MAGIC: Topology-Aware Analytic Graph Few-Shot Class-Incremental Learning

Junlin Chen; Yuhan Wang; Xuefei Wang; Xiao Wang; Ruijie Wang; Jianxin Li

cs.LGOct 4, 2026

MAGIC: Topology-Aware Analytic Graph Few-Shot Class-Incremental Learning

Authors: Junlin Chen, Yuhan Wang, Xuefei Wang, Xiao Wang, Ruijie Wang, Jianxin Li

Organizations: Beihang University, Beijing, China

Abstract

Graph few-shot class-incremental learning (GFSCIL) requires a model to continually recognize emerging classes from only a few labeled nodes while preserving previously acquired knowledge. Beyond the catastrophic forgetting inherited from conventional graph continual learning, GFSCIL presents two distinctive challenges: extremely limited novel-class supervision causes severe overfitting, while cross-session edges---edges connecting newly arriving nodes with historical nodes---alter historical propagation neighborhoods and thereby induce representation drift. We propose MAGIC, a replay-free GFSCIL framework that combines a frozen graph representation backbone (e.g., an intrinsically parameter-free backbone such as SGC or a pretrained graph foundation model) with closed-form analytic continual learning. To alleviate novel-session overfitting, MAGIC learns a topological prior from the base graph that can characterize both homophilous and heterophilous relations, and injects this prior through Potts Markov random field inference to refine supervision for novel classes. To mitigate representation drift, MAGIC transfers previous predictions from the old representations of affected historical nodes to their updated representations through drift-aware analytic distillation. Experiments across five datasets and eight baselines demonstrate the effectiveness of MAGIC. Under the 5-shot setting, MAGIC improves Mean Accuracy and Final Accuracy by 5.48 percentage points and 9.33 percentage points on average, and reduces Performance Drop by 10.78 percentage points on average compared with the best baselines. MAGIC also shows clear advantages under the 1- and 3-shot settings, with larger gains as the number of supports increases. Moreover, MAGIC requires substantially less training time.

Figures & tables

Figure 1: On the base stage, MAGIC learns a topological prior. In novel sessions, limited labeled supports first update an initial classifier, while drift-aware distillation protects historical nodes affected by cross-session edges. Finally, MAGIC extracts a subgraph around novel supports and performs Potts MRF inference with the topological prior to adjust the pseudo-labels predicted by the initial classifier, and subsequently updates the classifier using these adjusted labels.

	CoraFull			ogbn-arxiv			Coauthor CS			Amazon Computers			WikiCS
Method	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD
LwF	16.06	3.82	79.86	18.16	4.65	82.03	35.83	17.16	79.73	35.05	13.55	82.07	35.83	12.90	79.78
LwF (std)	$\pm$ 1.24	$\pm$ 1.44	$\pm$ 2.35	$\pm$ 0.97	$\pm$ 5.80	$\pm$ 6.57	$\pm$ 3.44	$\pm$ 5.45	$\pm$ 5.73	$\pm$ 1.73	$\pm$ 5.61	$\pm$ 4.53	$\pm$ 2.33	$\pm$ 3.96	$\pm$ 4.33
EWC	16.14	3.86	79.82	15.87	6.07	80.52	36.38	17.32	79.58	35.13	13.96	81.54	35.89	12.86	79.82
EWC (std)	$\pm$ 1.31	$\pm$ 1.39	$\pm$ 2.30	$\pm$ 2.23	$\pm$ 6.70	$\pm$ 7.19	$\pm$ 3.85	$\pm$ 5.54	$\pm$ 5.78	$\pm$ 1.74	$\pm$ 5.92	$\pm$ 4.90	$\pm$ 2.49	$\pm$ 3.86	$\pm$ 4.27
MAS	16.31	6.07	77.61	34.40	27.37	59.25	45.91	20.77	76.12	34.98	13.35	82.17	35.24	12.42	80.26

Table 1: Main results under the 5-shot setting. MAGIC Backbone: SGC. MAGIC improves Mean Accuracy and Final Accuracy by 5.48 percentage points and 9.33 percentage points on average, and reduces Performance Drop by 10.78 percentage points on average compared with the best baselines.

Figure 4: Main results on CoraFull under the 1- and 3-shot settings. MAGIC Backbone: SGC

	CoraFull			ogbn-arxiv			Coauthor CS			Amazon Computers			WikiCS
Backbone	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD
SGC	65.45	56.02	24.19	63.50	49.81	34.37	94.03	91.45	5.54	86.54	81.04	9.70	80.33	74.64	14.09
SGC (std)	$\pm$ 0.95	$\pm$ 1.05	$\pm$ 3.65	$\pm$ 3.92	$\pm$ 2.35	$\pm$ 2.55	$\pm$ 0.79	$\pm$ 0.28	$\pm$ 1.34	$\pm$ 1.68	$\pm$ 2.88	$\pm$ 5.06	$\pm$ 1.74	$\pm$ 2.14	$\pm$ 3.01
S 2 GC	64.42	54.74	25.48	61.23	47.05	36.43	94.25	91.77	5.43	87.26	81.69	9.76	80.61	74.86	14.20
S 2 GC (std)	$\pm$ 0.57	$\pm$ 1.20	$\pm$ 4.24	$\pm$ 4.01	$\pm$ 2.39	$\pm$ 2.66	$\pm$ 0.78	$\pm$ 0.48	$\pm$ 1.40	$\pm$ 1.58	$\pm$ 2.72	$\pm$ 4.79	$\pm$ 1.55	$\pm$ 2.09	$\pm$ 3.34
PPR	66.92	57.62	22.84	65.40	51.34	34.13	94.26	91.90	5.02	85.89	79.96	10.58	80.12	73.90	14.98

Table 2: Results (%) with different frozen graph backbones under the 5-shot setting. RGVT is excluded from ogbn-arxiv because its released checkpoint was supervised-pretrained on that dataset.

Variant	Mean Acc.	Final Acc.	PD
w/o Prior	53.69 $\pm$ 7.74	37.29 $\pm$ 7.28	46.89 $\pm$ 6.72
w/o Distill	61.88 $\pm$ 3.61	48.02 $\pm$ 1.69	36.16 $\pm$ 4.61
MAGIC	63.50 $\pm$ 3.92	49.81 $\pm$ 2.35	34.37 $\pm$ 2.55

Table 3: Ablation results (%) on ogbn-arxiv under the 5-shot setting using SGC.

Figure 5: Novel-class performance on CoraFull.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Nodes	Edges	Features	Classes	$h_{\mathrm{edge}}$
CoraFull	19,793	126,842	8,710	70	0.57
Coauthor CS	18,333	163,788	6,805	15	0.81
ogbn-arxiv	169,343	1,166,243	128	40	0.65
WikiCS	11,701	216,123	300	10	0.65
Amazon Computers	13,752	491,722	767	10	0.78

Appendix

Table 4: Statistics of the node-classification datasets.

Dataset	Base Classes	Way
CoraFull	20	5
ogbn-arxiv	10	3
Coauthor CS	5	2
Amazon Computers	4	2
WikiCS	4	2

Appendix

Table 5: Class-incremental split configurations.

	CoraFull			ogbn-arxiv			Coauthor CS			Amazon Computers			WikiCS
Method	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD
LwF	13.18	2.28	81.39	16.64	5.29	81.38	35.23	16.68	80.21	32.84	13.17	82.40	34.56	11.45	81.14
LwF (std)	$\pm$ 0.93	$\pm$ 0.93	$\pm$ 2.91	$\pm$ 1.53	$\pm$ 6.77	$\pm$ 7.35	$\pm$ 3.34	$\pm$ 5.40	$\pm$ 5.82	$\pm$ 2.10	$\pm$ 5.34	$\pm$ 4.25	$\pm$ 2.40	$\pm$ 4.66	$\pm$ 4.76
EWC	13.53	2.83	80.85	17.48	9.11	77.57	36.50	17.14	79.76	33.16	14.63	80.92	34.83	11.76	80.91
EWC (std)	$\pm$ 1.09	$\pm$ 1.71	$\pm$ 2.75	$\pm$ 1.25	$\pm$ 5.30	$\pm$ 5.67	$\pm$ 4.02	$\pm$ 5.25	$\pm$ 5.64	$\pm$ 2.62	$\pm$ 6.77	$\pm$ 5.92	$\pm$ 2.48	$\pm$ 4.98	$\pm$ 5.12
MAS	16.40	6.16	77.52	30.77	18.51	68.16	51.31	24.55	72.34	34.88	12.71	82.95	35.65	12.35	80.26

Appendix

Table 6: Main results (%) under the 1-shot setting. The mean and standard deviation over five runs are reported in consecutive rows. The best result in each column is shown in bold. MAGIC Backbone: SGC.

	CoraFull			ogbn-arxiv			Coauthor CS			Amazon Computers			WikiCS
Method	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD	MA	FA	PD
LwF	15.46	3.51	80.17	18.14	5.29	81.33	35.72	16.99	79.90	34.54	13.39	82.23	35.02	12.51	80.11
LwF (std)	$\pm$ 1.24	$\pm$ 1.15	$\pm$ 2.46	$\pm$ 0.66	$\pm$ 6.95	$\pm$ 7.53	$\pm$ 3.54	$\pm$ 5.19	$\pm$ 5.42	$\pm$ 2.29	$\pm$ 5.47	$\pm$ 4.37	$\pm$ 0.70	$\pm$ 3.58	$\pm$ 3.92
EWC	15.56	3.61	80.07	16.05	6.13	80.49	36.66	17.07	79.82	35.00	14.46	81.12	35.16	12.57	80.11
EWC (std)	$\pm$ 1.36	$\pm$ 1.45	$\pm$ 2.43	$\pm$ 2.05	$\pm$ 6.67	$\pm$ 7.13	$\pm$ 4.20	$\pm$ 5.07	$\pm$ 5.32	$\pm$ 2.59	$\pm$ 6.46	$\pm$ 5.58	$\pm$ 0.80	$\pm$ 3.74	$\pm$ 4.14
MAS	16.04	6.08	77.60	32.89	27.88	58.80	49.00	21.31	75.58	34.83	12.54	83.04	35.23	12.35	80.33

Appendix

Table 7: Main results (%) under the 3-shot setting. The mean and standard deviation over five runs are reported in consecutive rows. The best result in each column is shown in bold. MAGIC Backbone: SGC.

	CoraFull		ogbn-arxiv		Coauthor CS		Amazon Computers		WikiCS
Method	AN	FN	AN	FN	AN	FN	AN	FN	AN	FN
LwF	16.22	3.27	11.26	6.84	43.70	22.85	47.56	33.32	46.27	23.89
LwF (std)	$\pm$ 2.05	$\pm$ 1.27	$\pm$ 4.13	$\pm$ 8.03	$\pm$ 2.48	$\pm$ 9.78	$\pm$ 10.84	$\pm$ 13.99	$\pm$ 4.14	$\pm$ 9.25
EWC	16.93	3.94	13.75	10.75	43.77	23.17	46.60	33.48	47.07	24.47
EWC (std)	$\pm$ 1.67	$\pm$ 2.26	$\pm$ 3.60	$\pm$ 6.83	$\pm$ 3.45	$\pm$ 9.73	$\pm$ 11.08	$\pm$ 13.98	$\pm$ 3.77	$\pm$ 9.73
MAS	20.32	8.79	7.99	8.17	58.28	30.91	59.58	32.25	50.77	26.07

Appendix

Table 8: Novel-class results (%) under the 1-shot setting. The mean and standard deviation over five runs are reported in consecutive rows. The best result in each column is shown in bold. MAGIC Backbone: SGC.

	CoraFull		ogbn-arxiv		Coauthor CS		Amazon Computers		WikiCS
Method	AN	FN	AN	FN	AN	FN	AN	FN	AN	FN
LwF	22.19	4.99	15.97	6.85	45.59	23.23	57.41	33.81	49.51	26.29
LwF (std)	$\pm$ 1.20	$\pm$ 1.35	$\pm$ 3.74	$\pm$ 8.27	$\pm$ 3.44	$\pm$ 9.26	$\pm$ 12.08	$\pm$ 14.12	$\pm$ 9.38	$\pm$ 6.89
EWC	22.33	5.10	17.01	7.89	45.86	23.22	58.02	33.94	50.15	26.40
EWC (std)	$\pm$ 1.46	$\pm$ 1.80	$\pm$ 3.79	$\pm$ 7.96	$\pm$ 3.43	$\pm$ 9.13	$\pm$ 12.46	$\pm$ 14.22	$\pm$ 9.32	$\pm$ 7.20
MAS	22.38	8.59	9.94	8.05	57.42	28.54	59.77	31.85	49.37	26.04

Appendix

Table 9: Novel-class results (%) under the 3-shot setting. The mean and standard deviation over five runs are reported in consecutive rows. The best result in each column is shown in bold. MAGIC Backbone: SGC.

	CoraFull		ogbn-arxiv		Coauthor CS		Amazon Computers		WikiCS
Method	AN	FN	AN	FN	AN	FN	AN	FN	AN	FN
LwF	23.86	5.41	15.06	6.01	46.25	23.51	60.18	34.25	51.46	27.22
LwF (std)	$\pm$ 0.88	$\pm$ 1.72	$\pm$ 3.72	$\pm$ 6.89	$\pm$ 4.24	$\pm$ 9.79	$\pm$ 8.12	$\pm$ 14.62	$\pm$ 7.31	$\pm$ 8.14
EWC	23.88	5.47	16.26	7.57	46.48	23.71	59.76	34.16	51.65	27.16
EWC (std)	$\pm$ 0.95	$\pm$ 1.65	$\pm$ 3.72	$\pm$ 8.06	$\pm$ 4.32	$\pm$ 9.88	$\pm$ 7.98	$\pm$ 14.46	$\pm$ 7.30	$\pm$ 8.00
MAS	23.51	8.60	10.06	7.04	55.78	28.19	60.05	33.65	49.31	26.31

Appendix

Table 10: Novel-class results (%) under the 5-shot setting. The mean and standard deviation over five runs are reported in consecutive rows. The best result in each column is shown in bold. MAGIC Backbone: SGC.

Figure 6: Hyperparameter sensitivity of MAGIC on CoraFull under the 5-shot setting. Each subplot varies one hyperparameter while fixing all others to their default values. MAGIC Backbone: SGC

Dataset	$\eta$	$\rho$	$\kappa$	$B$	$T_{D}$	$\tau_{u}$	$k$
CoraFull	3.0	1.0	0.2	3	0.50	1.0	3
ogbn-arxiv	6.0	1.0	0.5	10	0.25	1.0	3
Coauthor CS	1.0	1.0	0.5	10	0.25	1.0	3
Amazon Computers	1.0	1.0	0.5	10	0.25	1.0	3
WikiCS	3.0	1.0	0.5	10	0.25	1.0	3

Appendix

Table 11: Hyperparameter configurations used in the main experiments. The same configurations are used for the 1-, 3-, and 5-shot settings.

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