NeurIPS 2020

Towards Deeper Graph Neural Networks with Differentiable Group Normalization

Kaixiong Zhou, Xiao Huang, Yuening Li, D. Zha, Rui Chen, Xia Hu

Main figure for Towards Deeper Graph Neural Networks with Differentiable Group Normalization

Abstract

Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance of GNNs as the number of layers increases. It is because the stacked aggregators would make node representations converge to indistinguishable vectors. Several attempts have been made to tackle the issue by bringing linked node pairs close and unlinked pairs distinct. However, they often ignore the intrinsic community structures and would result in sub-optimal performance. The representations of nodes within the same community/class need be similar to facilitate the classification, while different classes are expected to be separated in embedding space. To bridge the gap, we introduce two over-smoothing metrics and a novel technique, i.e., differentiable group normalization (DGN). It normalizes nodes within the same group independently to increase their smoothness, and separates node distributions among different groups to significantly alleviate the over-smoothing issue. Experiments on real-world datasets demonstrate that DGN makes GNN models more robust to over-smoothing and achieves better performance with deeper GNNs.

Proposed method: DGN

Benchmark Results

Tested on 4 datasets 9 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 #507 486 places worse
0.9004
best reported
actual #21 vs paper #507 486 places worse
paper 0.8220
paper 0.8220 Δ at pub 0.0497 Δ today 0.0784
39
SAGE
0.8911 ±0.0012
44
GAT
actual #44 vs paper #614 570 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #614 570 places worse
paper 0.8090
532
DGN
0.8200
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 #610 575 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #610 575 places worse
paper 0.7020
paper 0.7020 Δ at pub 0.0230 Δ today 0.1060
44
GCN
actual #44 vs paper #584 540 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #584 540 places worse
paper 0.7060
paper 0.7060 Δ at pub 0.0060 Δ today 0.0973
61
GraphSAGE
0.7923 ±0.0053
96
SGC
actual #96 vs paper #634 538 places worse
0.7765 ±0.0012
best reported
actual #96 vs paper #634 538 places worse
paper 0.6960
350
MLP
0.7289 ±0.0010
637
DGN
0.6950
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
actual #18 vs paper #551 533 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #551 533 places worse
paper 0.7930
paper 0.7930 Δ at pub 0.0020 Δ today 0.1366
20
GAT
actual #20 vs paper #694 674 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #694 674 places worse
paper 0.7780
116
SAGE
0.8881 ±0.0015
141
SGC
actual #141 vs paper #826 685 places worse
0.8832 ±0.0055
best reported
actual #141 vs paper #826 685 places worse
paper 0.7150
paper 0.7150 Δ at pub 0.0740 Δ today 0.1682
210
MLP
0.8690 ±0.0074
507
DGN
0.7950
This paper
#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
12
GCN
actual #12 vs paper #107 95 places worse
0.9514 ±0.0025
best reported
actual #12 vs paper #107 95 places worse
paper 0.9230
best today: Graph Wave Networks (WWW 2025)
paper 0.9230 Δ at pub 0.0130 Δ today 0.0284
21
GAT
actual #21 vs paper #136 115 places worse
0.9437 ±0.0028
best reported
actual #21 vs paper #136 115 places worse
paper 0.9150
best today: Graph Wave Networks (WWW 2025)
paper 0.9150 Δ at pub 0.0230 Δ today 0.0287
88
MLP
0.9280 ±0.0020
96
SGC
actual #96 vs paper #163 67 places worse
0.8990
actual #96 vs paper #163 67 places worse
paper 0.8990
111
DGN
0.9230
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere