ICLR 2024

Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning

Yuankai Luo, Qijiong Liu, Lei Shi, Xiao-Ming Wu

Main figure for Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning

Abstract

We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.

Benchmark Results

Tested on 12 datasets 10 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 #54 33 places worse
0.9004
best reported
actual #21 vs paper #54 33 places worse
paper 0.8877 ±0.0061
paper 0.8877 ±0.0061 Δ at pub 0.0127
39
SAGE
0.8911 ±0.0012
44
GAT
actual #44 vs paper #81 37 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #81 37 places worse
paper 0.8822 ±0.0124

Difference within reported uncertainty; not counted as underperformance.

paper 0.8822 ±0.0124 Δ at pub 0.0068 Δ today 0.0075
107
NID_GCN
0.8788 ±0.0069
This paper
128
NID_GAT
0.8735 ±0.0057
This paper
143
Graph-MLP
actual #143 vs paper #143
0.8706 ±0.0138
actual #143 vs paper #143
paper 0.8706 ±0.0138
184
VQGraph
actual #184 vs paper #184
0.8611 ±0.0126
actual #184 vs paper #184
paper 0.8611 ±0.0126
paper 0.8611 ±0.0126 Δ at pub 0.0218
620
NID_MAE
0.8080 ±0.0070
This paper
724
MLP
actual #724 vs paper #882 158 places worse
0.7768
best reported
actual #724 vs paper #882 158 places worse
paper 0.5780 ±0.0050
paper 0.5780 ±0.0050 Δ at pub 0.1988
#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 #111 76 places worse
0.8080 ±0.0026
best reported
actual #35 vs paper #111 76 places worse
paper 0.7708 ±0.0084
paper 0.7708 ±0.0084 Δ at pub 0.0372
44
GCN
actual #44 vs paper #101 57 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #101 57 places worse
paper 0.7753 ±0.0092
paper 0.7753 ±0.0092 Δ at pub 0.0190 Δ today 0.0280
61
GraphSAGE
0.7923 ±0.0053
69
Graph-MLP
actual #69 vs paper #124 55 places worse
0.7886 ±0.0008
best reported
actual #69 vs paper #124 55 places worse
paper 0.7643 ±0.0144
116
NID_GCN
0.7689 ±0.0109
This paper
130
NID_GAT
0.7613 ±0.0135
This paper
152
VQGraph
0.7564 ±0.0092
This paper
224
NID_MAE
0.7420 ±0.0060
This paper
350
MLP
actual #350 vs paper #854 504 places worse
0.7289 ±0.0010
best reported
actual #350 vs paper #854 504 places worse
paper 0.5470 ±0.0040
paper 0.5470 ±0.0040 Δ at pub 0.1720 Δ today 0.1819
#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 #69 51 places worse
0.9004 ±0.0025
actual #18 vs paper #69 51 places worse
paper 0.9004 ±0.0025
20
GAT
actual #20 vs paper #88 68 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #88 68 places worse
paper 0.8947 ±0.0025
90
NID_GCN
0.8942 ±0.0044
This paper
106
VQGraph
actual #106 vs paper #158 52 places worse
0.8905 ±0.0032
best reported
actual #106 vs paper #158 52 places worse
paper 0.8803 ±0.0063
111
NID_GAT
0.8897 ±0.0036
This paper
113
Graph-MLP
actual #113 vs paper #113
0.8893 ±0.0063
actual #113 vs paper #113
paper 0.8893 ±0.0063
116
SAGE
0.8881 ±0.0015
210
MLP
actual #210 vs paper #813 603 places worse
0.8690 ±0.0074
best reported
actual #210 vs paper #813 603 places worse
paper 0.7330 ±0.0060
paper 0.7330 ±0.0060 Δ at pub 0.1360
759
NID_MAE
0.7640 ±0.0080
This paper
#ModelAccuracy ↑Paper
1
GCN
0.9302 ±0.0011
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
111
NID_GAT
0.7956 ±0.0043
This paper
157
NID_GCN
0.7855 ±0.0015
This paper
178
VQGraph
0.7792 ±0.0061
This paper
229
Graph-MLP
0.7535 ±0.0055
This paper
237
MLP
0.7469 ±0.0085

OGB

#ModelAccuracy ↑Paper
1
Jacobi
0.8968
2
GPR
0.8953
3
LEMP4HG
0.8939
4
SAGE
actual #4 vs paper #74 70 places worse
0.8327 ±0.0035
actual #4 vs paper #74 70 places worse
paper 0.8327 ±0.0035
6
GCN
0.8868
79
Polynormer
0.8297 ±0.0028
This paper
104
NID_SAGE
0.8183 ±0.0026
This paper
293
SGFormer
0.7416 ±0.0031
This paper
323
LINKX
0.7159 ±0.0071
This paper
351
MLP
0.6605 ±0.0020
#ModelHits@50 ↑Paper
1
PROXI
0.7650 ±0.0027
2
OGB Leader
0.7129 ±0.0018
3
GIDN
0.7096 ±0.0055
9
GCN
actual #9 vs paper #25 16 places worse
0.6405 ±0.0063
actual #9 vs paper #25 16 places worse
paper 0.6405 ±0.0063
prev best: GNNBenchmark (JMLR 2023)
paper 0.6405 ±0.0063 Δ at pub 0.1509 Δ today 0.0216
10
Neo-GNN
actual #10 vs paper #32 22 places worse
0.6613 ±0.0061
best reported
actual #10 vs paper #32 22 places worse
paper 0.5752 ±0.0037
paper 0.5752 ±0.0037 Δ today 0.0861
14
BUDDY
0.6594 ±0.0058
This paper
19
NCN
0.6476 ±0.0087
This paper
20
SEAL
0.6474 ±0.0043
This paper
24
NID_GCN
0.6431 ±0.0048
This paper
28
SAGE
0.5944 ±0.0137
94
MLP
0.4438 ±0.0347
#ModelAccuracy ↑Paper
1
GIANT-XRT
0.7612 ±0.0016
2
GEGCN
0.7576 ±0.0064
3
AGDN
0.7522 ±0.0007
23
GCN
0.7300 ±0.0017
26
SAGE
0.7267 ±0.0031
This paper
28
SGFormer
0.7263 ±0.0013
This paper
51
Polynormer
0.7182 ±0.0023
This paper
55
GPRGNN
actual #55 vs paper #72 17 places worse
0.7168 ±0.0044
best reported
actual #55 vs paper #72 17 places worse
paper 0.7110 ±0.0012

Difference within reported uncertainty; not counted as underperformance.

paper 0.7110 ±0.0012 Δ at pub 0.0058
75
GraphGPS
0.7097 ±0.0041
This paper
80
NID_SAGE
0.7052 ±0.0014
This paper
99
LINKX
0.6618 ±0.0033
This paper
107
MLP
0.5765 ±0.0012
#ModelROC-AUC ↑Paper
1
LD
0.8942 ±0.0007
2
X_WO/LD
0.8915 ±0.0012
3
X_PNE
0.8894 ±0.0014
16
GraphSAGE
0.8430
27
SGFormer
actual #27 vs paper #27
0.7984 ±0.0061
best reported
actual #27 vs paper #27
paper 0.7953 ±0.0038

Difference within reported uncertainty; not counted as underperformance.

paper 0.7953 ±0.0038 Δ today 0.0031
29
SAGE
0.7943 ±0.0075
This paper
30
Polynormer
actual #30 vs paper #53 23 places worse
0.7941 ±0.0056
best reported
actual #30 vs paper #53 23 places worse
paper 0.7597 ±0.0047
46
GraphGPS
actual #46 vs paper #49 3 places worse
0.7725 ±0.0042
best reported
actual #46 vs paper #49 3 places worse
paper 0.7683 ±0.0026

Difference within reported uncertainty; not counted as underperformance.

paper 0.7683 ±0.0026 Δ today 0.0042
50
NID_SAGE
0.7678 ±0.0059
This paper
54
GPRGNN
0.7568 ±0.0049
This paper
65
LINKX
0.7137 ±0.0058
This paper

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
actual #3 vs paper #234 231 places worse
0.8560
best reported
actual #3 vs paper #234 231 places worse
paper 0.4344 ±0.0300
52
GCN
actual #52 vs paper #218 166 places worse
0.7033
best reported
actual #52 vs paper #218 166 places worse
paper 0.4611 ±0.0316
paper 0.4611 ±0.0316 Δ at pub 0.2422
108
SAGE
0.6340 ±0.0300
169
MLP
0.5429
217
NID_GCN
0.4629 ±0.0292
This paper
240
NID_GAT
0.4283 ±0.0342
This paper
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
46
GCN
0.6067
118
NID_GCN
0.4509 ±0.0172
This paper
172
MLP
0.3930 ±0.0079
191
NID_GAT
0.3768 ±0.0204
This paper

Heterophily Benchmark

#ModelROC-AUC ↑Paper
1
NID_GAT
0.9703 ±0.0002
This paper
2
NID_GCN
0.9685 ±0.0010
This paper
3
UniGAP
0.8421 ±0.0080
16
GCN
actual #16 vs paper #38 22 places worse
0.7740 ±0.0107
actual #16 vs paper #38 22 places worse
paper 0.7740 ±0.0107
prev best: Evolving Computation Graphs (ICML 2023)

Improvement within reported uncertainty; not highlighted.

paper 0.7740 ±0.0107 Δ at pub 0.0131 Δ today 0.0162
26
GAT
actual #26 vs paper #26
0.7835 ±0.0116
actual #26 vs paper #26
paper 0.7835 ±0.0116

Improvement within reported uncertainty; not highlighted.

paper 0.7835 ±0.0116 Δ at pub 0.0092
46
GraphSAGE
0.7721 ±0.0130
96
MLP
0.7082 ±0.0010

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
SAGE
0.8597 ±0.0021
This paper
2
Polynormer
0.8595 ±0.0007
This paper
3
NID_SAGE
0.8563 ±0.0031
This paper
23
GCN
0.7601 ±0.0049
25
SGFormer
0.7376 ±0.0024
This paper
31
MLP
0.7048 ±0.0077
SOTA performance (not significantly different from the best) 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