Learning Discriminative and Generalizable Anomaly Detector for Dynamic Graph with Limited Supervision

Yuxing Tian; Yiyan Qi; Fengran Mo; Weixu Zhang; Jian Guo; Jian-Yun Nie

cs.LGFeb 23, 2026

Learning Discriminative and Generalizable Anomaly Detector for Dynamic Graph with Limited Supervision

Authors: Yuxing Tian, Yiyan Qi, Fengran Mo, Weixu Zhang, Jian Guo, Jian-Yun Nie

Organizations: Universit´e de Montréal · International Digital Economy Academy (IDEA) · McGill University · Mila - Quebec Artificial Intelligence Institute.

Abstract

Dynamic graph anomaly detection is critical for many real-world applications but remains challenging due to the scarcity of labeled anomalies. Existing methods are either unsupervised or semi-supervised: unsupervised methods avoid the need for labeled anomalies but often produce ambiguous boundary, whereas semi-supervised methods can overfit to the limited labeled anomalies and generalize poorly to unseen anomalies. To address this gap, we consider a largely underexplored problem: learning a discriminative boundary from normal/unlabeled data, while leveraging limited labeled anomalies when available without sacrificing generalization to unseen anomalies. In this paper, we propose an effective, generalizable, and model-agnostic framework with three main components: (i) residual representation encoding that capture deviations between current interactions and their historical context, providing anomaly-relevant signals; (ii) a restriction loss that constrain the normal representations within an interval bounded by two co-centered hyperspheres, ensuring consistent scales while keeping anomalies separable; (iii) a bi-boundary optimization strategy that learns a discriminative and robust boundary using the log-likelihood distribution modeled by a normalizing flow. Extensive experiments demonstrate the superiority of our framework across diverse evaluation settings.

Figures & tables

Figure 1: Conceptual illustration. (a) Unsupervised methods often yield ambiguous decision boundaries, with anomaly scores collapse into a narrow range. (b) The objective of our framework.

Figure 2: Framework overview. We first encode each sample’s residual representation by contrasting two node-pair embeddings (Sec 4.1 ). Then the residual representations of normal samples (green dots) are constrained into an interval region between two co-centered hypersphere, while anomalous samples (red dots) are pushed outside (Sec 4.2 ). Finally, normalizing flow is used to model the normal log-likelihood distribution and then a discriminative and robust boundary is explicitly learned by the bi-boundary optimization(Sec 4.3 ).

DTDG-based DGAD Methods
Methods	Wikipedia			Reddit			MOOC
Methods	AUROC	AP	F1	AUROC	AP	F1	AUROC	AP	F1
Netwalk	$73.10{\scriptstyle\pm 2.12}$	$1.28{\scriptstyle\pm 1.14}$	$0{\scriptstyle\pm 0}$	$59.18{\scriptstyle\pm 2.02}$	$0.09{\scriptstyle\pm 0.04}$	$0{\scriptstyle\pm 0}$	$64.12{\scriptstyle\pm 0.98}$	$2.21{\scriptstyle\pm 0.43}$	$0{\scriptstyle\pm 0}$
AddGraph	$74.80{\scriptstyle\pm 1.98}$	$1.63{\scriptstyle\pm 1.19}$	$0.92{\scriptstyle\pm 0.15}$	$58.37{\scriptstyle\pm 4.28}$	$0.12{\scriptstyle\pm 0.05}$	$0{\scriptstyle\pm 0}$	$66.35{\scriptstyle\pm 1.76}$	$2.52{\scriptstyle\pm 0.39}$	$0{\scriptstyle\pm 0}$
STRGNN	$72.87{\scriptstyle\pm 3.31}$	$2.24{\scriptstyle\pm 2.01}$	$0{\scriptstyle\pm 0}$	$59.26{\scriptstyle\pm 3.14}$	$0.10{\scriptstyle\pm 0.03}$	$0{\scriptstyle\pm 0}$	$63.47{\scriptstyle\pm 2.05}$	$1.98{\scriptstyle\pm 0.37}$	$0{\scriptstyle\pm 0}$
Taddy	$75.40{\scriptstyle\pm 2.88}$	$2.52{\scriptstyle\pm 1.41}$	$1.34{\scriptstyle\pm 0.17}$	$61.04{\scriptstyle\pm 2.33}$	$0.14{\scriptstyle\pm 0.06}$	$0.10{\scriptstyle\pm 0.05}$	$67.02{\scriptstyle\pm 1.64}$	$3.83{\scriptstyle\pm 0.41}$	$0{\scriptstyle\pm 0}$

Table 1: Performance comparison (

Avg{\scriptstyle\pm std}

in %) on datasets with real anomalies under S1 . Best results are highlighted in green .

CTDG-based DGAD Methods
Methods	UCI			Enron			LastFM
Methods	AUROC	AP	F1	AUROC	AP	F1	AUROC	AP	F1
SAD	$86.57{\scriptstyle\pm 6.70}$	$16.90{\scriptstyle\pm 5.18}$	$0{\scriptstyle\pm 0}$	$79.59{\scriptstyle\pm 3.82}$	$3.58{\scriptstyle\pm 2.97}$	$0{\scriptstyle\pm 0}$	$85.37{\scriptstyle\pm 1.33}$	$1.79{\scriptstyle\pm 0.40}$	$0{\scriptstyle\pm 0}$
GeneralDyG	$82.25{\scriptstyle\pm 7.72}$	$7.63{\scriptstyle\pm 8.86}$	$4.85{\scriptstyle\pm 10.84}$	$84.26{\scriptstyle\pm 4.16}$	$5.90{\scriptstyle\pm 3.11}$	$0{\scriptstyle\pm 0}$	$83.84{\scriptstyle\pm 0.24}$	$8.46{\scriptstyle\pm 0.02}$	$0{\scriptstyle\pm 0}$
Representative CTDG Models
JODIE	$56.58{\scriptstyle\pm 8.30}$	$0.44{\scriptstyle\pm 0.14}$	$0.15{\scriptstyle\pm 0.33}$	$37.40{\scriptstyle\pm 4.64}$	$1.30{\scriptstyle\pm 0.31}$	$0{\scriptstyle\pm 0}$	$40.83{\scriptstyle\pm 4.64}$	$3.46{\scriptstyle\pm 0.74}$	$0{\scriptstyle\pm 0}$

Table 2: Performance comparison (

Avg{\scriptstyle\pm std}

in %) on datasets with synthetic anomalies under S3 . Best results are highlighted in green .

Panel of Figure 3 — Figure 3: Visualization of log-likelihood distributions under different ablation variants. Top: baseline without any components ( Left ) vs. adding residual representations without restriction ( Right ). Bottom: representation restriction without bi-boundary optimization ( Left ) vs. full framework ( Right ).

Variant	Wikipedia			MOOC
Variant	AUROC	AP	F1	AUROC	AP	F1
SDGAD	${\color[rgb]{20,128,85}\mathbf{80.36{\scriptstyle\pm 0.69}}}$	${\color[rgb]{20,128,85}\mathbf{5.41{\scriptstyle\pm 1.23}}}$	${\color[rgb]{20,128,85}\mathbf{8.34{\scriptstyle\pm 2.72}}}$	${\color[rgb]{20,128,85}\mathbf{72.87{\scriptstyle\pm 1.40}}}$	${\color[rgb]{20,128,85}\mathbf{7.89{\scriptstyle\pm 0.38}}}$	${\color[rgb]{20,128,85}\mathbf{7.15{\scriptstyle\pm 0.64}}}$
w/o Res	$77.79{\scriptstyle\pm 3.17}$	$3.83{\scriptstyle\pm 2.48}$	$5.29{\scriptstyle\pm 5.69}$	$69.14{\scriptstyle\pm 2.48}$	$5.14{\scriptstyle\pm 2.48}$	${\color[rgb]{20,104,168}6.58{\scriptstyle\pm 2.48}}$
w/o $\mathcal{L_{RR}}$	${\color[rgb]{236,84,20}79.44{\scriptstyle\pm 0.80}}$	${\color[rgb]{236,84,20}5.33{\scriptstyle\pm 1.47}}$	${\color[rgb]{236,84,20}6.01{\scriptstyle\pm 0.72}}$	$71.02{\scriptstyle\pm 1.28}$	$7.41{\scriptstyle\pm 0.62}$	$5.96{\scriptstyle\pm 0.81}$
w/o $\mathcal{L_{BO}}$	${\color[rgb]{20,104,168}80.36{\scriptstyle\pm 1.00}}$	${\color[rgb]{20,104,168}5.38{\scriptstyle\pm 1.32}}$	${\color[rgb]{20,104,168}7.41{\scriptstyle\pm 3.29}}$	${\color[rgb]{20,104,168}72.54{\scriptstyle\pm 1.35}}$	$7.56{\scriptstyle\pm 0.55}$	${\color[rgb]{236,84,20}6.42{\scriptstyle\pm 0.97}}$
TCL	$77.69{\scriptstyle\pm 0.74}$	$5.28{\scriptstyle\pm 1.21}$	$2.41{\scriptstyle\pm 0.00}$	${\color[rgb]{236,84,20}72.51{\scriptstyle\pm 1.76}}$	${\color[rgb]{20,104,168}7.87{\scriptstyle\pm 0.71}}$	$0{\scriptstyle\pm 0}$

Table 3: Ablation studies on Wikipedia and MOOC. Highlighted are the results ranked first , second , and third .

Panel of Figure 4 — Figure 4: Visualization of anomaly score distributions on the Wikipedia (1) and Enron (2) test set. (a–b) Kernel Density Estimates (KDE) of anomaly scores. (c–d) Corresponding anomaly score of each sample over time. Our framework provides significant better score separability and threshold-ability. Results on other datasets are provided in Fig. 5 in the Appendix.

Table 4: Effect of hyperparameters

\tau

and

\gamma

on performance on Wikipedia and MOOC datasets. The best results are highlighted in green , and the underlined entries correspond to the results reported in Table. 1 .

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Nodes	Edges	Unique Edges	Timesteps	Edge Feature	Anomaly Ratio	Density
Wikipedia	9227	157474	18257	152757	172	0.14%	4.30E-03
Reddit	10984	672447	78516	669065	172	0.05%	8.51E-03
MOOC	7144	411749	178443	345600	4	0.99%	1.26E-02
LastFm	1980	1293103	154993	1283614	0	-	5.57E-01
Enron	184	125235	3125	22632	0	-	5.53E+00
UCI	1899	59835	20296	58911	0	-	3.66E-02

Appendix

Table 5: Dataset statistics

$\lambda_{1}$ / $\lambda_{2}$	Wikipedia			MOOC
$\lambda_{1}$ / $\lambda_{2}$	AUROC	AP	F1	AUROC	AP	F1
0.5/0.5	$71.73{\scriptstyle\pm 8.80}$	$4.08{\scriptstyle\pm 3.17}$	$4.18{\scriptstyle\pm 3.93}$	${\color[rgb]{20,128,85}\mathbf{72.87{\scriptstyle\pm 1.40}}}$	${\color[rgb]{20,128,85}\mathbf{7.89{\scriptstyle\pm 0.38}}}$	$7.15{\scriptstyle\pm 0.64}$
1/0.1	${\color[rgb]{20,128,85}\mathbf{80.67{\scriptstyle\pm 1.14}}}$	$4.47{\scriptstyle\pm 0.74}$	$8.32{\scriptstyle\pm 2.00}$	$70.02{\scriptstyle\pm 1.15}$	$5.22{\scriptstyle\pm 1.26}$	$4.74{\scriptstyle\pm 4.92}$
1/0.5	$80.36{\scriptstyle\pm 0.69}$	${\color[rgb]{20,128,85}\mathbf{5.41{\scriptstyle\pm 1.23}}}$	${\color[rgb]{20,128,85}\mathbf{8.34{\scriptstyle\pm 2.72}}}$	$70.48{\scriptstyle\pm 0.76}$	$5.37{\scriptstyle\pm 1.14}$	${\color[rgb]{20,128,85}\mathbf{7.69{\scriptstyle\pm 4.52}}}$
1/0.7	$80.64{\scriptstyle\pm 0.47}$	$5.33{\scriptstyle\pm 1.47}$	$6.41{\scriptstyle\pm 3.08}$	$66.10{\scriptstyle\pm 7.71}$	$4.30{\scriptstyle\pm 2.74}$	$4.90{\scriptstyle\pm 5.27}$
1/1	$76.65{\scriptstyle\pm 9.03}$	$4.71{\scriptstyle\pm 2.19}$	$6.78{\scriptstyle\pm 4.27}$	$70.87{\scriptstyle\pm 0.51}$	$5.45{\scriptstyle\pm 0.73}$	$6.24{\scriptstyle\pm 2.01}$

Appendix

Table 6: Results when varying different

\lambda_{1}

\lambda_{2}

values for balancing loss terms.

Threshold	F1	TPR	FPR
0.01	0	0	0
0.1	0	0	0
0.3	0	0	0
0.5	0	0	0

Appendix

Table 7: TCL on UCI

Threshold	F1	TPR	FPR
0.01	0.444444	1	0.002298
0.1	0.444444	1	0.002298
0.3	0.444444	1	0.002298
0.5	0.444444	1	0.002298

Appendix

Table 8: SDGAD on UCI

Threshold	F1	TPR	FPR
0.01	0.029557	0.073171	0.000555
0.1	0.032520	0.024390	0.000620
0.3	0.020408	0.012195	0.000238
0.5	0.021277	0.012195	0.000175

Appendix

Table 9: TCL on Wiki

Threshold	F1	TPR	FPR
0.01	0.002664	1	0.976140
0.1	0.006867	0.695122	0.261700
0.3	0.031718	0.439024	0.034209
0.5	0.111111	0.097561	0.000858

Appendix

Table 10: SDGADG on Wiki

CTDG-based DGAD Methods
Methods	UCI			Enron			LastFM
Methods	AUROC	AP	F1	AUROC	AP	F1	AUROC	AP	F1
SAD	$96.27{\scriptstyle\pm 3.11}$	$21.59{\scriptstyle\pm 4.91}$	$12.14{\scriptstyle\pm 3.48}$	$92.47{\scriptstyle\pm 2.16}$	$12.33{\scriptstyle\pm 2.83}$	$8.91{\scriptstyle\pm 3.59}$	$99.88{\scriptstyle\pm 0.01}$	$31.47{\scriptstyle\pm 1.27}$	$44.86{\scriptstyle\pm 0.52}$
GeneralDyG	$78.19{\scriptstyle\pm 10.20}$	$8.78{\scriptstyle\pm 7.70}$	$4.57{\scriptstyle\pm 10.22}$	$86.94{\scriptstyle\pm 3.91}$	$7.00{\scriptstyle\pm 3.45}$	$0{\scriptstyle\pm 0}$	$99.85{\scriptstyle\pm 0.03}$	$29.34{\scriptstyle\pm 0.16}$	$44.61{\scriptstyle\pm 0.76}$
Representative CTDG Models
JODIE	$42.26{\scriptstyle\pm 3.26}$	$0.40{\scriptstyle\pm 0.15}$	$0.28{\scriptstyle\pm 0.63}$	$44.83{\scriptstyle\pm 1.32}$	$2.90{\scriptstyle\pm 2.01}$	$0{\scriptstyle\pm 0}$	$97.94{\scriptstyle\pm 0.61}$	$27.18{\scriptstyle\pm 0.49}$	$42.08{\scriptstyle\pm 1.19}$

Appendix

Table 11: Performance comparison (

Avg{\scriptstyle\pm std}

in %) on datasets with synthetic anomalies under S1 . Best results are highlighted in green .

Methods	Few-shot=1			Few-shot=2			Few-shot=3
Methods	AUROC	AP	F1	AUROC	AP	F1	AUROC	AP	F1
SAD	$64.11{\scriptstyle\pm 4.20}$	$1.03{\scriptstyle\pm 0.24}$	$0{\scriptstyle\pm 0}$	$63.49{\scriptstyle\pm 3.18}$	$0.74{\scriptstyle\pm 0.17}$	$0{\scriptstyle\pm 0}$	$64.56{\scriptstyle\pm 3.07}$	$0.90{\scriptstyle\pm 0.08}$	$0{\scriptstyle\pm 0}$
GeneralDyG	$63.02{\scriptstyle\pm 5.01}$	$0.26{\scriptstyle\pm 0.06}$	$0{\scriptstyle\pm 0}$	$63.83{\scriptstyle\pm 5.45}$	$0.28{\scriptstyle\pm 0.07}$	$0{\scriptstyle\pm 0}$	$64.73{\scriptstyle\pm 3.47}$	$0.29{\scriptstyle\pm 0.05}$	$0{\scriptstyle\pm 0}$
JODIE	$80.96{\scriptstyle\pm 2.87}$	$0.63{\scriptstyle\pm 0.03}$	$0{\scriptstyle\pm 0}$	$81.00{\scriptstyle\pm 2.75}$	$0.86{\scriptstyle\pm 0.23}$	$0{\scriptstyle\pm 0}$	$81.42{\scriptstyle\pm 2.25}$	$0.64{\scriptstyle\pm 0.04}$	$0{\scriptstyle\pm 0}$
+ours	$81.15{\scriptstyle\pm 2.63}$	$0.67{\scriptstyle\pm 0.05}$	$1.05{\scriptstyle\pm 0.19}$	$81.86{\scriptstyle\pm 2.97}$	$0.87{\scriptstyle\pm 0.05}$	$1.06{\scriptstyle\pm 0.19}$	$82.23{\scriptstyle\pm 2.64}$	$0.73{\scriptstyle\pm 0.05}$	$1.51{\scriptstyle\pm 0.24}$
DyRep	$80.70{\scriptstyle\pm 1.86}$	$0.66{\scriptstyle\pm 0.05}$	$0{\scriptstyle\pm 0}$	$80.64{\scriptstyle\pm 1.75}$	$0.66{\scriptstyle\pm 0.05}$	$0{\scriptstyle\pm 0}$	$82.05{\scriptstyle\pm 2.22}$	$0.68{\scriptstyle\pm 0.06}$	$0{\scriptstyle\pm 0}$

Appendix

Table 12: Performance comparison (

Avg{\scriptstyle\pm std}

in %) on Wikipedia dataset under S2 .

Panel of Figure 5 — Figure 5: Visualization of anomaly score distributions on the MOOC (1) and UCI (2) test sets, respectively.

Methods	Few-shot=1			Few-shot=2			Few-shot=3
Methods	AUROC	AP	F1	AUROC	AP	F1	AUROC	AP	F1
SAD	$65.17{\scriptstyle\pm 1.11}$	$2.30{\scriptstyle\pm 1.39}$	$0{\scriptstyle\pm 0}$	$65.28{\scriptstyle\pm 1.03}$	$2.22{\scriptstyle\pm 1.40}$	$0{\scriptstyle\pm 0}$	$66.28{\scriptstyle\pm 1.24}$	$2.30{\scriptstyle\pm 1.39}$	$0{\scriptstyle\pm 0}$
GeneralDyG	$64.49{\scriptstyle\pm 0.07}$	$1.89{\scriptstyle\pm 0.04}$	$0{\scriptstyle\pm 0}$	$65.52{\scriptstyle\pm 0.14}$	$1.43{\scriptstyle\pm 0.17}$	$0{\scriptstyle\pm 0}$	$66.20{\scriptstyle\pm 0.15}$	$2.21{\scriptstyle\pm 0.05}$	$0{\scriptstyle\pm 0}$
JODIE	$57.34{\scriptstyle\pm 4.61}$	$1.39{\scriptstyle\pm 0.20}$	$0{\scriptstyle\pm 0}$	$57.91{\scriptstyle\pm 4.45}$	$1.43{\scriptstyle\pm 0.17}$	$0{\scriptstyle\pm 0}$	$58.32{\scriptstyle\pm 4.66}$	$1.43{\scriptstyle\pm 0.19}$	$0{\scriptstyle\pm 0}$
+ours	$60.21{\scriptstyle\pm 1.09}$	$1.48{\scriptstyle\pm 0.03}$	$3.20{\scriptstyle\pm 0.18}$	$60.68{\scriptstyle\pm 1.21}$	$1.49{\scriptstyle\pm 0.02}$	$3.23{\scriptstyle\pm 0.16}$	$61.35{\scriptstyle\pm 1.02}$	$1.67{\scriptstyle\pm 0.03}$	$3.25{\scriptstyle\pm 0.19}$
DyRep	$63.31{\scriptstyle\pm 0.93}$	$1.65{\scriptstyle\pm 0.07}$	$0{\scriptstyle\pm 0}$	$63.92{\scriptstyle\pm 0.73}$	$1.69{\scriptstyle\pm 0.08}$	$0{\scriptstyle\pm 0}$	$63.73{\scriptstyle\pm 0.75}$	$1.68{\scriptstyle\pm 0.07}$	$0{\scriptstyle\pm 0}$

Appendix

Table 13: Performance comparison (

Avg{\scriptstyle\pm std}

in %) on MOOC dataset under S2 .

Table 14: Effect of hyperparameters

L

and

\alpha

on performance on Wikipedia and MOOC datasets. The best results are highlighted in green and the underlined results correspond to those reported in Table. 1 .

Panel of Figure 6 — Figure 6: Parameter sensitivity with different $\alpha$ and $\gamma$ on Enron dataset

Panel of Figure 7 — Figure 7: Parameter sensitivity with different $\alpha$ and $\gamma$ on UCI dataset

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Driven by the pressing demand for graph anomaly detection (GAD) in high-stakes domains, the generalist GAD paradigm, which trains a single detector transferable across new graphs, has recently gained growing attention. However, existing methods often rely on scarce and costly annotations for training and sometimes even require few-shot support at inference, which limits their robustness to diverse and unseen anomaly patterns. To address this limitation, we introduce ProMoS, the first unsupervised generalist GAD framework, which detects anomalies by modeling the abundant normality in unlabeled data. ProMoS adopts a knowledge-distillation paradigm to distill normality priors from a frozen self-supervised graph neural network (GNN) teacher to a mixture-of-students model with shared global and lightweight personalized branches, enabling efficient and expressive normality modeling without learning from scratch. We further propose prototype-guided soft-label distillation to align teacher and student in a shared prototype space, enhancing cross-graph generalizability. During inference, ProMoS performs zero-shot anomaly detection on unseen graphs via distillation bias and prototype geometric deviation. Extensive experiments show the effectiveness and efficiency of ProMoS, charting a practical path toward label-free, zero-shot generalist GAD.

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