From Message-Passing to Linearized Graph Sequence Models

Joël Mathys, Basil Rohner, Saku Peltonen, R. Wattenhofer

Main figure for From Message-Passing to Linearized Graph Sequence Models

Abstract

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises the question of how graph learning can benefit from these advances. We introduce Linearized Graph Sequence Models, a framework that recasts message-passing graph computation from the perspective of sequence modeling to simplify architectural choices. Our approach systematically separates the computational processing depth from the information propagation depth, allowing core graph architectural decisions to be treated as sequence modeling choices. Specifically, we analyze, both empirically and theoretically, what sequence properties make methods effective for learning and preserving the graph inductive bias. In particular, we validate our findings, demonstrating improved performance on long-range information tasks in graphs. Our findings provide a principled way to integrate modern sequence modeling advances into message-passing based graph learning. Beyond this, our work demonstrates how the separation of processing and information depth can recast central architectural questions as input modeling choices.

Proposed method: LGSM

Benchmark Results

Tested on 3 datasets 3 baseline values reported too low

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

LRGB

#ModelMAE ↓Paper
1
GCN
0.2421 ±0.0016
This paper
2
IPR-MPNN
0.2422 ±0.0007
3
TANGO-GPS
0.2422 ±0.0014
5
GIN
0.2429 ±0.0019
This paper
7
GatedGCN
0.2431 ±0.0020
This paper
30
GRAMA_GatedGCN
0.2459 ±0.0020
This paper
37
NeuralWalker
actual #37 vs paper #37
0.2463 ±0.0005
actual #37 vs paper #37
paper 0.2463 ±0.0005

Improvement within reported uncertainty; not highlighted.

paper 0.2463 ±0.0005 Δ at pub 0.0005
45
LGSM
0.2470 ±0.0019
This paper
49
GINE
0.2473 ±0.0017
This paper
50
GMN
0.2473 ±0.0025
This paper
62
Graph-Mamba
0.2478 ±0.0016
This paper
68
SWAN
0.2485 ±0.0009
This paper
88
GraphGPS+LapPE
0.2500 ±0.0005
This paper
104
DRew-GCN+LapPE
actual #104 vs paper #104
0.2517 ±0.0011
actual #104 vs paper #104
paper 0.2517 ±0.0011

Improvement within reported uncertainty; not highlighted.

paper 0.2517 ±0.0011 Δ at pub 0.0019
113
Transformer+LapPE
0.2529 ±0.0016
This paper
116
DRew-GCN
actual #116 vs paper #165 49 places worse
0.2536
best reported
actual #116 vs paper #165 49 places worse
paper 0.2781 ±0.0028
best at pub: Towards Dynamic Message Passing on Graphs (NeurIPS 2024)
paper 0.2781 ±0.0028 Δ at pub 0.0245
120
DRew-GatedGCN+LapPE
0.2539 ±0.0007
This paper
146
DRew-GIN+LapPE
0.2606 ±0.0014
This paper
149
MixHop-GCN+LapPE
0.2614 ±0.0023
This paper
150
DIGL+MPNN+LapPE
0.2616 ±0.0018
This paper
155
SAN+LapPE
actual #155 vs paper #155
0.2680 ±0.0040
best reported
actual #155 vs paper #155
paper 0.2683 ±0.0043

Difference within reported uncertainty; not counted as underperformance.

paper 0.2683 ±0.0043 Δ at pub 0.0003
158
DRew-GatedGCN
0.2699 ±0.0018
This paper
165
GraphCON
0.2778 ±0.0018
This paper
166
DRew-GIN
0.2799 ±0.0016
This paper
170
A-DGN
0.2874 ±0.0021
This paper
171
MixHop-GCN
0.2921 ±0.0023
This paper
174
DIGL+MPNN
0.3173 ±0.0007
This paper
182
GRAND
0.3418 ±0.0015
This paper
201
MLP
0.4351 ±0.0008
#ModelAP ↑Paper
1
S^2GCN
0.7311 ±0.0066
2
S4G
0.7293 ±0.0004
3
BuNN
0.7276 ±0.0065
4
GCN
actual #4 vs paper #4
0.7261 ±0.0011
actual #4 vs paper #4
paper 0.7261 ±0.0011
11
DRew-GCN
actual #11 vs paper #34 23 places worse
0.7150 ±0.0044
best reported
actual #11 vs paper #34 23 places worse
paper 0.6996 ±0.0076
best at pub: Spatio-Spectral Graph Neural Networks (NeurIPS 2024)
paper 0.6996 ±0.0076 Δ at pub 0.0154
12
DRew-GCN+LapPE
0.7150 ±0.0044
This paper
17
DRew-GIN+LapPE
0.7126 ±0.0045
This paper
20
NeuralWalker
0.7096 ±0.0078
This paper
24
GMN
0.7071 ±0.0083
This paper
26
GIN
actual #26 vs paper #26
0.7059 ±0.0089
actual #26 vs paper #26
paper 0.7059 ±0.0089
paper 0.7059 ±0.0089 Δ at pub 0.0989
27
GRAMA_GatedGCN
0.7049 ±0.0051
This paper
34
GatedGCN
actual #34 vs paper #34
0.7006 ±0.0033
actual #34 vs paper #34
paper 0.7006 ±0.0033
paper 0.7006 ±0.0033 Δ at pub 0.0241
38
DRew-GatedGCN+LapPE
0.6977 ±0.0026
This paper
46
DRew-GIN
0.6940 ±0.0074
This paper
51
MixHop-GCN+LapPE
0.6843 ±0.0049
This paper
52
DIGL+MPNN+LapPE
0.6830 ±0.0026
This paper
60
SWAN
0.6751 ±0.0039
This paper
62
Graph-Mamba
0.6739 ±0.0087
This paper
63
DRew-GatedGCN
0.6733 ±0.0094
This paper
72
LGSM
0.6685 ±0.0136
This paper
75
GRAND
actual #75 vs paper #156 81 places worse
0.6630 ±0.0160
best reported
actual #75 vs paper #156 81 places worse
paper 0.5789 ±0.0062
78
GINE
0.6621 ±0.0067
This paper
81
MixHop-GCN
0.6592 ±0.0036
This paper
92
GraphGPS+LapPE
0.6535 ±0.0041
This paper
108
DIGL+MPNN
0.6469 ±0.0019
This paper
116
SAN+LapPE
0.6384 ±0.0121
This paper
118
Transformer+LapPE
0.6326 ±0.0126
This paper
137
GraphCON
0.6022 ±0.0068
This paper
139
A-DGN
0.5975 ±0.0044
This paper
181
MLP
0.4060 ±0.0021

LRIM Graph Benchmark

#Modellog-MSE ↓Paper
1
GPS-RWSE
-4.3450 ±0.0650
This paper
2
GPS-Base
-4.3400 ±0.1010
This paper
3
GPS-LapPE
actual #3 vs paper #4 1 place worse
-4.3340 ±0.0650
best reported
actual #3 vs paper #4 1 place worse
paper -4.2480 ±0.1100

Difference within reported uncertainty; not counted as underperformance.

paper -4.2480 ±0.1100 Δ today 0.0860
4
LGSM
-4.2840 ±0.1330
This paper
6
GatedGCN
-3.9190 ±0.2230
This paper
7
GatedGCN-VN_G
-3.7560 ±0.0630
This paper
8
GIN
-2.4060 ±0.1480
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