cs.LGOct 26, 2026
SaveCoPE-CGL: Community-aware Prototype Extraction for Replay-Free Continual Graph Learning
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
Abstract
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, -hop Laplacian smoothing maps each task graph to , on which a task-specific bottleneck adapter is trained and from which community-aware prototypes are extracted into memory. During inference, 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 |
| 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 | 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 ; column: task ). Darker is higher.
| 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 ( , ) | 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 ( ) | 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 |
| 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 mixed setting.
| Method | Arxiv | |||||
| 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 ( ): 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 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 | range | ( ) | ( ) | 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 |
| 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 and Spearman (two-sided ) between per-task AP and modularity for CoPE-CGL. Baselines: number of baselines (TPP, TAAM, SAFER, CAGNN) whose AP– correlation reaches (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 |
| 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 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 , adapter scaling weight , and prototype count . Horizontal lines mark CAGNN, SAFER, TPP, and TAAM at their default settings (Table 2 means). 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 | 2 ( sym.-normalized, self-loops) |
| TIBA adapter | Bottleneck width | |
| Residual scale | 1.0 (up-projection zero-initialized) | |
| Classifier head | linear, Xavier-uniform init. | |
| Optimization | Optimizer | Adam, full batch |
| Learning rate | 0.01 |
Table 12. Hyperparameters of CoPE-CGL, shared by all datasets and settings.
| Dataset | Bound | Relative gap | |
| CoraFull | 0.1745 | 0.4906 | 9.80% |
| Arxiv | 0.0191 | 0.2640 | 4.87% |
| 0.0103 | 0.0718 | 0.57% | |
| Products | 0.3300 | 1.2292 | 17.32% |
Table 13. Top- truncation at : measured gap , its upper bound from Corollary 1, and 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 |
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 |
Table 15. Per-task training time and peak GPU memory on Arxiv (A100, seed 1024).
| 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 |
Table 16. Storage and routing on a 70-task CoraFull stream (one class per task, default configuration, seed 1024).
| Dataset | 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 |
| 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 |
Table 17. Graph-level routing accuracy (%) with sampled test nodes per test graph (mean ± std over seeds 1024–1026).
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