AAAI 2023

Feature Transportation Improves Graph Neural Networks

Moshe Eliasof, E. Haber, Eran Treister

Main figure for Feature Transportation Improves Graph Neural Networks

Abstract

Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we propose a novel GNN architecture inspired by Advection-Diffusion-Reaction systems, called ADR-GNN. Advection models feature transportation, while diffusion captures the local smoothing of features, and reaction represents the non-linear transformation between feature channels. We provide an analysis of the qualitative behavior of ADR-GNN, that shows the benefit of combining advection, diffusion, and reaction. To demonstrate its efficacy, we evaluate ADR-GNN on real-world node classification and spatio-temporal datasets, and show that it improves or offers competitive performance compared to state-of-the-art networks.

Benchmark Results

Tested on 8 datasets 30 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
actual #21 vs paper #195 174 places worse
0.9004
best reported
actual #21 vs paper #195 174 places worse
paper 0.8577
paper 0.8577 Δ at pub 0.0140 Δ today 0.0427
32
ADR-GNN_S
0.8943
This paper
39
SAGE
0.8911 ±0.0012
42
C&S
0.8905
This paper
44
GAT
actual #44 vs paper #175 131 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #175 131 places worse
paper 0.8637
45
GCNII
actual #45 vs paper #66 21 places worse
0.8893 ±0.0137
best reported
actual #45 vs paper #66 21 places worse
paper 0.8849
best at pub: Orthogonal Graph Neural Networks (AAAI 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8849 Δ today 0.0044
51
H2GCN
actual #51 vs paper #107 56 places worse
0.8787
actual #51 vs paper #107 56 places worse
paper 0.8787

Improvement within reported uncertainty; not highlighted.

paper 0.8787 Δ at pub 0.0018 Δ today 0.0095
55
JKNet
actual #55 vs paper #218 163 places worse
0.8870
best reported
actual #55 vs paper #218 163 places worse
paper 0.8525
paper 0.8525 Δ at pub 0.0345
60
PDE-GCN
0.8860
This paper
62
GREAD
0.8857
This paper
80
ACMII
0.8825
This paper
82
WRGAT
actual #82 vs paper #82
0.8820
actual #82 vs paper #82
paper 0.8820

Improvement within reported uncertainty; not highlighted.

paper 0.8820 Δ at pub 0.0025
87
GRAND
actual #87 vs paper #87
0.8815
actual #87 vs paper #87
paper 0.8815
prev best: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.8815 Δ at pub 0.0455
96
GRAFF
0.8801
This paper
103
GGCN
0.8795
This paper
108
APPNP
0.8787
This paper
113
MixHop
0.8761
This paper
138
NSD
0.8714
This paper
168
DMP
0.8652
This paper
170
FLODE
actual #170 vs paper #713 543 places worse
0.8644 ±0.0117
best reported
actual #170 vs paper #713 543 places worse
paper 0.7807
207
Geom-GCN
actual #207 vs paper #214 7 places worse
0.8540 ±0.0040
best reported
actual #207 vs paper #214 7 places worse
paper 0.8527
paper 0.8527 Δ at pub 0.0003 Δ today 0.0013
243
LINKX
0.8464
This paper
724
MLP
0.7768
734
Ord. GNN
0.7731
This paper
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
8
Ord. GNN
0.9015
This paper
12
FLODE
0.8902
This paper
20
APPNP
actual #20 vs paper #122 102 places worse
0.8142 ±0.0026
best reported
actual #20 vs paper #122 102 places worse
paper 0.7653
paper 0.7653 Δ at pub 0.0489
35
GAT
actual #35 vs paper #209 174 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #209 174 places worse
paper 0.7432
paper 0.7432 Δ at pub 0.0648
36
GCNII
actual #36 vs paper #108 72 places worse
0.8076 ±0.0030
best reported
actual #36 vs paper #108 72 places worse
paper 0.7713
paper 0.7713 Δ at pub 0.0363
44
GCN
actual #44 vs paper #257 213 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #257 213 places worse
paper 0.7368
61
GraphSAGE
0.7923 ±0.0053
62
JKNet
actual #62 vs paper #145 83 places worse
0.7920
best reported
actual #62 vs paper #145 83 places worse
paper 0.7585
paper 0.7585 Δ at pub 0.0335
79
PDE-GCN
0.7848
This paper
83
ADR-GNN
0.7836
This paper
88
Geom-GCN
actual #88 vs paper #88
0.7799
actual #88 vs paper #88
paper 0.7799

Improvement within reported uncertainty; not highlighted.

paper 0.7799 Δ at pub 0.0171
99
GREAD
0.7760
This paper
104
GRAFF
0.7730
This paper
107
NSD
0.7714
This paper
108
GGCN
0.7714
This paper
109
ACMII
0.7712
This paper
111
H2GCN
0.7711
This paper
117
DMP
0.7687
This paper
119
WRGAT
0.7681
This paper
122
GRAND
actual #122 vs paper #122
0.7657
actual #122 vs paper #122
paper 0.7657
paper 0.7657 Δ at pub 0.0247
126
MixHop
actual #126 vs paper #126
0.7626
actual #126 vs paper #126
paper 0.7626
paper 0.7626 Δ at pub 0.0486
127
C&S
0.7622
This paper
312
LINKX
actual #312 vs paper #312
0.7319
actual #312 vs paper #312
paper 0.7319
350
MLP
0.7289 ±0.0010
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
16
H2GCN
actual #16 vs paper #87 71 places worse
0.9361 ±0.0013
best reported
actual #16 vs paper #87 71 places worse
paper 0.8949
17
APPNP
actual #17 vs paper #90 73 places worse
0.9355 ±0.0060
best reported
actual #17 vs paper #90 73 places worse
paper 0.8940
18
GCN
actual #18 vs paper #156 138 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #156 138 places worse
paper 0.8813
20
GAT
actual #20 vs paper #180 160 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #180 160 places worse
paper 0.8762
24
JKNet
actual #24 vs paper #112 88 places worse
0.9160
best reported
actual #24 vs paper #112 88 places worse
paper 0.8894
paper 0.8894 Δ at pub 0.0266
52
ADR-GNN_S
0.9055
This paper
58
GCNII
actual #58 vs paper #58
0.9030
actual #58 vs paper #58
paper 0.9030
paper 0.9030 Δ at pub 0.1000
62
GREAD
0.9023
This paper
69
Geom-GCN
0.9005
This paper
70
MixHop
actual #70 vs paper #247 177 places worse
0.8531
actual #70 vs paper #247 177 places worse
paper 0.8531

Improvement within reported uncertainty; not highlighted.

paper 0.8531 Δ at pub 0.0021 Δ today 0.0473
71
GRAFF
0.9004
This paper
74
PDE-GCN
0.8993
This paper
81
C&S
0.8974
This paper
82
ACMII
0.8971
This paper
88
NSD
0.8949
This paper
96
DMP
0.8927
This paper
98
GGCN
0.8915
This paper
109
GRAND
actual #109 vs paper #109
0.8902
actual #109 vs paper #109
paper 0.8902
prev best: Framelet Message Passing (2023)
paper 0.8902 Δ at pub 0.0932
116
SAGE
0.8881 ±0.0015
129
WRGAT
0.8852
This paper
138
Ord. GNN
0.8837
This paper
162
LINKX
actual #162 vs paper #162
0.8786
actual #162 vs paper #162
paper 0.8786
210
MLP
0.8690 ±0.0074
224
FLODE
0.8644
This paper

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
18
ADR-GNN_S
0.9361 ±0.0426
This paper
34
MLP
0.9230 ±0.0070
39
GGCN
actual #39 vs paper #148 109 places worse
0.9213 ±0.0305
best reported
actual #39 vs paper #148 109 places worse
paper 0.8486 ±0.0455
best today: Graph Wave Networks (WWW 2025)
paper 0.8486 ±0.0455 Δ today 0.0727
40
H2GCN
actual #40 vs paper #148 108 places worse
0.9189 ±0.0393
best reported
actual #40 vs paper #148 108 places worse
paper 0.8486 ±0.0723

Difference within reported uncertainty; not counted as underperformance.

paper 0.8486 ±0.0723 Δ at pub 0.0104 Δ today 0.0703
53
GraphSAGE
0.9000 ±0.0365
61
FAGCN
actual #61 vs paper #193 132 places worse
0.8961 ±0.0152
best reported
actual #61 vs paper #193 132 places worse
paper 0.8243 ±0.0287
paper 0.8243 ±0.0287 Δ at pub 0.0718
70
GCNII
actual #70 vs paper #398 328 places worse
0.8918 ±0.0443
best reported
actual #70 vs paper #398 328 places worse
paper 0.6946 ±0.0383
paper 0.6946 ±0.0383 Δ at pub 0.1100 Δ today 0.1972
82
GRAFF
0.8838 ±0.0453
This paper
83
ACMII-GCN
0.8838 ±0.0343
This paper
96
G^2
0.8757 ±0.0386
This paper
115
ACMP-GCN
0.8620 ±0.0300
This paper
121
NSD
0.8595 ±0.0551
This paper
181
MagNet
actual #181 vs paper #181
0.8330 ±0.0610
actual #181 vs paper #181
paper 0.8330 ±0.0610

Improvement within reported uncertainty; not highlighted.

paper 0.8330 ±0.0610 Δ at pub 0.0090
211
GAT
actual #211 vs paper #533 322 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #533 322 places worse
paper 0.5838 ±0.0663
paper 0.5838 ±0.0663 Δ at pub 0.2142 Δ today 0.2324
217
GRAND
actual #217 vs paper #308 91 places worse
0.8140 ±0.0350
best reported
actual #217 vs paper #308 91 places worse
paper 0.7568 ±0.0725

Difference within reported uncertainty; not counted as underperformance.

paper 0.7568 ±0.0725 Δ today 0.0572
257
GCN
actual #257 vs paper #576 319 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #576 319 places worse
paper 0.5216 ±0.0516
best today: Graph Wave Networks (WWW 2025)
paper 0.5216 ±0.0516 Δ at pub 0.2624 Δ today 0.2717
325
LINKX
0.7460 ±0.0837
This paper
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
38
GCNII
actual #38 vs paper #290 252 places worse
0.4082 ±0.0179
best reported
actual #38 vs paper #290 252 places worse
paper 0.3287 ±0.0130
paper 0.3287 ±0.0130 Δ at pub 0.0574 Δ today 0.0795
42
MLP
0.4026 ±0.0108
52
GPRGNN
actual #52 vs paper #247 195 places worse
0.3992 ±0.0067
best reported
actual #52 vs paper #247 195 places worse
paper 0.3463 ±0.0122
paper 0.3463 ±0.0122 Δ at pub 0.0529 Δ today 0.0529
56
FAGCN
actual #56 vs paper #240 184 places worse
0.3970
best reported
actual #56 vs paper #240 184 places worse
paper 0.3487 ±0.0135
paper 0.3487 ±0.0135 Δ at pub 0.0483
62
GGCN
actual #62 vs paper #99 37 places worse
0.3781 ±0.0156
actual #62 vs paper #99 37 places worse
paper 0.3781 ±0.0156

Improvement within reported uncertainty; not highlighted.

paper 0.3781 ±0.0156 Δ at pub 0.0027
65
ADR-GNN_S
0.3916 ±0.0113
This paper
68
GraphSAGE
0.3899 ±0.0085
71
H2GCN
actual #71 vs paper #198 127 places worse
0.3885 ±0.0117
best reported
actual #71 vs paper #198 127 places worse
paper 0.3570 ±0.0100
paper 0.3570 ±0.0100 Δ at pub 0.0270 Δ today 0.0315
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
87
Geom-GCN
actual #87 vs paper #305 218 places worse
0.3810
best reported
actual #87 vs paper #305 218 places worse
paper 0.3163 ±0.0115
paper 0.3163 ±0.0115 Δ at pub 0.0647
100
NSD
actual #100 vs paper #105 5 places worse
0.3781 ±0.0115
best reported
actual #100 vs paper #105 5 places worse
paper 0.3779 ±0.0115
best today: Graph Parsing Networks (ICLR 2024)

Difference within reported uncertainty; not counted as underperformance.

paper 0.3779 ±0.0115 Δ today 0.0002
118
G^2
0.3730 ±0.0101
This paper
129
GRAFF
0.3711 ±0.0108
This paper
131
ACMII-GCN
0.3709 ±0.0132
This paper
135
GCN
actual #135 vs paper #411 276 places worse
0.3690
best reported
actual #135 vs paper #411 276 places worse
paper 0.2686 ±0.0110
paper 0.2686 ±0.0110 Δ at pub 0.1004
162
MixHop
actual #162 vs paper #297 135 places worse
0.3648 ±0.0120
best reported
actual #162 vs paper #297 135 places worse
paper 0.3222 ±0.0234
paper 0.3222 ±0.0234 Δ at pub 0.0426
180
LINKX
0.3610 ±0.0155
This paper
182
GAT
actual #182 vs paper #385 203 places worse
0.3605 ±0.0035
best reported
actual #182 vs paper #385 203 places worse
paper 0.2845 ±0.0089
paper 0.2845 ±0.0089 Δ at pub 0.0760
203
GRAND
0.3562 ±0.0101
This paper
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
15
ADR-GNN_S
0.7254 ±0.0220
This paper
26
ACMII-GCN
0.6740 ±0.0221
This paper
31
G^2
0.6426 ±0.0238
This paper
39
H2GCN
actual #39 vs paper #202 163 places worse
0.6190 ±0.0140
best reported
actual #39 vs paper #202 163 places worse
paper 0.3648 ±0.0186
paper 0.3648 ±0.0186 Δ at pub 0.0427 Δ today 0.2542
40
LINKX
0.6181 ±0.0180
This paper
46
GCN
actual #46 vs paper #267 221 places worse
0.6067
best reported
actual #46 vs paper #267 221 places worse
paper 0.2396 ±0.0201
paper 0.2396 ±0.0201 Δ at pub 0.3174 Δ today 0.3671
53
GRAFF
0.5901 ±0.0131
This paper
65
NSD
0.5634 ±0.0132
This paper
67
GAT
actual #67 vs paper #241 174 places worse
0.5630 ±0.0220
best reported
actual #67 vs paper #241 174 places worse
paper 0.3003 ±0.0155
paper 0.3003 ±0.0155 Δ at pub 0.2627
69
GGCN
actual #69 vs paper #71 2 places worse
0.5567 ±0.0187
best reported
actual #69 vs paper #71 2 places worse
paper 0.5517 ±0.0158

Difference within reported uncertainty; not counted as underperformance.

paper 0.5517 ±0.0158 Δ today 0.0050
76
GPRGNN
actual #76 vs paper #235 159 places worse
0.5435 ±0.0087
best reported
actual #76 vs paper #235 159 places worse
paper 0.3161 ±0.0124
paper 0.3161 ±0.0124 Δ at pub 0.1854 Δ today 0.2274
96
WRGAT
0.4885 ±0.0078
This paper
120
SAGE
0.4460 ±0.0130
127
MixHop
0.4380 ±0.0148
This paper
139
FAGCN
0.4259 ±0.0069
This paper
164
GRAND
0.4005 ±0.0150
This paper
172
MLP
0.3930 ±0.0079
176
GCNII
actual #176 vs paper #178 2 places worse
0.3881 ±0.0197
best reported
actual #176 vs paper #178 2 places worse
paper 0.3847 ±0.0158

Difference within reported uncertainty; not counted as underperformance.

paper 0.3847 ±0.0158 Δ today 0.0034
179
Geom-GCN
actual #179 vs paper #179
0.3832 ±0.0092
actual #179 vs paper #179
paper 0.3832 ±0.0092

Improvement within reported uncertainty; not highlighted.

paper 0.3832 ±0.0092 Δ at pub 0.0017

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
LargeScaleNet
0.6582 ±0.0036
2
S² DirGCN
0.6495 ±0.0033
3
FaberNet
0.6462 ±0.0101
6
G^2
0.6330 ±0.0184
This paper
8
ADR-GNN_S
0.6117 ±0.0154
This paper
30
L Prop (2 hop)
0.4607 ±0.0015
This paper
31
GCN
0.4602 ±0.0026
40
C&S (2 hop)
0.4217 ±0.0027
This paper
56
MLP
0.3670 ±0.0021
59
SGC (2 hop)
0.3227 ±0.0006
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