Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks

Acong Zhang, Jincheng Huang, Ping Li, Kai Zhang

Main figure for Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks

Abstract

Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.

Benchmark Results

Tested on 6 datasets 28 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 #558 537 places worse
0.9004
best reported
actual #21 vs paper #558 537 places worse
paper 0.8170 ±0.0040
paper 0.8170 ±0.0040 Δ at pub 0.0547 Δ today 0.0834
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
55
JKNet
actual #55 vs paper #583 528 places worse
0.8870
best reported
actual #55 vs paper #583 528 places worse
paper 0.8130 ±0.0060
paper 0.8130 ±0.0060 Δ at pub 0.0740
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
113
MixHop
actual #113 vs paper #536 423 places worse
0.8761 ±0.0203
best reported
actual #113 vs paper #536 423 places worse
paper 0.8190 ±0.0040
121
SDRF
actual #121 vs paper #439 318 places worse
0.8751 ±0.0029
best reported
actual #121 vs paper #439 318 places worse
paper 0.8280 ±0.0020
paper 0.8280 ±0.0020 Δ today 0.0471
134
GRACE
actual #134 vs paper #389 255 places worse
0.8720 ±0.0020
best reported
actual #134 vs paper #389 255 places worse
paper 0.8330 ±0.0050
paper 0.8330 ±0.0050 Δ at pub 0.0032 Δ today 0.0390
177
DGI
actual #177 vs paper #465 288 places worse
0.8630 ±0.0020
best reported
actual #177 vs paper #465 288 places worse
paper 0.8250 ±0.0070
334
BAGCN-mul
0.8370 ±0.0020
This paper
397
BAGCN-add
0.8330 ±0.0020
This paper
534
BGCN
0.8200 ±0.0010
This paper
572
GCN + FA
0.8160 ±0.0020
This paper
724
MLP
actual #724 vs paper #871 147 places worse
0.7768
best reported
actual #724 vs paper #871 147 places worse
paper 0.6160 ±0.0060
paper 0.6160 ±0.0060 Δ at pub 0.1315 Δ today 0.1608
#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 #481 461 places worse
0.8142 ±0.0026
best reported
actual #20 vs paper #481 461 places worse
paper 0.7170 ±0.0060
paper 0.7170 ±0.0060 Δ at pub 0.0880 Δ today 0.0972
35
GAT
actual #35 vs paper #388 353 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #388 353 places worse
paper 0.7250 ±0.0060
paper 0.7250 ±0.0060 Δ at pub 0.0763 Δ today 0.0830
44
GCN
actual #44 vs paper #561 517 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #561 517 places worse
paper 0.7090 ±0.0050
paper 0.7090 ±0.0050 Δ at pub 0.0853 Δ today 0.0943
61
GraphSAGE
0.7923 ±0.0053
62
JKNet
actual #62 vs paper #596 534 places worse
0.7920
best reported
actual #62 vs paper #596 534 places worse
paper 0.7040 ±0.0110
paper 0.7040 ±0.0110 Δ at pub 0.0880
66
DGI
actual #66 vs paper #496 430 places worse
0.7890 ±0.0020
best reported
actual #66 vs paper #496 430 places worse
paper 0.7160 ±0.0070
126
MixHop
actual #126 vs paper #519 393 places worse
0.7626 ±0.0295
best reported
actual #126 vs paper #519 393 places worse
paper 0.7140 ±0.0080
201
GRACE
actual #201 vs paper #446 245 places worse
0.7450 ±0.0010
best reported
actual #201 vs paper #446 245 places worse
paper 0.7210 ±0.0050
paper 0.7210 ±0.0050 Δ at pub 0.0016 Δ today 0.0240
248
SDRF
actual #248 vs paper #373 125 places worse
0.7374 ±0.0034
best reported
actual #248 vs paper #373 125 places worse
paper 0.7260 ±0.0020
paper 0.7260 ±0.0020 Δ today 0.0114
332
BAGCN-add
0.7300 ±0.0070
This paper
350
MLP
actual #350 vs paper #823 473 places worse
0.7289 ±0.0010
best reported
actual #350 vs paper #823 473 places worse
paper 0.6100 ±0.0100
paper 0.6100 ±0.0100 Δ at pub 0.0858 Δ today 0.1189
379
BAGCN-mul
0.7260 ±0.0010
This paper
470
BGCN
0.7190
This paper
592
GCN + FA
0.7050 ±0.0020
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 ±0.0020
18
GCN
actual #18 vs paper #614 596 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #614 596 places worse
paper 0.7880 ±0.0060
20
GAT
actual #20 vs paper #574 554 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #574 554 places worse
paper 0.7910 ±0.0040
24
JKNet
actual #24 vs paper #668 644 places worse
0.9160
best reported
actual #24 vs paper #668 644 places worse
paper 0.7810 ±0.0040
paper 0.7810 ±0.0040 Δ at pub 0.1350
70
MixHop
actual #70 vs paper #383 313 places worse
0.9004 ±0.0141
best reported
actual #70 vs paper #383 313 places worse
paper 0.8080 ±0.0060
paper 0.8080 ±0.0060 Δ today 0.0924
116
SAGE
0.8881 ±0.0015
194
GRACE
actual #194 vs paper #585 391 places worse
0.8730 ±0.0010
best reported
actual #194 vs paper #585 391 places worse
paper 0.7900 ±0.0020
paper 0.7900 ±0.0020 Δ at pub 0.0745 Δ today 0.0830
204
DGI
actual #204 vs paper #646 442 places worse
0.8708 ±0.0017
best reported
actual #204 vs paper #646 442 places worse
paper 0.7840 ±0.0070
210
MLP
actual #210 vs paper #807 597 places worse
0.8690 ±0.0074
best reported
actual #210 vs paper #807 597 places worse
paper 0.7420 ±0.0070
paper 0.7420 ±0.0070 Δ at pub 0.1218 Δ today 0.1270
513
GCN + FA
0.7950 ±0.0010
This paper
535
BGCN
0.7940 ±0.0010
This paper
582
SDRF
0.7910 ±0.0010
This paper
640
BAGCN-mul
0.7850 ±0.0010
This paper
641
BAGCN-add
0.7850 ±0.0010
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #503 501 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #503 501 places worse
paper 0.8572 ±0.2030

Difference within reported uncertainty; not counted as underperformance.

paper 0.8572 ±0.2030 Δ at pub 0.0722 Δ today 0.1097
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #395 387 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #395 387 places worse
paper 0.9121 ±0.0120
87
GCNII
actual #87 vs paper #484 397 places worse
0.9430 ±0.0020
best reported
actual #87 vs paper #484 397 places worse
paper 0.8848 ±0.0210
paper 0.8848 ±0.0210 Δ at pub 0.0140 Δ today 0.0582
203
GRACE
actual #203 vs paper #375 172 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #375 172 places worse
paper 0.9146 ±0.0028
paper 0.9146 ±0.0028 Δ at pub 0.0134 Δ today 0.0167
260
DAGNN
actual #260 vs paper #337 77 places worse
0.9269
best reported
actual #260 vs paper #337 77 places worse
paper 0.9202 ±0.0080

Difference within reported uncertainty; not counted as underperformance.

paper 0.9202 ±0.0080 Δ at pub 0.0067
307
BAGCN-add
0.9235 ±0.0090
This paper
378
GraphSAGE-mean
actual #378 vs paper #378
0.9143 ±0.0130
actual #378 vs paper #378
paper 0.9143 ±0.0130

Improvement within reported uncertainty; not highlighted.

paper 0.9143 ±0.0130 Δ at pub 0.0003
390
MLP
actual #390 vs paper #558 168 places worse
0.9128 ±0.0063
best reported
actual #390 vs paper #558 168 places worse
paper 0.6964 ±0.0380
paper 0.6964 ±0.0380 Δ at pub 0.1853 Δ today 0.2164
393
MoNet
actual #393 vs paper #393
0.9124 ±0.0130
actual #393 vs paper #393
paper 0.9124 ±0.0130

Improvement within reported uncertainty; not highlighted.

paper 0.9124 ±0.0130 Δ at pub 0.0004
414
GraphSAGE-meanpool
0.9072 ±0.0160
This paper
416
BAGCN-mul
0.9071 ±0.0110
This paper
434
GraphSAGE-maxpool
0.9042 ±0.0130
This paper
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
0.9796 ±0.0081
6
GAT
actual #6 vs paper #252 246 places worse
0.9782 ±0.0028
best reported
actual #6 vs paper #252 246 places worse
paper 0.9253 ±0.0090
paper 0.9253 ±0.0090 Δ at pub 0.0367 Δ today 0.0529
9
GCN
actual #9 vs paper #246 237 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #246 237 places worse
paper 0.9278 ±0.0100
paper 0.9278 ±0.0100 Δ at pub 0.0372 Δ today 0.0496
17
SAGE
0.9739 ±0.0018
54
BAGCN-mul
0.9608 ±0.0050
This paper
58
MLP
actual #58 vs paper #274 216 places worse
0.9597 ±0.0007
best reported
actual #58 vs paper #274 216 places worse
paper 0.8891 ±0.0110
paper 0.8891 ±0.0110 Δ at pub 0.0600 Δ today 0.0706
59
GCNII
actual #59 vs paper #201 142 places worse
0.9394 ±0.0040
actual #59 vs paper #201 142 places worse
paper 0.9394 ±0.0040

Improvement within reported uncertainty; not highlighted.

paper 0.9394 ±0.0040 Δ at pub 0.0015 Δ today 0.0203
64
BAGCN-add
0.9588 ±0.0080
This paper
77
GRACE
actual #77 vs paper #95 18 places worse
0.9563 ±0.0010
actual #77 vs paper #95 18 places worse
paper 0.9563 ±0.0010

Improvement within reported uncertainty; not highlighted.

paper 0.9563 ±0.0010 Δ at pub 0.0024
197
DAGNN
actual #197 vs paper #197
0.9401 ±0.0060
actual #197 vs paper #197
paper 0.9401 ±0.0060

Improvement within reported uncertainty; not highlighted.

paper 0.9401 ±0.0060 Δ at pub 0.0020
239
GraphSAGE-mean
0.9306 ±0.0080
This paper
247
GraphSAGE-meanpool
0.9265 ±0.0100
This paper
253
MoNet
actual #253 vs paper #255 2 places worse
0.9250 ±0.0090
best reported
actual #253 vs paper #255 2 places worse
paper 0.9246 ±0.0090

Difference within reported uncertainty; not counted as underperformance.

paper 0.9246 ±0.0090 Δ at pub 0.0004 Δ today 0.0004
273
GraphSAGE-maxpool
0.9026 ±0.0120
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 #148 136 places worse
0.9514 ±0.0025
best reported
actual #12 vs paper #148 136 places worse
paper 0.9113 ±0.0150
best today: Graph Wave Networks (WWW 2025)
paper 0.9113 ±0.0150 Δ at pub 0.0247 Δ today 0.0401
21
GAT
actual #21 vs paper #157 136 places worse
0.9437 ±0.0028
best reported
actual #21 vs paper #157 136 places worse
paper 0.9049 ±0.0060
best today: Graph Wave Networks (WWW 2025)
paper 0.9049 ±0.0060 Δ at pub 0.0331 Δ today 0.0388
69
GRACE
actual #69 vs paper #101 32 places worse
0.9301 ±0.0003
best reported
actual #69 vs paper #101 32 places worse
paper 0.9253 ±0.0010
paper 0.9253 ±0.0010 Δ at pub 0.0040 Δ today 0.0048
88
MLP
actual #88 vs paper #171 83 places worse
0.9280 ±0.0020
best reported
actual #88 vs paper #171 83 places worse
paper 0.8830 ±0.0070
paper 0.8830 ±0.0070 Δ at pub 0.0340 Δ today 0.0450
91
DAGNN
actual #91 vs paper #92 1 place worse
0.9278 ±0.0090
actual #91 vs paper #92 1 place worse
paper 0.9278 ±0.0090

Improvement within reported uncertainty; not highlighted.

paper 0.9278 ±0.0090 Δ at pub 0.0082
104
GCNII
actual #104 vs paper #104
0.9241 ±0.0050
actual #104 vs paper #104
paper 0.9241 ±0.0050
paper 0.9241 ±0.0050 Δ at pub 0.0138
112
BAGCN-add
0.9227 ±0.0050
This paper
137
BAGCN-mul
0.9148 ±0.0090
This paper
139
GraphSAGE-mean
actual #139 vs paper #139
0.9132 ±0.0290
actual #139 vs paper #139
paper 0.9132 ±0.0290

Improvement within reported uncertainty; not highlighted.

paper 0.9132 ±0.0290 Δ at pub 0.0002
155
MoNet
actual #155 vs paper #155
0.9082 ±0.0160
actual #155 vs paper #155
paper 0.9082 ±0.0160

Improvement within reported uncertainty; not highlighted.

paper 0.9082 ±0.0160 Δ at pub 0.0002
166
GraphSAGE-meanpool
0.8966 ±0.0090
This paper
185
GraphSAGE-maxpool
0.8504 ±0.0110
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 Best today — OK at publication; today's leaderboard best is elsewhere