Wide & Deep Learning for Node Classification

Yancheng Chen, Wenguo Yang, Zhipeng Jiang

Main figure for Wide & Deep Learning for Node Classification

Abstract

Wide&Deep, a simple yet effective learning architecture for recommendation systems developed by Google, has had a significant impact in both academia and industry due to its combination of the memorization ability of generalized linear models and the generalization ability of deep models. Graph convolutional networks (GCNs) remain dominant in node classification tasks; however, recent studies have highlighted issues such as heterophily and expressiveness, which focus on graph structure while seemingly neglecting the potential role of node features. In this paper, we propose a flexible framework GCNIII, which leverages the Wide&Deep architecture and incorporates three techniques: Intersect memory, Initial residual and Identity mapping. We provide comprehensive empirical evidence showing that GCNIII can more effectively balance the trade-off between over-fitting and over-generalization on various semi- and full- supervised tasks. Additionally, we explore the use of large language models (LLMs) for node feature engineering to enhance the performance of GCNIII in cross-domain node classification tasks. Our implementation is available at https://github.com/CYCUCAS/GCNIII.

Proposed method: GCNIII

Benchmark Results

Tested on 4 datasets 15 baseline values reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

Classic

#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 ±0.0030
paper 0.7180 ±0.0030 Δ at pub 0.0962
35
GAT
actual #35 vs paper #642 607 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #642 607 places worse
paper 0.6930 ±0.0080
paper 0.6930 ±0.0080 Δ at pub 0.1150
36
GCNII
actual #36 vs paper #353 317 places worse
0.8076 ±0.0030
best reported
actual #36 vs paper #353 317 places worse
paper 0.7280 ±0.0060
paper 0.7280 ±0.0060 Δ at pub 0.0796
44
GCN
actual #44 vs paper #474 430 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #474 430 places worse
paper 0.7180 ±0.0010
paper 0.7180 ±0.0010 Δ at pub 0.0853
61
GraphSAGE
0.7923 ±0.0053
330
GCNIII
0.7300 ±0.0050
This paper
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
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 ±0.0020
paper 0.8010 ±0.0020 Δ at pub 0.1345
18
GCN
actual #18 vs paper #504 486 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #504 486 places worse
paper 0.7950 ±0.0030
20
GAT
actual #20 vs paper #646 626 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #646 626 places worse
paper 0.7840 ±0.0090
58
GCNII
actual #58 vs paper #474 416 places worse
0.9030 ±0.0043
best reported
actual #58 vs paper #474 416 places worse
paper 0.7980 ±0.0040
116
SAGE
0.8881 ±0.0015
210
MLP
0.8690 ±0.0074
415
GCNIII
0.8040 ±0.0040
This paper
#ModelF1 ↑Paper
1
GAMLP(JK)
0.9982 ±0.0001
2
GraphCON-GCN
0.9960
3
GCNII
actual #3 vs paper #6 3 places worse
0.9953 ±0.0001
best reported
actual #3 vs paper #6 3 places worse
paper 0.9948 ±0.0400
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)

Difference within reported uncertainty; not counted as underperformance.

paper 0.9948 ±0.0400 Δ at pub 0.0002 Δ today 0.0005
5
GCNIII
0.9950 ±0.0300
This paper
9
Cluster-GCN
actual #9 vs paper #10 1 place worse
0.9940
best reported
actual #9 vs paper #10 1 place worse
paper 0.9936
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.9936 Δ at pub 0.0004
21
GCN
0.9850
42
VR-GCN
0.9780
This paper
57
GAT
actual #57 vs paper #57
0.9732 ±0.0032
best reported
actual #57 vs paper #57
paper 0.9730

Difference within reported uncertainty; not counted as underperformance.

paper 0.9730 Δ at pub 0.0002
101
GraphSAGE
actual #101 vs paper #153 52 places worse
0.7860
best reported
actual #101 vs paper #153 52 places worse
paper 0.6120
paper 0.6120 Δ at pub 0.1740
173
MLP
0.4620

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
34
MLP
0.9230 ±0.0070
46
APPNP
actual #46 vs paper #438 392 places worse
0.9131 ±0.0197
best reported
actual #46 vs paper #438 392 places worse
paper 0.6541
paper 0.6541 Δ at pub 0.2590
53
GraphSAGE
0.9000 ±0.0365
70
GCNII
actual #70 vs paper #435 365 places worse
0.8918 ±0.0443
best reported
actual #70 vs paper #435 365 places worse
paper 0.6568
paper 0.6568 Δ at pub 0.1589 Δ today 0.2350
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
paper 0.5838 Δ at pub 0.2244 Δ today 0.2324
247
GCNIII
0.7973
This paper
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
best at pub: Graph Wave Networks (WWW 2025)
paper 0.5216 Δ at pub 0.2717
348
Geom-GCN-S
actual #348 vs paper #508 160 places worse
0.7350
best reported
actual #348 vs paper #508 160 places worse
paper 0.5973
paper 0.5973 Δ at pub 0.1377
416
Geom-GCN-P
0.6757
This paper
548
Geom-GCN-I
0.5758
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)