CoPE-CGL: Community-aware Prototype Extraction for Replay-Free Continual Graph Learning
Authors: Bo-Young Lim, Seokhwan Kim, Kisung Lee, Hyuk-Yoon Kwon
Organizations: Graduate School of Data Science Seoul National University of Science and Technology Seoul, South Korea · Division of Computer Science and Engineering Louisiana State University Baton Rouge, Louisiana, USA
Continual graph learning (CGL) maintains models as graphs evolve without retraining from scratch, while mitigating catastrophic forgetting. Existing methods typically target either transductive or inductive settings and often store past subgraphs or require task identifiers at inference. We propose Community-aware Prototype Extraction for Continual Graph Learning (CoPE-CGL), a replay-free framework that uses a parameter-free structural prior, precomputed by multi-hop Laplacian smoothing, to anchor learning, memory, and inference. CoPE-CGL combines topology-infused bottleneck adaptation, community-level prototypes, and dynamic routing by majority vote over node-to-prototype matches. The default protocol assumes each test graph comes from one learned task; a node-level variant handles mixed-task graphs. Each task adds at most a constant amount of storage, with no past graph data retained. At equal storage and without task identifiers, CoPE-CGL matches the strongest replay baseline even when it receives true task identifiers: average performance (AP) is 95.17% and 95.72% versus 94.28% and 95.82% on Arxiv and CoraFull, respectively, with 5.9-14.0 times faster runtime and zero forgetting. Across four transductive and three inductive benchmarks and mixed streams, CoPE-CGL exceeds the second-best of up to eleven baselines by up to 1.41, 6.32, and 9.33 AP percentage points, respectively. It runs 1.3-7.9 times faster end-to-end than the most accurate competitor on each benchmark and scales to the largest benchmark graph. On graphs mixing two tasks, its node-level variant achieves the best AP among CGL methods. The design targets homophilic graphs with community structure.
Figures & tables
Figure 1. Overview of CoPE-CGL. During training, K -hop Laplacian smoothing maps each task graph to Zbase , on which a task-specific bottleneck adapter is trained and from which community-aware prototypes Pt are extracted into memory. During inference, Ztest is routed to the matching adapter and classifier via graph-level majority voting over the prototype memory, or node by node in a node-level variant.
Dataset
# Nodes
# Edges
# Features
# Classes
# Tasks
CoraFull
19,793
130,622
8,710
70
35
Arxiv
169,343
1,166,243
128
40
20
Reddit
227,853
114,615,892
602
40
20
Products
2,449,028
61,859,036
100
46
23
Kindle
38,450
458,018
457
6
5
DBLP
54,265
2,751,530
244
4
10
Table 1. Dataset statistics; rows with the subscript mixed (e.g., CoraFull mixed ) are the mixed-setting streams.
Category
Methods
CoraFull
Arxiv
Reddit
Products
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
Lower bound
Finetuning
3.21±1.12
-95.01±0.31
104.58±5.81
4.99±0.11
-96.51±0.11
71.56±7.56
4.96±0.28
-99.31±0.56
477.47±6.06
7.03±0.09
-92.21±0.27
984.67±9.22
Regularization
EWC
2.94±0.45
-94.03±2.77
363.52±8.63
4.94±0.01
-96.87±0.17
127.05±2.36
5.10±0.10
-99.4±0.11
270.7±4.25
14.18±0.23
-92.54±0.45
430.00±1.42
MAS
2.84±0.21
-94.13±0.75
162.34±1.62
4.93±0.53
-94.53±1.13
80.62±0.45
10.26±2.52
-93.43±2.72
208.65±1.62
9.45±1.21
-89.51±1.71
362.92±0.12
TWP
20.90±2.23
-61.47±0.82
650.71±10.65
6.07±1.84
-51.24±1.92
295.19±7.73
2.11±2.63
-54.49±4.39
2698.21±1.06
3.19±2.12
-39.30±2.46
4811.18±4.77
Replay
ER-GNN
72.34±0.25
-7.45±0.12
45.11±1.32
65.63±0.31
-11.72±0.24
15.18±2.35
88.91±0.18
-1.38±0.05
38.81±3.92
38.97±0.29
-15.84±0.36
51.29±1.77
Table 2. Transductive results: AP, BWT, and wall-clock running time. Bold: best AP excluding Joint. OOM: out of memory.
Category
Methods
Kindle
DBLP
ACM
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
Lower bound
Finetuning
67.42±10.13
-17.61±10.42
1.20±0.03
65.73±7.86
-19.34±6.58
1.43±0.02
59.28±8.74
-17.92±8.89
1.12±0.01
Regularization
EWC
75.41±7.92
-9.62±8.03
60.29±0.12
77.26±4.43
-7.94±3.75
65.16±0.04
64.73±6.01
-11.28±5.84
71.77±0.23
MAS
70.58±6.84
-7.12±6.87
62.5±0.10
72.33±3.92
-5.89±3.12
102.5±0.03
59.84±5.12
-8.76±4.02
106.92±0.19
TWP
77.42 ±4.38
-8.12 ±4.54
108.73±0.34
78.31 ±3.48
-7.36 ±3.01
187.41±0.11
64.12 ±6.84
-12.08 ±6.52
192.63±0.27
Replay
ER-GNN
51.27±1.33
5.75±1.14
3.83±0.02
81.98±0.32
1.40±0.08
30.38±0.91
64.74±0.41
3.11±0.15
31.53±1.02
Table 3. Main results in the inductive setting: AP, BWT, and wall-clock running time. Bold: best AP excluding Joint.
Figure 2. Per-task accuracy matrices on Products (row: after training task t ; column: task j ). Darker is higher.
Kindlemixed
Trans: Induct
1:9
3:7
5:5
7:3
9:1
Methods
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
AP (%) ↑
BWT (%) ↑
Time (secs) ↓
TACO
56.56±0.11
-2.84±0.05
42.59±0.17
55.95±0.14
-3.27±0.02
47.18±0.09
61.51±0.11
-0.64±0.03
42.67±0.14
61.16±0.05
-1.37±0.02
43.50±0.09
59.18±0.10
-3.57±0.04
46.42±0.13
TPP
71.37±0.03
0.00±0.00
18.90±0.08
71.53±0.05
0.00±0.00
18.90±0.03
72.22±0.04
0.00±0.00
18.70±0.02
69.40±0.09
0.00±0.00
18.70±0.06
70.78±0.05
0.00±0.00
18.80±0.03
TAAM
82.36±0.08
0.00±0.00
18.50±0.07
83.50±0.09
0.00±0.00
18.20±0.07
81.10±0.08
0.00±0.00
18.40±0.10
83.90±0.05
0.00±0.00
18.40±0.11
82.91±0.06
0.00±0.00
18.50±0.05
CAGNN
82.16±1.83
-5.43±0.62
82.56±10.26
83.92±0.75
-1.88±1.56
81.89±10.06
82.73±2.44
-3.44±1.43
82.09±9.51
84.73±0.64
-4.19±0.93
81.43±10.39
85.12±2.52
-3.96±2.81
82.56±10.06
Table 4. Mixed-setting results of CoPE-CGL and the strongest replay and replay-free baselines. Bold: best AP. On DBLP mixed , the CoPE-CGL row was rerun on an NVIDIA A100 (80GB) with the same non-deterministic GPU kernels as the baselines.
Methods
CoraFull
Kindle
AP (%) ↑
BWT (%) ↑
Time (s) ↓
AP (%) ↑
BWT (%) ↑
Time (s) ↓
w/o Laplacian Smoothing
92.93±0.62
0.00±0.00
56.01±3.13
44.41±0.32
0.00±0.00
8.85±1.16
w/o Bottleneck
95.65±0.05
0.00±0.00
36.04±2.90
78.48±0.51
− 0.38±0.66
4.84±0.69
w/o Community-aware
90.54±0.14
5.59±0.05
54.85±1.76
83.09±0.07
− 2.89±0.03
7.48±0.27
w/o Majority Voting
89.56±1.53
0.00±0.00
54.98±1.12
76.31±0.78
− 9.20±0.81
8.49±0.42
CoPE-CGL (Final)
95.80±0.26
0.00±0.00
59.60±1.65
84.52±1.09
− 0.84±1.45
8.30±0.44
Table 5. Ablation study of CoPE-CGL’s four components on CoraFull (transductive) and Kindle (inductive). All rows use seeds 1024–1026, so the Final row differs slightly from Tables 2 and 3 . On CoraFull, a misrouted test graph scores 0.
Dataset
Method
Memory (MB)
AP (%) ↑
BWT (%) ↑
Time (s) ↓
Arxiv ( T=20 , d=128 )
ER-GNN (budget 40)
0.4288
48.12±1.02
-16.05±0.36
43.24±2.56
SSM (budget 40)
0.4162
52.87±0.68
-16.49±1.11
45.38±2.42
CaT (budget 40)
0.4288
61.69±2.58
-12.01±1.74
225.76±3.23
CaT (task-IL)
0.4288
94.28±0.83
-0.02±0.25
225.76±3.23
TAAM (rank 8)
0.3863
84.94±0.46
-1.43±0.43
71.51±0.68
SAFER ( r=14 )
0.4069
93.28±0.17
0.00±0.00
151.19±1.60
Table 6. Comparison at matched final storage. Italic: CAGNN in its default configuration, far above the matched storage. CaT (task-IL) is given the true task identifier at test time and is not ranked; its training, storage, and time are those of CaT.
Dataset
Graph-level routing (%)
Node-level routing (%)
Edge-error correlation
CoraFull
100.00
75.35
0.899
Arxiv
100.00
55.46
0.354
Reddit
100.00
97.10
0.253
Products
100.00
60.55
0.820
Pooled
100.00
72.26
0.581
Table 7. Routing accuracy of CoPE-CGL on the four transductive benchmarks: graph- and node-level routing accuracy (%) and edge-error correlation (Pearson correlation of node routing errors between edge endpoints). Pooled covers all 98 test graphs over three runs; its correlation is the mean over the four benchmarks.
Figure 3. Task-ID accuracy under the 5:5 mixed setting.
Method
Arxiv
Reddit
Native AP
Mixed AP
Time (s)
Native AP
Mixed AP
Time (s)
Finetuning
4.92±0.00
1.92±0.00
69.50±1.08
4.96±0.01
3.50±0.01
532.94±1.63
EWC
5.00±0.11
1.96±0.08
149.35±1.20
6.42±1.21
4.73±1.14
608.91±2.15
MAS
5.13±0.12
2.44±0.13
114.69±29.69
8.61±0.26
7.31±0.42
569.80±2.80
TWP
5.65±1.83
8.21±2.61
318.71±1.28
2.05±3.26
1.79±1.45
3247.51±252.87
ER-GNN
27.65±0.24
28.79±0.58
67.72±1.26
30.13±4.59
27.52±5.80
539.59±10.67
Table 8. Mixed-task test graphs on Arxiv and Reddit ( T=20 ): AP ↑ on single-task (Native) and mixed-task (Mixed) test graphs, and running time (s). Seeds 1042–1044 differ from those of Table 2 . Replay buffers hold 29 (Arxiv) and 40 (Reddit) nodes per task. TWP uses two GAT heads on Reddit (eight run out of memory). CoPE-CGL’s Native AP is from a run without mixed evaluation, with its default graph-level vote.
Dataset
Method
0%
+10%
+20%
+30%
+50%
CoraFull
TPP
90.57
87.99
85.90
83.61
80.20
TAAM
89.65
87.61
85.78
85.92
83.00
SAFER
94.86
90.49
86.94
86.35
82.54
CAGNN
94.48
87.56
85.92
85.38
83.37
CoPE-CGL
95.43
90.53
88.03
88.03
85.25
Arxiv
TPP
94.58
94.20
93.28
92.35
90.93
Table 9. Robustness to random edge noise: AP ↑ after adding random undirected edges numbering x% of each task’s edge list. Single run (seed 42, 200 epochs), so the 0% column differs from Tables 2 and 3 (by up to 2.61 points for CoPE-CGL).
Dataset
Tasks
Q range
r ( p )
ρ ( p )
Baselines
CoraFull
35
0.04–0.50
0.24 (0.16)
0.28 (0.11)
0/4 / 0/4
Arxiv
20
0.00–0.50
− 0.12 (0.60)
− 0.38 (0.10)
0/4 / 0/4
Reddit
20
0.04–0.50
0.14 (0.55)
0.26 (0.26)
0/3 / 0/3
Products
23
0.00–0.50
0.11 (0.61)
0.49 (0.02)
0/3 / 3/3
Kindle
5
0.40–0.66
− 0.85 (0.07)
− 0.60 (0.28)
3/4 / 1/4
DBLP
10
0.31–0.48
0.62 (0.06)
0.85 ( < 0.01)
1/4 / 3/4
Table 10. Pearson r and Spearman ρ (two-sided p ) between per-task AP and modularity Q for CoPE-CGL. Baselines: number of baselines (TPP, TAAM, SAFER, CAGNN) whose AP– Q correlation reaches p<0.05 (Pearson / Spearman).
Dataset
Setting
Tasks
Data transfer
Laplacian smoothing
Community detection
Prototype extraction
Adapter training
Routing
Classification
Re-eval. (protocol)
Other
Total
CoraFull
Trans.
35
0.41 (0.6%)
0.21 (0.3%)
0.18 (0.3%)
0.06 (0.1%)
52.46 (82.9%)
0.27 (0.4%)
0.05 (0.1%)
8.80 (13.9%)
0.85 (1.3%)
63.30
Arxiv
Trans.
20
0.09 (0.3%)
0.12 (0.4%)
2.69 (8.9%)
0.12 (0.4%)
25.44 (83.8%)
0.07 (0.2%)
0.02 (0.1%)
1.24 (4.1%)
0.57 (1.9%)
30.35
Reddit
Trans.
20
2.31 (1.2%)
1.64 (0.9%)
133.99 (70.1%)
0.12 (0.1%)
34.03 (17.8%)
0.09 (0.0%)
0.04 (0.0%)
18.13 (9.5%)
0.85 (0.4%)
191.20
Products
Trans.
23
3.72 (0.9%)
1.91 (0.5%)
294.64 (69.6%)
1.57 (0.4%)
66.09 (15.6%)
0.10 (0.0%)
0.06 (0.0%)
54.60 (12.9%)
0.81 (0.2%)
423.51
Kindle
Ind.
5
0.11 (1.1%)
0.12 (1.2%)
0.68 (6.9%)
0.02 (0.2%)
8.35 (84.3%)
0.01 (0.1%)
0.01 (0.1%)
0.13 (1.3%)
0.48 (4.9%)
9.91
DBLP
Ind.
10
0.13 (0.6%)
0.12 (0.6%)
4.55 (21.9%)
0.05 (0.2%)
14.95 (71.9%)
0.03 (0.1%)
0.01 (0.1%)
0.43 (2.1%)
0.51 (2.5%)
20.78
Table 11. Running-time breakdown of CoPE-CGL: wall-clock time of each component in seconds, with its share of the total in parentheses (NVIDIA RTX A4000). Re-eval. evaluates all earlier tasks after each new task and is needed only for AP and BWT.
Figure 4. Scalability of CoPE-CGL, TPP, and TAAM on Products: (a) AP, (b) wall-clock running time. The 100% points are from Table 2 ; the others are means over seeds 1024–1026.
Figure 5. Sensitivity of CoPE-CGL’s AP on Products to three hyperparameters: smoothing hops K , adapter scaling weight α , and prototype count M . Horizontal lines mark CAGNN, SAFER, TPP, and TAAM at their default settings (Table 2 means). α is a fixed weight. CoPE-CGL curves are single runs (seed 1024); horizontal lines are three-seed means.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Component
Hyperparameter
Value
Structural prior
Propagation hops K
2 ( A^ sym.-normalized, self-loops)
TIBA adapter
Bottleneck width b
min(max(⌊d/4⌋,16),128)
Residual scale α
1.0 (up-projection zero-initialized)
Classifier head
linear, Xavier-uniform init.
Optimization
Optimizer
Adam, full batch
Learning rate
0.01
Appendix
Table 12. Hyperparameters of CoPE-CGL, shared by all datasets and settings.
Dataset
ϵ^M
Bound
Relative gap
CoraFull
0.1745
0.4906
9.80%
Arxiv
0.0191
0.2640
4.87%
Reddit
0.0103
0.0718
0.57%
Products
0.3300
1.2292
17.32%
Appendix
Table 13. Top- M truncation at M=10 : measured gap ϵ^M , its upper bound 2Ev∈Vtest[r(v)] from Corollary 1, and ϵ^M relative to the mean pairwise squared distance between community prototypes.
Algorithm
AP (%) ↑
Graph routing (%)
Node routing (%)
Louvain (default)
95.78±0.24
100.00±0.00
75.35±0.12
Leiden
95.78±0.24
100.00±0.00
75.12±0.09
Infomap
95.79±0.22
100.00±0.00
70.76±0.17
Fast-Greedy
95.78±0.24
100.00±0.00
75.84±0.00
Label Propagation
95.78±0.24
100.00±0.00
72.90±0.62
Appendix
Table 14. CoPE-CGL on CoraFull with five community detection algorithms (three seeds).
Method
Mean time per task (s)
First task (s)
Last task (s)
Max peak memory (MB)
Last-task peak memory (MB)
CaT
14.93
17.15
14.58
265.87
92.77
TPP
3.37
17.62
2.47
235.57
89.87
CoPE-CGL
3.15
2.08
2.74
170.39
81.34
Appendix
Table 15. Per-task training time and peak GPU memory on Arxiv (A100, seed 1024).
T
Adapters (MB)
Heads (MB)
Prototypes (MB)
Total (MB)
Routing (ms/graph)
Routing accuracy (%)
10
89.54
0.35
3.34
93.24
3.42
100.00
35
313.40
1.22
12.05
326.68
8.19
100.00
70
626.81
2.44
24.07
653.32
15.18
97.14
Appendix
Table 16. Storage and routing on a 70-task CoraFull stream (one class per task, default configuration, seed 1024).
Dataset
N=1
N=10
N=100
All nodes
CoraFull
72.70±4.50
97.78±0.55
100.00±0.00
100.00±0.00
Arxiv
52.78±6.73
93.89±3.47
100.00±0.00
100.00±0.00
Reddit
98.89±0.96
100.00±0.00
100.00±0.00
100.00±0.00
Products
57.97±6.32
86.48±2.21
98.07±1.67
100.00±0.00
Appendix
Table 17. Graph-level routing accuracy (%) with N sampled test nodes per test graph (mean ± std over seeds 1024–1026).
Continual Graph Learning (CGL) aims to incrementally learn from graph-structured data while preserving knowledge acquired from previous tasks. A major challenge in this setting is catastrophic forgetting, where learning new tasks degrades performance on previously learned ones. Hierarchical Prototype Networks (HPNs) address this problem through a prototype-based memory mechanism that avoids storing historical data, but their reliance on linear feature extractors limits their ability to exploit graph topology, while point-based prototypes often lead to inefficient prototype growth on structurally diverse graphs. In this work, we propose HCPN-GCN, a graph-aware extension of HPN that replaces the original linear feature extractors with Graph Convolutional Networks (GCNs) and introduces cone-based prototypes with a diversity regularization objective. The proposed design produces richer graph-aware representations while compactly modeling the embedding space, reducing prototype proliferation without sacrificing discriminability. Experimental results on six continual graph learning benchmarks demonstrate that HCPN-GCN consistently improves average classification accuracy over the original HPN and representative continual learning baselines while maintaining near-zero forgetting. Furthermore, our analysis shows that the proposed model learns substantially richer class-level prototype hierarchies using approximately 30× fewer atomic prototypes than the original HPN, providing a more compact and effective memory representation for continual graph learning.
Sammuel R. Silva, Vander L. S. Freitas, Gladston Moreira +2
Universidade Federal de Ouro Preto, Ouro Preto 35402-163, Brasil
Continual graph learning (CGL) aims to learn from dynamically evolving graphs while mitigating catastrophic forgetting. Existing CGL approaches typically adopt a task-based formulation, where the data stream is partitioned into a sequence of discrete tasks with pre-defined boundaries. However, such assumptions rarely hold in real-world environments, where data distributions evolve continuously and task identity is often unavailable. To better reflect realistic non-stationary environments, we revisit continual graph learning from a task-free perspective. We propose a unified formulation that models the data stream as a time-varying mixture of latent task distributions, enabling continuous modeling of distribution drift. Based on this formulation, we construct DRIFT, a benchmark that spans a spectrum of transition dynamics ranging from hard task switches to smooth distributional drift through a Gaussian parameterization. We evaluate representative continual learning methods under this task-free setting and observe substantial performance degradation compared to traditional task-based protocols. Our findings indicate that many existing approaches implicitly rely on task boundary information and struggle under realistic task-free graph streams. This work highlights the importance of studying continual graph learning under realistic non-stationary conditions and provides a benchmark for future research in this direction. Our code is available at https://github.com/UConn-DSIS/DRIFT.
Guiquan Sun, Xikun Zhang, Jingchao Ni +1
University of Connecticut · RMIT University · University of Houston
Self-supervised Continual Graph Learning (CGL) aims to successively learn from a graph sequence with different tasks without label supervision - a paradigm that has attracted widespread attention. Most existing self-supervised CGL methods rely on instance-level consistency objectives that enforce stability of individual node (or node-pair) embeddings. Due to optimizing nodes in isolation, these methods fail to maintain global relational structure, causing inter-node correspondences to progressively distort under continual learning. To this end, we propose a novel Structure-Aware Optimal Transport (SAOT) framework that explicitly captures and preserves relational structure within graph representations across sequential tasks. Specifically, SAOT leverages optimal transport theory to capture global inter-node correspondences, thereby facilitating and enhancing graph representation learning. Simultaneously, SAOT incorporates a cross-task knowledge distillation mechanism to preserve the previous structural knowledge. Extensive experiments on four CGL benchmark datasets demonstrate that SAOT outperforms existing self-supervised baselines. In particular, SAOT achieves significant performance gains, improving average accuracy by up to 5% on CoraFull-CL and over 15% on Products-CL compared with state-of-the-art methods in the Class-IL setting.
Yuting Zhang, Yanbei Liu, Zhitao Xiao +3
School of Electronics and Information Engineering, Tiangong University, Tianjin, China · School of Life Sciences, Tiangong University, Tianjin, China · School of Electrical and Infomation Engineering, Tianjin University, Tianjin, China +1