NeurIPS 2021

Node Dependent Local Smoothing for Scalable Graph Learning

Wentao Zhang, Mingyu Yang, Zeang Sheng, Yang Li, Wenbin Ouyang, Yangyu Tao, Zhi Yang, Bin Cui

Main figure for Node Dependent Local Smoothing for Scalable Graph Learning

Abstract

Recent works reveal that feature or label smoothing lies at the core of Graph Neural Networks (GNNs). Concretely, they show feature smoothing combined with simple linear regression achieves comparable performance with the carefully designed GNNs, and a simple MLP model with label smoothing of its prediction can outperform the vanilla GCN. Though an interesting finding, smoothing has not been well understood, especially regarding how to control the extent of smoothness. Intuitively, too small or too large smoothing iterations may cause under-smoothing or over-smoothing and can lead to sub-optimal performance. Moreover, the extent of smoothness is node-specific, depending on its degree and local structure. To this end, we propose a novel algorithm called node-dependent local smoothing (NDLS), which aims to control the smoothness of every node by setting a node-specific smoothing iteration. Specifically, NDLS computes influence scores based on the adjacency matrix and selects the iteration number by setting a threshold on the scores. Once selected, the iteration number can be applied to both feature smoothing and label smoothing. Experimental results demonstrate that NDLS enjoys high accuracy -- state-of-the-art performance on node classifications tasks, flexibility -- can be incorporated with any models, scalability and efficiency -- can support large scale graphs with fast training.

Benchmark Results

Tested on 2 datasets 5 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 #550 529 places worse
0.9004
best reported
actual #21 vs paper #550 529 places worse
paper 0.8180 ±0.0050
paper 0.8180 ±0.0050 Δ at pub 0.0537 Δ today 0.0824
39
SAGE
0.8911 ±0.0012
44
GAT
actual #44 vs paper #424 380 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #424 380 places worse
paper 0.8300 ±0.0070
paper 0.8300 ±0.0070 Δ at pub 0.0590 Δ today 0.0597
108
APPNP
actual #108 vs paper #389 281 places worse
0.8787
best reported
actual #108 vs paper #389 281 places worse
paper 0.8330 ±0.0050
best at pub: Orthogonal Graph Neural Networks (AAAI 2021)
paper 0.8330 ±0.0050 Δ at pub 0.0457 Δ today 0.0457
161
SIGN
actual #161 vs paper #517 356 places worse
0.8672 ±0.0137
best reported
actual #161 vs paper #517 356 places worse
paper 0.8210 ±0.0030
195
JK-Net
actual #195 vs paper #550 355 places worse
0.8579 ±0.0001
best reported
actual #195 vs paper #550 355 places worse
paper 0.8180 ±0.0050
223
SGC
actual #223 vs paper #606 383 places worse
0.8509 ±0.0648
best reported
actual #223 vs paper #606 383 places worse
paper 0.8100 ±0.0020
paper 0.8100 ±0.0020 Δ at pub 0.0090 Δ today 0.0409
246
NDLS
0.8460 ±0.0050
This paper
259
DAGNN (Gate)
0.8440 ±0.0050
This paper
279
SGC+NDLS-L
0.8420 ±0.0020
This paper
290
NDLS-F+MLP
0.8410 ±0.0060
This paper
308
GBP
0.8390 ±0.0070
This paper
366
S^2GC
actual #366 vs paper #447 81 places worse
0.8350 ±0.0020
best reported
actual #366 vs paper #447 81 places worse
paper 0.8270 ±0.0030
paper 0.8270 ±0.0030 Δ today 0.0080
382
AP-GCN
0.8340 ±0.0030
This paper
473
PPRGo
0.8240 ±0.0020
This paper
724
MLP
actual #724 vs paper #872 148 places worse
0.7768
best reported
actual #724 vs paper #872 148 places worse
paper 0.6110 ±0.0060
paper 0.6110 ±0.0060 Δ at pub 0.0050 Δ today 0.1658

OGB

#ModelAccuracy ↑Paper
1
SGC
actual #1 vs paper #77 76 places worse
0.7910
best reported
actual #1 vs paper #77 76 places worse
paper 0.6320 ±0.0020
paper 0.6320 ±0.0020 Δ at pub 0.0009 Δ today 0.1590
2
GAMLP
0.7036 ±0.0002
3
GLEM-GNN
0.7036 ±0.0002
35
SAGE
0.6644 ±0.0017
38
SIGN
actual #38 vs paper #68 30 places worse
0.6636 ±0.0005
best reported
actual #38 vs paper #68 30 places worse
paper 0.6420 ±0.0020
55
NDLS
actual #55 vs paper #55
0.6561 ±0.0029
best reported
actual #55 vs paper #55
paper 0.6560 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.6560 ±0.0030 Δ today 0.0001
58
NDLS-F+MLP
0.6530 ±0.0050
This paper
59
GBP
actual #59 vs paper #59
0.6524 ±0.0013
best reported
actual #59 vs paper #59
paper 0.6520 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.6520 ±0.0030 Δ today 0.0004
63
SGC+NDLS-L
0.6490 ±0.0030
This paper
64
S^2GC
actual #64 vs paper #65 1 place worse
0.6473 ±0.0021
best reported
actual #64 vs paper #65 1 place worse
paper 0.6470 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.6470 ±0.0030 Δ today 0.0003
66
MLP+NDLS-L
0.6460 ±0.0040
This paper
70
MLP+C&S
0.6390
This paper
95
MLP
actual #95 vs paper #98 3 places worse
0.4960 ±0.0030
best reported
actual #95 vs paper #98 3 places worse
paper 0.4720 ±0.0030
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 today — OK at publication; today's leaderboard best is elsewhere