Tackling Over-Smoothing for General Graph Convolutional Networks

Wenbing Huang, Yu Rong, Tingyang Xu, Fuchun Sun, Junzhou Huang

Main figure for Tackling Over-Smoothing for General Graph Convolutional Networks

Abstract

Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act with the increase in depth, including generic GCN, GCN with bias, ResGCN, and APPNP. We find that all these models are characterized by a universal process: all nodes converging to a cuboid. Upon this theorem, we propose DropEdge to alleviate over-smoothing by randomly removing a certain number of edges at each training epoch. Theoretically, DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by dimension collapse. Experimental evaluations on simulated dataset have visualized the difference in over-smoothing between different GCNs. Moreover, extensive experiments on several real benchmarks support that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs.

Benchmark Results

Tested on 3 datasets SOTA at publication on 3 1 baseline value 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 #194 173 places worse
0.9004
best reported
actual #21 vs paper #194 173 places worse
paper 0.8580
paper 0.8580 Δ at pub 0.0137 Δ today 0.0424
39
SAGE
0.8911 ±0.0012
41
APPNP+DropEdge
0.8910
This paper
43
DropEdge
actual #43 vs paper #43
0.8900
actual #43 vs paper #43
paper 0.8900
paper 0.8900 Δ at pub 0.0620
44
GAT
actual #44 vs paper #126 82 places worse
0.8740
actual #44 vs paper #126 82 places worse
paper 0.8740
56
DAGNN+DropEdge
0.8870
This paper
55
JKNet
actual #55 vs paper #161 106 places worse
0.8870
best reported
actual #55 vs paper #161 106 places worse
paper 0.8670
paper 0.8670 Δ today 0.0200
70
DAGNN
0.8840
This paper
99
JKNet+DropEdge
0.8800
This paper
108
APPNP
actual #108 vs paper #112 4 places worse
0.8770
actual #108 vs paper #112 4 places worse
paper 0.8770
paper 0.8770 Δ at pub 0.0460 Δ today 0.0017
117
GCN-b+DropEdge
0.8760
This paper
116
GCN-b
0.8760
This paper
125
AS-GCN
actual #125 vs paper #126 1 place worse
0.8744
best reported
actual #125 vs paper #126 1 place worse
paper 0.8740
141
GraphSAGE
actual #141 vs paper #507 366 places worse
0.8708 ±0.0085
best reported
actual #141 vs paper #507 366 places worse
paper 0.8220
147
ResGCN+DropEdge
0.8700
This paper
157
DCNN
actual #157 vs paper #157
0.8680
actual #157 vs paper #157
paper 0.8680
167
GCN+DropEdge
0.8660
This paper
211
ResGCN
0.8540
This paper
226
FastGCN
actual #226 vs paper #226
0.8500
actual #226 vs paper #226
paper 0.8500
paper 0.8500 Δ at pub 0.1270
495
KLED
0.8230
This paper
724
MLP
0.7768
908
GLASSO
0.4320
This paper
912
ER-Graph
0.3190
This paper
#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 #40 20 places worse
0.8050
actual #20 vs paper #40 20 places worse
paper 0.8050
paper 0.8050 Δ at pub 0.0780 Δ today 0.0092
24
DropEdge
actual #24 vs paper #24
0.8130
actual #24 vs paper #24
paper 0.8130
paper 0.8130 Δ at pub 0.0900
26
APPNP+DropEdge
0.8130
This paper
35
GAT
actual #35 vs paper #74 39 places worse
0.7860
actual #35 vs paper #74 39 places worse
paper 0.7860
paper 0.7860 Δ at pub 0.0610 Δ today 0.0220
44
GCN
actual #44 vs paper #119 75 places worse
0.7680
actual #44 vs paper #119 75 places worse
paper 0.7680
47
JKNet+DropEdge
0.8020
This paper
51
AS-GCN
0.7970
This paper
52
GCN-b
0.7970
This paper
54
DAGNN+DropEdge
0.7950
This paper
56
ResGCN+DropEdge
0.7940
This paper
61
GraphSAGE
actual #61 vs paper #519 458 places worse
0.7923 ±0.0053
best reported
actual #61 vs paper #519 458 places worse
paper 0.7140
63
GCN-b+DropEdge
0.7920
This paper
62
JKNet
0.7920
This paper
65
GCN+DropEdge
0.7900
This paper
68
ResGCN
0.7890
This paper
75
DAGNN
0.7860
This paper
97
FastGCN
actual #97 vs paper #98 1 place worse
0.7765 ±0.0005
best reported
actual #97 vs paper #98 1 place worse
paper 0.7760

Difference within reported uncertainty; not counted as underperformance.

paper 0.7760 Δ today 0.0005
259
SAGE
0.7361 ±0.0190
350
MLP
0.7289 ±0.0010
898
ER-Graph
0.2330
This paper
899
GLASSO
0.2200
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 #52 35 places worse
0.9050
actual #17 vs paper #52 35 places worse
paper 0.9050
18
GCN
actual #18 vs paper #83 65 places worse
0.8970
actual #18 vs paper #83 65 places worse
paper 0.8970
20
GAT
actual #20 vs paper #83 63 places worse
0.8970
actual #20 vs paper #83 63 places worse
paper 0.8970
25
JKNet+DropEdge
0.9160
This paper
24
JKNet
0.9160
This paper
31
GCN-b+DropEdge
0.9130
This paper
30
GCN-b
0.9130
This paper
37
ResGCN+DropEdge
0.9110
This paper
36
ResGCN
0.9110
This paper
40
GCN+DropEdge
0.9100
This paper
43
DropEdge
actual #43 vs paper #228 185 places worse
0.8610
actual #43 vs paper #228 185 places worse
paper 0.8610
49
APPNP+DropEdge
0.9070
This paper
51
AS-GCN
0.9060
This paper
78
DCNN
actual #78 vs paper #78
0.8980
actual #78 vs paper #78
paper 0.8980
116
SAGE
0.8881 ±0.0015
125
GraphSAGE
actual #125 vs paper #200 75 places worse
0.8710
actual #125 vs paper #200 75 places worse
paper 0.8710
paper 0.8710 Δ at pub 0.0640 Δ today 0.0154
159
FastGCN
actual #159 vs paper #159
0.8800
actual #159 vs paper #159
paper 0.8800
paper 0.8800 Δ at pub 0.1590
201
DAGNN+DropEdge
0.8710
This paper
210
MLP
0.8690 ±0.0074
226
DAGNN
0.8640
This paper
323
KLED
0.8230
This paper
882
ER-Graph
0.4070
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 Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere