximize such effect to guide attention attending to more meaningful neighbors. Our method can serve as a plug-and-play module for any canonical attention-based GNNs in an end-to-end fashion. Extensive experiments on a wide range of benchmark datasets illustrated that, by directly supervising attention functions, the model is able to converge faster with a clearer decision boundary, and thus yields better performances.

Proposed method: GAT

Benchmark Results

Tested on 8 datasets 21 baseline values reported too low

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
44
GAT
actual #44 vs paper #180 136 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #180 136 places worse
paper 0.8621 ±0.0078
paper 0.8621 ±0.0078 Δ at pub 0.0269 Δ today 0.0276
123
UniMP+CSA-I
0.8747 ±0.0087
This paper
151
UniMP
0.8689 ±0.0090
This paper
182
GAT+CSA-I
0.8616 ±0.0095
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
35
GAT
actual #35 vs paper #147 112 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #147 112 places worse
paper 0.7573 ±0.0123
paper 0.7573 ±0.0123 Δ at pub 0.0507
44
GCN
0.8033 ±0.0088
95
GAT+CSA-I
0.7772 ±0.0125
This paper
98
UniMP+CSA-I
0.7761 ±0.0082
This paper
174
UniMP
0.7514 ±0.0068
This paper
350
MLP
0.7289 ±0.0010

OGB

#ModelAccuracy ↑Paper
1
Jacobi
0.8968
2
GPR
0.8953
3
LEMP4HG
0.8939
4
SAGE
0.8933
9
GAT
actual #9 vs paper #230 221 places worse
0.8829
best reported
actual #9 vs paper #230 221 places worse
paper 0.7702 ±0.0063
85
UniMP
actual #85 vs paper #113 28 places worse
0.8256 ±0.0031
best reported
actual #85 vs paper #113 28 places worse
paper 0.8137 ±0.0047
paper 0.8137 ±0.0047 Δ at pub 0.0119 Δ today 0.0119
92
UniMP+CSA-I
0.8224 ±0.0063
This paper
214
GAT+CSA-I
0.7836 ±0.0072
This paper
351
MLP
0.6605 ±0.0020

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
30
GPR-GNN
actual #30 vs paper #253 223 places worse
0.9291 ±0.0132
best reported
actual #30 vs paper #253 223 places worse
paper 0.7944 ±0.0517
paper 0.7944 ±0.0517 Δ at pub 0.1347
34
MLP
actual #34 vs paper #220 186 places worse
0.9230 ±0.0070
best reported
actual #34 vs paper #220 186 places worse
paper 0.8132 ±0.0622
40
H2GCN
actual #40 vs paper #153 113 places worse
0.9189 ±0.0393
best reported
actual #40 vs paper #153 113 places worse
paper 0.8481 ±0.0694
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8481 ±0.0694 Δ at pub 0.0009 Δ today 0.0708
46
APPNP
actual #46 vs paper #207 161 places worse
0.9131 ±0.0197
best reported
actual #46 vs paper #207 161 places worse
paper 0.8193 ±0.0577
paper 0.8193 ±0.0577 Δ at pub 0.0925 Δ today 0.0938
53
GraphSAGE
0.9000 ±0.0365
61
FAGCN
actual #61 vs paper #191 130 places worse
0.8961 ±0.0152
best reported
actual #61 vs paper #191 130 places worse
paper 0.8254 ±0.0689

Difference within reported uncertainty; not counted as underperformance.

paper 0.8254 ±0.0689 Δ at pub 0.0707
104
WRGAT
actual #104 vs paper #173 69 places worse
0.8698
best reported
actual #104 vs paper #173 69 places worse
paper 0.8362 ±0.0550

Difference within reported uncertainty; not counted as underperformance.

paper 0.8362 ±0.0550 Δ today 0.0336
148
WRGAT+CSA-I
0.8488 ±0.0523
This paper
154
FAGCN+CSA-I
0.8472 ±0.0671
This paper
211
GAT
actual #211 vs paper #568 357 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #568 357 places worse
paper 0.5521 ±0.0570
paper 0.5521 ±0.0570 Δ at pub 0.2459 Δ today 0.2641
257
GCN
actual #257 vs paper #562 305 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #562 305 places worse
paper 0.5559 ±0.0596
best today: Graph Wave Networks (WWW 2025)
paper 0.5559 ±0.0596 Δ at pub 0.2281 Δ today 0.2374
469
SGCN
actual #469 vs paper #557 88 places worse
0.6243 ±0.0443
best reported
actual #469 vs paper #557 88 places worse
paper 0.5641 ±0.0429

Difference within reported uncertainty; not counted as underperformance.

paper 0.5641 ±0.0429 Δ at pub 0.0602
535
CSA
0.5821 ±0.0479
This paper
541
GAT+CSA-I
0.5804 ±0.0527
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
0.9480 ±0.0380
3
RF-GCN
0.9429
11
GPR-GNN
actual #11 vs paper #182 171 places worse
0.9279 ±0.0312
best reported
actual #11 vs paper #182 171 places worse
paper 0.7991 ±0.0660
paper 0.7991 ±0.0660 Δ at pub 0.1288
21
APPNP
actual #21 vs paper #157 136 places worse
0.9181 ±0.0196
best reported
actual #21 vs paper #157 136 places worse
paper 0.8192 ±0.0612
paper 0.8192 ±0.0612 Δ at pub 0.0989
24
MLP
actual #24 vs paper #115 91 places worse
0.9136 ±0.0070
best reported
actual #24 vs paper #115 91 places worse
paper 0.8392 ±0.0588

Difference within reported uncertainty; not counted as underperformance.

paper 0.8392 ±0.0588 Δ at pub 0.0744
38
FAGCN
actual #38 vs paper #185 147 places worse
0.8852 ±0.0133
best reported
actual #38 vs paper #185 147 places worse
paper 0.7924 ±0.0992

Difference within reported uncertainty; not counted as underperformance.

paper 0.7924 ±0.0992 Δ at pub 0.0928
68
H2GCN
actual #68 vs paper #155 87 places worse
0.8623 ±0.0471
best reported
actual #68 vs paper #155 87 places worse
paper 0.8208 ±0.0471
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8208 ±0.0471 Δ at pub 0.0062 Δ today 0.0415
138
SAGE
0.8269
145
WRGAT+CSA-I
0.8243 ±0.0400
This paper
158
GAT
actual #158 vs paper #358 200 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #358 200 places worse
paper 0.6189 ±0.0608
paper 0.6189 ±0.0608 Δ at pub 0.2001
160
WRGAT
0.8162 ±0.0390
This paper
169
FAGCN+CSA-I
0.8094 ±0.0977
This paper
170
GCN
actual #170 vs paper #375 205 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #375 205 places worse
paper 0.6001 ±0.0567
paper 0.6001 ±0.0567 Δ at pub 0.1919 Δ today 0.2081
341
CSA
0.6426 ±0.0521
This paper
348
GAT+CSA-I
0.6358 ±0.0603
This paper
356
SGCN
actual #356 vs paper #356
0.6252 ±0.0510
actual #356 vs paper #356
paper 0.6252 ±0.0510

Improvement within reported uncertainty; not highlighted.

paper 0.6252 ±0.0510 Δ at pub 0.0009
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
41
APPNP
actual #41 vs paper #190 149 places worse
0.4046 ±0.0064
best reported
actual #41 vs paper #190 149 places worse
paper 0.3590 ±0.0096
paper 0.3590 ±0.0096 Δ at pub 0.0400 Δ today 0.0456
42
MLP
actual #42 vs paper #181 139 places worse
0.4026 ±0.0108
best reported
actual #42 vs paper #181 139 places worse
paper 0.3609 ±0.0135
paper 0.3609 ±0.0135 Δ at pub 0.0417
53
GPR-GNN
actual #53 vs paper #229 176 places worse
0.3992 ±0.0067
best reported
actual #53 vs paper #229 176 places worse
paper 0.3511 ±0.0082
paper 0.3511 ±0.0082 Δ at pub 0.0480 Δ today 0.0481
56
FAGCN
actual #56 vs paper #240 184 places worse
0.3970
best reported
actual #56 vs paper #240 184 places worse
paper 0.3485 ±0.0124
paper 0.3485 ±0.0124 Δ at pub 0.0485
68
GraphSAGE
0.3899 ±0.0085
71
H2GCN
actual #71 vs paper #193 122 places worse
0.3885 ±0.0117
best reported
actual #71 vs paper #193 122 places worse
paper 0.3583 ±0.0096
paper 0.3583 ±0.0096 Δ at pub 0.0257 Δ today 0.0302
75
WRGAT
actual #75 vs paper #158 83 places worse
0.3860 ±0.0110
best reported
actual #75 vs paper #158 83 places worse
paper 0.3653 ±0.0077
paper 0.3653 ±0.0077 Δ at pub 0.0207
135
GCN
actual #135 vs paper #387 252 places worse
0.3690
best reported
actual #135 vs paper #387 252 places worse
paper 0.2840 ±0.0088
paper 0.2840 ±0.0088 Δ at pub 0.0850
137
WRGAT+CSA-I
0.3689 ±0.0072
This paper
228
FAGCN+CSA-I
0.3512 ±0.0098
This paper
337
SGCN
0.3050 ±0.0094
This paper
359
GAT+CSA-I
0.2972 ±0.0086
This paper
#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
actual #3 vs paper #139 136 places worse
0.8560
best reported
actual #3 vs paper #139 136 places worse
paper 0.5932 ±0.0154
24
GPR-GNN
actual #24 vs paper #215 191 places worse
0.7830 ±0.0060
best reported
actual #24 vs paper #215 191 places worse
paper 0.4676 ±0.0210
paper 0.4676 ±0.0210 Δ at pub 0.2302 Δ today 0.3154
52
GCN
actual #52 vs paper #118 66 places worse
0.7033
best reported
actual #52 vs paper #118 66 places worse
paper 0.6154 ±0.0259
paper 0.6154 ±0.0259 Δ at pub 0.0606 Δ today 0.0879
79
APPNP
actual #79 vs paper #148 69 places worse
0.6670 ±0.0270
best reported
actual #79 vs paper #148 69 places worse
paper 0.5780 ±0.0247
paper 0.5780 ±0.0247 Δ at pub 0.0890
86
WRGAT+CSA-I
0.6536 ±0.0105
This paper
91
WRGAT
0.6524 ±0.0087
This paper
107
FAGCN
actual #107 vs paper #120 13 places worse
0.6344 ±0.0205
best reported
actual #107 vs paper #120 13 places worse
paper 0.6121 ±0.0313

Difference within reported uncertainty; not counted as underperformance.

paper 0.6121 ±0.0313 Δ at pub 0.0223
108
SAGE
0.6340 ±0.0300
117
FAGCN+CSA-I
0.6186 ±0.0298
This paper
126
SGCN
0.6089 ±0.0221
This paper
127
GAT+CSA-I
0.6073 ±0.0135
This paper
133
H2GCN
actual #133 vs paper #147 14 places worse
0.6030 ±0.0231
best reported
actual #133 vs paper #147 14 places worse
paper 0.5827 ±0.0263

Difference within reported uncertainty; not counted as underperformance.

paper 0.5827 ±0.0263 Δ at pub 0.0203
169
MLP
actual #169 vs paper #217 48 places worse
0.5429
best reported
actual #169 vs paper #217 48 places worse
paper 0.4621 ±0.0289
paper 0.4621 ±0.0289 Δ at pub 0.0199 Δ today 0.0808
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
10
GPR-GNN
actual #10 vs paper #232 222 places worse
0.7480 ±0.0050
best reported
actual #10 vs paper #232 222 places worse
paper 0.3233 ±0.0242
39
H2GCN
actual #39 vs paper #184 145 places worse
0.6190 ±0.0140
best reported
actual #39 vs paper #184 145 places worse
paper 0.3795 ±0.0189
paper 0.3795 ±0.0189 Δ at pub 0.0280 Δ today 0.2395
46
GCN
actual #46 vs paper #77 31 places worse
0.6067
best reported
actual #46 vs paper #77 31 places worse
paper 0.5398 ±0.0153
paper 0.5398 ±0.0153 Δ at pub 0.0172 Δ today 0.0669
67
GAT
actual #67 vs paper #165 98 places worse
0.5630 ±0.0220
best reported
actual #67 vs paper #165 98 places worse
paper 0.4000 ±0.0099
paper 0.4000 ±0.0099 Δ at pub 0.1630
68
APPNP
actual #68 vs paper #173 105 places worse
0.5590 ±0.0290
best reported
actual #68 vs paper #173 105 places worse
paper 0.3908 ±0.0176
paper 0.3908 ±0.0176 Δ at pub 0.1682
79
SGCN
0.5274 ±0.0158
This paper
94
WRGAT+CSA-I
0.4946 ±0.0074
This paper
96
WRGAT
0.4885 ±0.0078
This paper
120
SAGE
0.4460 ±0.0130
139
FAGCN
actual #139 vs paper #139
0.4259 ±0.0069
best reported
actual #139 vs paper #139
paper 0.4255 ±0.0086

Difference within reported uncertainty; not counted as underperformance.

paper 0.4255 ±0.0086 Δ at pub 0.0004 Δ today 0.0004
140
FAGCN+CSA-I
0.4255 ±0.0074
This paper
159
GAT+CSA-I
0.4051 ±0.0098
This paper
172
MLP
actual #172 vs paper #242 70 places worse
0.3930 ±0.0079
best reported
actual #172 vs paper #242 70 places worse
paper 0.2898 ±0.0132
paper 0.2898 ±0.0132 Δ at pub 0.0437 Δ today 0.1032
SOTA performance (not significantly different from the best) 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