ICML 2022

TIDE: Time Derivative Diffusion for Deep Learning on Graphs

Maximilian Krahn, M. Behmanesh, M. Ovsjanikov

Main figure for TIDE: Time Derivative Diffusion for Deep Learning on Graphs

Abstract

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin

Benchmark Results

Tested on 14 datasets 18 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
0.9004
87
GRAND
actual #87 vs paper #624 537 places worse
0.8815
best reported
actual #87 vs paper #624 537 places worse
paper 0.8071 ±0.0086
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.8071 ±0.0086 Δ at pub 0.0289 Δ today 0.0744
612
DiffusionNet
0.8096 ±0.0050
This paper
724
MLP
0.7768
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
0.8033 ±0.0088
122
GRAND
actual #122 vs paper #685 563 places worse
0.7657
best reported
actual #122 vs paper #685 563 places worse
paper 0.6806 ±0.0018
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.6806 ±0.0018 Δ at pub 0.0534 Δ today 0.0851
350
MLP
0.7289 ±0.0010
602
TIDE-m
0.7032 ±0.0068
This paper
610
TIDE-s
0.7024 ±0.0080
This paper
623
DiffusionNet
0.7000 ±0.0091
This paper
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
18
GCN
0.9296 ±0.0015
109
GRAND
actual #109 vs paper #803 694 places worse
0.8902
best reported
actual #109 vs paper #803 694 places worse
paper 0.7461 ±0.0025
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.7461 ±0.0025 Δ at pub 0.0419 Δ today 0.1441
210
MLP
0.8690 ±0.0074
709
TIDE-m
0.7759 ±0.0004
This paper
725
TIDE-s
0.7724 ±0.0062
This paper
817
DiffusionNet
0.7309 ±0.0015
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
0.9669 ±0.0014
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
20
GRAND
actual #20 vs paper #516 496 places worse
0.9579 ±0.0059
best reported
actual #20 vs paper #516 496 places worse
paper 0.8417 ±0.0034
best today: Graph Wave Networks (WWW 2025)
paper 0.8417 ±0.0034 Δ today 0.1162
337
TIDE-s
0.9206 ±0.0051
This paper
387
TIDE-m
0.9133 ±0.0047
This paper
390
MLP
0.9128 ±0.0063
496
DiffusionNet
0.8717 ±0.0026
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
0.9412 ±0.0008
3
GAT
0.9398 ±0.0022
8
SAGE
0.9351 ±0.0006
144
GRAND
actual #144 vs paper #463 319 places worse
0.8937 ±0.0041
best reported
actual #144 vs paper #463 319 places worse
paper 0.7296 ±0.0049
best today: Graph Wave Networks (WWW 2025)
paper 0.7296 ±0.0049 Δ today 0.1641
320
MLP
0.8463
383
TIDE-s
0.8301 ±0.0002
This paper
401
TIDE-m
0.8211 ±0.0003
This paper
454
DiffusionNet
0.7472 ±0.0066
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
10
GRAND
actual #10 vs paper #156 146 places worse
0.9577 ±0.0028
best reported
actual #10 vs paper #156 146 places worse
paper 0.9059 ±0.0021
best today: Graph Wave Networks (WWW 2025)
paper 0.9059 ±0.0021 Δ today 0.0518
88
MLP
0.9280 ±0.0020
161
TIDE-s
0.9021 ±0.0012
This paper
164
TIDE-m
0.8986 ±0.0030
This paper
168
DiffusionNet
0.8952 ±0.0022
This paper

OGB

#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
90
TIDE-s
0.6843 ±0.0035
This paper
96
TIDE-m
0.6786 ±0.0110
This paper
106
GRAND
0.5929 ±0.0012
This paper
107
MLP
0.5765 ±0.0012
110
DiffusionNet
0.5479 ±0.0016
This paper

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
53
GraphSAGE
0.9000 ±0.0365
211
GAT
actual #211 vs paper #472 261 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #472 261 places worse
paper 0.6216 ±0.0008
paper 0.6216 ±0.0008 Δ at pub 0.1764 Δ today 0.1946
217
GRAND
actual #217 vs paper #414 197 places worse
0.8140 ±0.0350
best reported
actual #217 vs paper #414 197 places worse
paper 0.6762 ±0.0190
paper 0.6762 ±0.0190 Δ at pub 0.0806 Δ today 0.1378
257
GCN
actual #257 vs paper #457 200 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #457 200 places worse
paper 0.6351 ±0.0190
best today: Graph Wave Networks (WWW 2025)
paper 0.6351 ±0.0190 Δ at pub 0.1489 Δ today 0.1582
443
TIDE-m
0.6486 ±0.0150
This paper
452
TIDE-s
0.6381 ±0.0190
This paper
477
DiffusionNet
0.6216
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
0.9480 ±0.0380
3
RF-GCN
0.9429
24
MLP
0.9136 ±0.0070
138
SAGE
0.8269
142
GRAND
actual #142 vs paper #426 284 places worse
0.8246 ±0.0709
best reported
actual #142 vs paper #426 284 places worse
paper 0.5541 ±0.0190
paper 0.5541 ±0.0190 Δ at pub 0.2675 Δ today 0.2705
158
GAT
actual #158 vs paper #438 280 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #438 280 places worse
paper 0.5405 ±0.0110
paper 0.5405 ±0.0110 Δ at pub 0.2785
170
GCN
actual #170 vs paper #538 368 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #538 368 places worse
paper 0.4324 ±0.0130
paper 0.4324 ±0.0130 Δ at pub 0.3596 Δ today 0.3758
382
TIDE-s
0.5946 ±0.0190
This paper
403
TIDE-m
0.5811 ±0.0190
This paper
420
DiffusionNet
0.5676 ±0.0060
This paper
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
42
MLP
0.4026 ±0.0108
68
GraphSAGE
0.3899 ±0.0085
135
GCN
actual #135 vs paper #362 227 places worse
0.3690
best reported
actual #135 vs paper #362 227 places worse
paper 0.2938 ±0.0050
paper 0.2938 ±0.0050 Δ at pub 0.0752
154
TIDE-s
0.3664 ±0.0047
This paper
178
TIDE-m
0.3618 ±0.0047
This paper
182
GAT
actual #182 vs paper #376 194 places worse
0.3605 ±0.0035
best reported
actual #182 vs paper #376 194 places worse
paper 0.2888 ±0.0100
paper 0.2888 ±0.0100 Δ at pub 0.0717
203
GRAND
actual #203 vs paper #234 31 places worse
0.3562 ±0.0101
best reported
actual #203 vs paper #234 31 places worse
paper 0.3500 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.3500 ±0.0028 Δ at pub 0.0062 Δ today 0.0062
253
DiffusionNet
0.3444 ±0.0033
This paper
#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
actual #3 vs paper #227 224 places worse
0.8560
best reported
actual #3 vs paper #227 224 places worse
paper 0.4496 ±0.0620
52
GCN
actual #52 vs paper #225 173 places worse
0.7033
best reported
actual #52 vs paper #225 173 places worse
paper 0.4518 ±0.0062
paper 0.4518 ±0.0062 Δ at pub 0.2242 Δ today 0.2515
108
SAGE
0.6340 ±0.0300
151
GRAND
actual #151 vs paper #194 43 places worse
0.5772 ±0.0186
best reported
actual #151 vs paper #194 43 places worse
paper 0.5033 ±0.0047
169
MLP
0.5429
171
DiffusionNet
0.5384 ±0.0110
This paper
182
TIDE-m
0.5208 ±0.0110
This paper
185
TIDE-s
0.5175 ±0.0047
This paper
#ModelAccuracy ↑Paper
1
DMD++
0.9190 ±0.0260
2
F-GREAD-BS
0.9059 ±0.0380
3
APPNP
0.9010 ±0.0350
13
GRAND
actual #13 vs paper #148 135 places worse
0.8860 ±0.0210
best reported
actual #13 vs paper #148 135 places worse
paper 0.6486 ±0.0130
paper 0.6486 ±0.0130 Δ today 0.2374
37
MLP
0.8629 ±0.0450
53
GAT
actual #53 vs paper #183 130 places worse
0.8430 ±0.0370
best reported
actual #53 vs paper #183 130 places worse
paper 0.5588 ±0.0140
paper 0.5588 ±0.0140 Δ at pub 0.2842
63
GCN
actual #63 vs paper #187 124 places worse
0.8310 ±0.0320
best reported
actual #63 vs paper #187 124 places worse
paper 0.5492 ±0.0970
paper 0.5492 ±0.0970 Δ at pub 0.2818
69
GraphSAGE
0.8118 ±0.0556
130
TIDE-m
0.6961 ±0.0140
This paper
136
TIDE-s
0.6863 ±0.0140
This paper
159
DiffusionNet
0.6278 ±0.0280
This paper

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
FaberNet
0.7510 ±0.0003
2
LargeScaleNet
0.7505 ±0.0005
3
DirGNN
0.7395 ±0.0005
16
GCN
actual #16 vs paper #30 14 places worse
0.5102 ±0.0006
best reported
actual #16 vs paper #30 14 places worse
paper 0.3684 ±0.0037
paper 0.3684 ±0.0037 Δ at pub 0.0886 Δ today 0.1418
23
GAT
actual #23 vs paper #29 6 places worse
0.4540 ±0.0040
best reported
actual #23 vs paper #29 6 places worse
paper 0.3876 ±0.0075
paper 0.3876 ±0.0075 Δ at pub 0.0664
26
TIDE-s
0.4075 ±0.0058
This paper
27
TIDE-m
0.4056 ±0.0170
This paper
29
GRAND
0.3889 ±0.0042
This paper
32
MLP
0.3150
33
DiffusionNet
0.3069 ±0.0001
This paper
#ModelAccuracy ↑Paper
1
DGT
0.6609 ±0.0022
2
ICG_u-NN
0.6608 ±0.0074
3
LINKX
0.6606 ±0.0019
14
GraphSAGE
0.6473 ±0.0011
16
GCN
actual #16 vs paper #39 23 places worse
0.6434 ±0.0012
best reported
actual #16 vs paper #39 23 places worse
paper 0.6060 ±0.0019
best at pub: Deformable Graph Transformer (2022)
paper 0.6060 ±0.0019 Δ at pub 0.0374
25
GAT
actual #25 vs paper #48 23 places worse
0.6290 ±0.0022
best reported
actual #25 vs paper #48 23 places worse
paper 0.5308 ±0.0016
best at pub: Deformable Graph Transformer (2022)
paper 0.5308 ±0.0016 Δ at pub 0.0982
33
MLP
0.6114 ±0.0006
38
TIDE-m
0.6081 ±0.0004
This paper
41
TIDE-s
0.6040 ±0.0013
This paper
42
GRAND
0.5985 ±0.0003
This paper
48
DiffusionNet
0.5572 ±0.0160
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 today — OK at publication; today's leaderboard best is elsewhere