AAAI 2021

Orthogonal Graph Neural Networks

Kai Guo, Kaixiong Zhou, Xia Hu, Yu Li, Yi Chang, Xin Wang

Main figure for Orthogonal Graph Neural Networks

Abstract

Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature information from neighbors. However, stacking more convolutional layers significantly decreases the performance of GNNs. Most recent studies attribute this limitation to the over-smoothing issue, where node embeddings converge to indistinguishable vectors. Through a number of experimental observations, we argue that the main factor degrading the performance is the unstable forward normalization and backward gradient resulted from the improper design of the feature transformation, especially for shallow GNNs where the over-smoothing has not happened. Therefore, we propose a novel orthogonal feature transformation, named Ortho-GConv, which could generally augment the existing GNN backbones to stabilize the model training and improve the model's generalization performance. Specifically, we maintain the orthogonality of the feature transformation comprehensively from three perspectives, namely hybrid weight initialization, orthogonal transformation, and orthogonal regularization. By equipping the existing GNNs (e.g. GCN, JKNet, GCNII) with Ortho-GConv, we demonstrate the generality of the orthogonal feature transformation to enable stable training, and show its effectiveness for node and graph classification tasks.

Benchmark Results

Tested on 5 datasets 17 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
39
SAGE
0.8911 ±0.0012
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
0.8849
actual #45 vs paper #66 21 places worse
paper 0.8849
paper 0.8849 Δ at pub 0.0299
52
Ortho-GCNII
0.8881
This paper
55
JKNet
actual #55 vs paper #180 125 places worse
0.8870
best reported
actual #55 vs paper #180 125 places worse
paper 0.8620
paper 0.8620 Δ at pub 0.0250
70
DAGNN
actual #70 vs paper #259 189 places worse
0.8840
best reported
actual #70 vs paper #259 189 places worse
paper 0.8440
paper 0.8440 Δ at pub 0.0400
108
APPNP
actual #108 vs paper #108
0.8787
actual #108 vs paper #108
paper 0.8787
paper 0.8787 Δ at pub 0.0017
153
Incep(DropEdge)
0.8686
This paper
207
Geom-GCN
actual #207 vs paper #220 13 places worse
0.8540 ±0.0040
best reported
actual #207 vs paper #220 13 places worse
paper 0.8519
paper 0.8519 Δ at pub 0.0011 Δ today 0.0021
223
SGC
actual #223 vs paper #558 335 places worse
0.8509 ±0.0648
best reported
actual #223 vs paper #558 335 places worse
paper 0.8170
paper 0.8170 Δ at pub 0.0020 Δ today 0.0339
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
20
APPNP
actual #20 vs paper #474 454 places worse
0.8142 ±0.0026
best reported
actual #20 vs paper #474 454 places worse
paper 0.7180
paper 0.7180 Δ at pub 0.0870 Δ today 0.0962
35
GAT
actual #35 vs paper #570 535 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #570 535 places worse
paper 0.7080
paper 0.7080 Δ at pub 0.0780 Δ today 0.1000
36
GCNII
actual #36 vs paper #279 243 places worse
0.8076 ±0.0030
best reported
actual #36 vs paper #279 243 places worse
paper 0.7340 ±0.0060
paper 0.7340 ±0.0060 Δ at pub 0.0036 Δ today 0.0736
44
GCN
actual #44 vs paper #550 506 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #550 506 places worse
paper 0.7110
61
GraphSAGE
0.7923 ±0.0053
75
DAGNN
actual #75 vs paper #292 217 places worse
0.7860
best reported
actual #75 vs paper #292 217 places worse
paper 0.7330
paper 0.7330 Δ at pub 0.0530
96
SGC
actual #96 vs paper #481 385 places worse
0.7765 ±0.0012
best reported
actual #96 vs paper #481 385 places worse
paper 0.7170
217
Ortho-GCNII
0.7420 ±0.0040
This paper
350
MLP
0.7289 ±0.0010
372
Incep(Drop)
0.7270
This paper
380
JKNet(Drop)
0.7260
This paper
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
17
APPNP
actual #17 vs paper #439 422 places worse
0.9355 ±0.0060
best reported
actual #17 vs paper #439 422 places worse
paper 0.8010
18
GCN
actual #18 vs paper #585 567 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #585 567 places worse
paper 0.7900
20
GAT
actual #20 vs paper #632 612 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #632 612 places worse
paper 0.7850
58
GCNII
actual #58 vs paper #428 370 places worse
0.9030 ±0.0043
best reported
actual #58 vs paper #428 370 places worse
paper 0.8020 ±0.0040
116
SAGE
0.8881 ±0.0015
141
SGC
actual #141 vs paper #602 461 places worse
0.8832 ±0.0055
best reported
actual #141 vs paper #602 461 places worse
paper 0.7890
paper 0.7890 Δ at pub 0.0352 Δ today 0.0942
210
MLP
0.8690 ±0.0074
226
DAGNN
actual #226 vs paper #403 177 places worse
0.8640
best reported
actual #226 vs paper #403 177 places worse
paper 0.8050
paper 0.8050 Δ at pub 0.0590
443
Ortho-GCNII
0.8010 ±0.0030
This paper
515
Incep(Drop)
0.7950
This paper
566
JKNet(Drop)
0.7920
This paper

TU Dortmund

#ModelAccuracy ↑Paper
1
MSH-GNN
0.9410 ±0.0330
2
GRDL
0.8260 ±0.0120
3
GMN
0.8225
7
DiffPool
actual #7 vs paper #132 125 places worse
0.8161 ±0.0232
best reported
actual #7 vs paper #132 125 places worse
paper 0.7625
32
GIN
0.7880 ±0.0410
34
Ortho-g-U-Nets
0.7878
This paper
59
g-U-Nets
0.7768
This paper
132
DGCNN
actual #132 vs paper #132
0.7626
actual #132 vs paper #132
paper 0.7626
149
MLP
0.7600 ±0.0320
161
PSCN
actual #161 vs paper #245 84 places worse
0.7589 ±0.0276
best reported
actual #161 vs paper #245 84 places worse
paper 0.7500

Difference within reported uncertainty; not counted as underperformance.

paper 0.7500 Δ today 0.0089
#ModelAccuracy ↑Paper
1
GC-GNN (GCN)
0.9210 ±0.0810
2
SUGAR
0.8403 ±0.0133
3
Ortho-g-U-Nets
0.8387
This paper
4
g-U-Nets
actual #4 vs paper #4
0.8300
actual #4 vs paper #4
paper 0.8300
prev best: Graph U-Nets (2019)
paper 0.8300 Δ at pub 0.0057
15
SAGE
0.8088 ±0.0233
18
DiffPool
0.8064
This paper
37
DGCNN
0.7937
This paper
101
PSCN
actual #101 vs paper #113 12 places worse
0.7712 ±0.0241
best reported
actual #101 vs paper #113 12 places worse
paper 0.7627
paper 0.7627 Δ at pub 0.0085 Δ today 0.0085
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