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

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

REVIEW 5 major objections 6 minor 21 references

Detect dynamic-graph anomalies under label scarcity by learning the boundary from residual embedding shifts, not from the few labels.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 21:24 UTC pith:6LGK5YHC

load-bearing objection A solid modular detector for dynamic-graph anomaly detection, but the 'fully unsupervised' claim is undercut by label-based early stopping, and the appendix proof has a real math error. the 5 major comments →

arxiv 2602.20019 v2 pith:6LGK5YHC submitted 2026-02-23 cs.LG cs.AI

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 This is my paper

classification cs.LG cs.AI

keywords dynamic graph anomaly detectionlimited supervisionresidual representationnormalizing flowdecision boundarycontinuous-time dynamic graphhypersphere restrictionfew-shot anomaly detection

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that dynamic-graph anomaly detection under limited supervision fails not for lack of representation power but for lack of an explicit, discriminative decision boundary: unsupervised methods produce scores that collapse into a narrow ambiguous band, and semi-supervised methods skew the boundary toward the few anomaly patterns they have seen. The proposed framework, SDGAD, is a model-agnostic wrapper for continuous-time dynamic graph encoders. It represents each interaction by the residual change it causes in node embeddings (the encoding with the event minus the encoding without it), restricts normal residuals to a compact shell between two concentric hyperspheres, and then learns a two-sided margin between normal and anomalous log-likelihoods estimated by a normalizing flow. The paper reports that this yields well-separated, threshold-able anomaly scores and consistent improvements over diverse baselines in unsupervised, few-shot, and limited-supervision settings. A reader should care because the method is a drop-in module that addresses the practical operating condition of rare labels without sacrificing generalization to unseen anomaly types.

Core claim

Normal/unlabeled data alone can support a discriminative boundary if the representation is built at the right granularity. SDGAD represents each event by the residual ΔE = Enc(S) − Enc(S⁻), the change in a node's embedding caused by the current interaction. A restriction loss pulls these residuals into an interval bounded by two co-centered hyperspheres (r_min, r_max) so all normals share a consistent scale, while labeled anomalies are pushed outside r' = r_max + Δr. A normalizing flow models normal log-likelihood, and bi-boundary optimization enforces a margin between B_n and B_a = B_n − τ. The anomaly score is s(x) = 1 − exp(log p(x)); across six datasets and three supervision settings, th

What carries the argument

The central object is the residual representation ΔE^i_t = Enc(S^i_t) − Enc(S^{i,t-}), the change in a node embedding caused by the current interaction, computed by encoding the event once with and once without the current interaction. It carries the anomaly-relevant signal: normal interactions barely move the embedding, anomalous ones shift it. The second mechanism is the two co-centered hypersphere restriction: residuals are projected and measured with the pseudo-Huber norm n(x) = sqrt(||x||^2 + 1) − 1, and normal samples are constrained to n(x) ∈ [r_min, r_max] with r_min = γ r_max, while labeled anomalies are pushed outside r' = r_max + Δr. The third is the bi-boundary optimization: a no

Load-bearing premise

The load-bearing premise is that anomalous interactions produce a statistically detectable shift in the node embedding residual ΔE; if an anomaly is subtle enough not to move the embedding (e.g., an odd link between nodes with long, consistent histories), the residual signal collapses and neither the hypersphere restriction nor the bi-boundary can recover it.

What would settle it

Construct a benchmark where anomalies are deliberately camouflaged to keep embedding residuals small: e.g., precede each anomalous event with several normal filler interactions between the same node pair so the encoder's memory already incorporates the change. If SDGAD's AUROC and F1 fall to baseline levels while the residual norms of anomalies become indistinguishable from normal residuals, the residual representation is the bottleneck; if separation persists, the boundary objective is doing more than the residual encoding.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

Integrated with any of three continuous-time dynamic graph encoders, the framework improves F1 and average precision on real-anomaly datasets while keeping AUROC high.
The framework degrades gracefully from limited supervision to few-shot (1, 2, or 3 labels) to fully unsupervised; on synthetic-anomaly benchmarks it keeps near-perfect AUROC even with no labels.
Ablations show the residual encoding is the most critical component: removing it causes the largest performance drop and larger variance, corroborating that the residual is the primary anomaly signal.
The two-hypersphere restriction and the bi-boundary margin mainly improve F1 and threshold stability rather than ranking metrics, indicating they reduce boundary ambiguity rather than re-rank anomalies.
The method generalizes to unseen anomaly types: training on only temporal synthetic anomalies while testing on structural anomalies yields stable high scores.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The residual ΔE is effectively the first-order effect of the current event on the node embedding; this suggests SDGAD's sensitivity is bounded by how much an event can move an embedding, so harder anomalies (e.g., links between high-degree nodes with rich histories) could be where the advantage shrinks.
Because the decision boundary lives in likelihood space rather than in a label-conditioned classifier, the same pipeline could be adapted to anomaly type identification by training separate flows per type, though the paper only treats binary detection.
A natural stress test is to generate synthetic anomalies that interpolate between normal and anomalous residuals (e.g., by mixing historical patterns); the paper's own critique of trivial synthetic anomalies on low-repeat-rate datasets suggests such benchmarks are needed to separate representation quality from boundary learning.
The bi-boundary margin τ is a fixed hyperparameter, but the loss-sensitivity analysis shows the optimal weight of the boundary loss is dataset-dependent; an adaptive τ (tuned per validation set) might improve robustness further.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

A solid modular detector for dynamic-graph anomaly detection, but the 'fully unsupervised' claim is undercut by label-based early stopping, and the appendix proof has a real math error.

read the letter

You should know two things upfront. First, the core method is a reasonable and well-tested combination of existing ideas: residual representations, a two-hypersphere restriction loss, and a normalizing-flow boundary. Second, the headline claim of strong performance in the fully unsupervised (S3) setting is currently undermined by the experimental protocol: Appendix C says all models are selected by the checkpoint with best validation performance, and the validation splits contain labeled anomalies (Appendix B.2). That means labels are used for model selection, so S3 is not actually label-free. The near-perfect AUROC on synthetic data (Table 2) is consistent with this leak. The paper never states the validation metric or says labels were withheld during early stopping. This is the main thing to fix.

What the paper does well: the residual encoding idea is simple and effective — subtracting the history-only embedding from the full embedding gives a direct anomaly signal, and the ablation shows it is the most important component. The two-hypersphere restriction is a sensible answer to the soap-bubble problem in Deep SVDD, and the bi-boundary loss is a clean way to get a margin in likelihood space. The empirical work is otherwise thorough: six datasets, three supervision settings, three encoder backbones, ablations, standard deviations over five runs. As a plug-in for CTDG encoders it is clearly useful for the subfield.

Soft spots, in proportion: the S3 leak is serious because it directly threatens a central contribution. The proof in Appendix E.2.1 is invalid — Eq. 18 asserts Φθ'(x)^T Φθ'(x) = -1, which is impossible for a squared norm. The error-bound proposition is therefore unsupported; it should be removed or fixed. The circularity concern is real but weaker: the decision boundary is a percentile of the flow's outputs on a batch, and the model is trained to respect that same boundary, which creates a self-referential dependence. In low-label settings this could make the boundary unstable. Worth discussing, not fatal. Missing code and data also hurt reproducibility.

Who should read it: anyone working on temporal or dynamic graph anomaly detection, especially if they want a model-agnostic detector. It deserves a serious referee — not a desk reject — but the referee should insist on a corrected or clarified S3 protocol, a fixed proof, and ideally code release before the claims are accepted.

My recommendation: send to peer review, conditional on those revisions.

Referee Report

5 major / 6 minor

Summary. The paper proposes SDGAD, a model-agnostic framework for anomaly detection in continuous-time dynamic graphs under limited supervision. The method has three components: residual representation encoding that subtracts the historical-context embedding from the embedding computed with the current event (Eq. 3); a representation restriction loss that encourages normal residuals to lie between two co-centered hyperspheres and pushes anomalies outside (Eqs. 5-8); and a bi-boundary optimization loss that uses a normalizing-flow log-likelihood with separate boundaries Bn and Ba = Bn - τ (Eq. 11). The paper claims consistent gains over baselines on six datasets under three settings: limited supervision (S1), few-shot (S2), and fully unsupervised (S3), and reports ablations, hyperparameter studies, and an error-bound analysis. The empirical evaluation is broad, but the validity of the 'fully unsupervised' setting is compromised by the early-stopping protocol, and the theoretical bound in Appendix E.2.1 contains an impossible assumption.

Significance. If the empirical claims held, SDGAD would be a useful drop-in module for CTDG encoders: the framework is encoder-agnostic, the anomaly score is a calibrated complement of a flow log-likelihood, and the authors report F1/AP improvements beyond AUROC under severe class imbalance, together with ablations across multiple backbones. The paper also includes a more honest metric discussion than is typical for DGAD work. However, the central S3 claim—fully unsupervised performance comparable to limited-supervision—appears to rely on label-based model selection, and the theoretical support in Appendix E.2.1 is invalid as stated. The core empirical contribution needs verification under a genuinely label-free protocol before the paper's main claims can be accepted.

major comments (5)

[§5.1 and Appendix C (S3 protocol)] The 'fully unsupervised' setting S3 is defined as training 'without any label supervision,' yet Appendix C states that all models are trained with early stopping using 'the checkpoint achieving the best validation performance.' Appendix B.2 shows that the validation split contains labeled anomalies (e.g., 0.15% for Wikipedia, 0.065% for Reddit; injected T-anomalies for synthetic datasets). The paper never specifies the validation metric used for checkpoint selection, nor does it state that labels are withheld during model selection. If AUROC/AP/F1 on the validation set is used, S3 is not label-free, and the near-perfect S3 results on synthetic datasets (Table 2, AUROC ≈ 99.9) would reflect label leakage through model selection rather than unsupervised learning. Please disclose the validation criterion and either (a) use a criterion that requires no labels, or (b) relabel the setting as s
[Appendix E.2.1, Eq. (18)] The proof of Proposition 1 assumes Φθ'(x)^T Φθ'(x) = -1. This is impossible for a squared norm of a real vector, which is always nonnegative. The inequality chain in Eqs. (17)-(19) therefore does not establish the claimed bound, and the statement 'we assume a worst-case initialization' is internally inconsistent. Since Proposition 1 is the paper's only theoretical justification for the bi-boundary loss, this section either needs a corrected derivation (with a valid lower bound, e.g., ≥ 0) or should be removed and the empirical argument presented on its own.
[§4.1, Eq. (3)] The residual representation hypothesis—anomalies induce statistically detectable changes in ΔE = Enc(S_t) − Enc(S^{t−})—is the foundation of the entire pipeline. Section 4.1 provides qualitative motivation, and the ablation w/oRes (Table 3) shows degradation, but there is no direct verification that residual norms separate normal from anomalous interactions, nor an analysis of cases where the residual is small (e.g., anomalous edges between nodes with rich, consistent histories). Please report the distribution of residual norms for normal vs. anomalous test samples, and ideally show recall at high-precision thresholds. Without such evidence, it is unclear whether failures are attributable to the boundary module or to the absence of discriminative residual signal.
[§5.1 / Table 2] The S3 experiments on synthetic datasets report AUROC values of 99.86–99.88 with standard deviations of 0.01 for SDGAD, while the unsupervised baselines often collapse to chance (e.g., Table 2, JODIE/TCL). Given the early-stopping issue above, these numbers are not interpretable as unsupervised performance. Even setting aside label leakage, the extremely low variance and near-perfect scores suggest that the injected anomalies are trivially detectable from residual structure; Section A's own caveat about 'trivial cues such as rare repetition' applies to these benchmarks. Please validate S3 with a protocol that forbids any labeled validation signal and report the resulting numbers.
[Table 3] The ablation table reports w/o LBO with AUROC/AP essentially unchanged on Wikipedia (80.36±1.00 vs 80.36±0.69 AUROC) and only F1 dropping. Given that the paper's motivation is an explicit, robust boundary, the absence of an AUROC/AP effect is not itself a flaw, but the claim that bi-boundary optimization is 'essential' should be supported with a statistical test or a more sensitive metric. At minimum, report the p-value or confidence interval for the F1 difference across the five runs.

minor comments (6)

[§2.1] Typo: 'discrete-time (DTDG) or continuous-time (DTDG)' should read 'continuous-time (CTDG)'.
[§2.2] Typo: 'are are not generally satisfied.'
[§5.1 / Table 1] 'Area Under the Prevision Recall Curve' should be 'Precision–Recall'.
[Appendix D, Table 6] The hyperparameter study for L uses L=2 on Wikipedia but L=20 on MOOC in the main results, with no explanation for the dataset-specific choice. Please state the selection rule (e.g., validation-based) and whether the selected L values are fixed across backbones.
[Appendix B.2] For synthetic datasets, the validation set contains 0.1% injected T-anomalies but test contains 0.05% of each type. It would be helpful to state explicitly whether any S-anomalies appear in the validation set, since the paper claims S-anomalies are 'unseen during training.'
[Appendix E.2.2] The bound in Eq. (21) is stated as E_RR ≤ C_r log 2, but the derivation gives E_RR ≤ (C_r / log 2)(L_n + L_a). The constant/log-2 placement appears inconsistent; please fix the notation.

Circularity Check

0 steps flagged

No significant circularity: SDGAD's components are defined by their own equations and standard OOD practice; the only flagged concern is a potential label-based validation leak in the S3 experiments, which is an experimental-validity issue, not a circular derivation.

full rationale

Walking the claimed derivation chain: (i) the residual representation in Eq. 3 is an assumption about anomalous interactions producing larger encoding shifts, not a claim derived from something that already assumes the conclusion; (ii) the restriction loss in Eqs. 6-8 is a standard hypersphere/one-class objective with external citations (Ruff et al., 2018; Vershynin, 2018), and the anomaly score in Eq. 13 is a fixed monotone transform of the normalizing-flow log-likelihood; (iii) the decision boundary Bn is defined as the α-th percentile of the training batch's normal log-likelihood (Sec. 4.3), and LBO then trains the flow to respect that boundary and margin. This is self-referential in the same way any threshold-based density detector is—the threshold is estimated from the model's own training outputs and applied to held-out test samples—but it is standard OOD practice, not a logical reduction of the prediction to the fit by construction. No load-bearing self-citation or imported uniqueness theorem is used; the paper's self-citations (Tian et al., 2023, 2024a, 2024b) are baselines or related-work mentions, not justifications for the core method. The manuscript's own Appendix A limitation about overly simple synthetic-anomaly protocols is a validity caveat, not circularity. The one in-scope concern is that Appendix C selects checkpoints by 'best validation performance' and Appendix D tunes hyperparameters on validation splits that contain labeled anomalies; if that metric is label-based, the S3 'fully unsupervised' results are not strictly label-free. This is a serious experimental-validity risk, but it is not a circular derivation: the test labels remain independent, and the finding would not change the circularity score because the central method's equations do not reduce to their inputs by construction.

Axiom & Free-Parameter Ledger

9 free parameters · 6 axioms · 0 invented entities

The central method rests on several domain assumptions about residual informativeness and flow-likelihood reliability, plus a number of free hyperparameters tuned per dataset. No new physical or conceptual entities are introduced. The theoretical appendix contains an invalid assumption in Proposition 1.

free parameters (9)

r_max = 0.4
Outer hypersphere radius; set to approximate unit hypersphere under pseudo-Huber norm (Section 4.2).
gamma (γ) = 0.9 (tuned from {0.8, 0.9, 0.95, 0.99})
Ratio inner/outer radius; hyperparameter study in Appendix D.
tau (τ) = 0.1 (tuned)
Margin between normal and anomaly boundaries in log-likelihood space (Section 4.3, Appendix D).
alpha (α) = 0.01 (tuned)
Percentile of normal log-likelihoods used to set normal boundary Bn (Section 4.3, Appendix D).
L (historical neighbors) = 2 (Wikipedia), 20 (MOOC); grid 2-32
Number of historical interactions sampled in residual encoding; tuned per dataset (Appendix D, Table 6a).
lambda_1 (λ1) = 1 (Wikipedia), 0.5 (MOOC)
Weight of bi-boundary loss; per-dataset tuning (Appendix E.1, Table 7).
lambda_2 (λ2) = 0.5
Weight of restriction loss; selected as robust across datasets (Appendix E.1).
learning_rate = grid {1e-3, 1e-4, 1e-5}
Adam hyperparameter; grid search (Appendix C).
weight_decay = grid {1e-1, 1e-2, 1e-3, 1e-4, 1e-5}
Adam hyperparameter; grid search (Appendix C).

axioms (6)

domain assumption Residual representations Enc(S_t) - Enc(S_{t-}) capture anomaly-relevant deviations
Section 4.1; if this fails, the method has no discriminative signal.
domain assumption Normal events produce small residuals, anomalies large residuals (neighborhood-consistency principle)
Section 4.1; qualitative principle with no empirical verification provided.
domain assumption Normalizing flow log-likelihood provides a useful anomaly score despite known OOD pitfalls
Section 4.3; authors cite Kirichenko et al. 2020 and Kumar et al. 2021; the bi-boundary loss is an ad hoc remedy.
domain assumption Batch-level normal log-likelihood distribution D_n is a reliable estimate of the global normal distribution
Section 4.3; many batches have M=0 labeled anomalies; no batch-size sensitivity analysis for boundary stability.
domain assumption Pseudo-Huber norm satisfies 0 ≤ n(x) ≤ 1
Appendix E.2.2, Eq. 20; used to bound Proposition 2; not proven for the actual projected representations.
ad hoc to paper Worst-case initialization with Φθ'(x)^T Φθ'(x) = -1 exists
Appendix E.2.1, Eq. 18; impossible for real vectors, invalidates Proposition 1's bound.

pith-pipeline@v1.3.0-alltime-deepseek · 24081 in / 15047 out tokens · 123112 ms · 2026-08-02T21:24:41.358666+00:00 · methodology

0 comments

read the original 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 \textbf{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

Figures reproduced from arXiv: 2602.20019 by Fengran Mo, Jian Guo, Jian-Yun Nie, Weixu Zhang, Yiyan Qi, Yuxing Tian.

**Figure 1.** 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. research attention. Previous DGAD methods (Yu et al., 2018; Zheng et al., 2019; Cai et al., 2021; Liu et al., 2023) adopt discrete-time modeling, representing graph evolution as a sequence of snapshots sampled at fixed intervals.… view at source ↗

**Figure 2.** 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 distribu… view at source ↗

**Figure 3.** Figure 3: 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 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: 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). 5.4. Visualization Analysis To provide an intuitive view of the effect of each component, we visualize the log-li… view at source ↗

**Figure 5.** Figure 5: Parameter sensitivity with different α and γ on Enron dataset E. Loss Analysis λ1/λ2 Wikipedia MOOC AUROC AP F1 AUROC AP F1 0.5/0.5 71.73±8.80 4.08±3.17 4.18±3.93 72.87±1.40 7.89±0.38 7.15±0.64 1/0.1 80.67±1.14 4.47±0.74 8.32±2.00 70.02±1.15 5.22±1.26 4.74±4.92 1/0.5 80.36±0.69 5.41±1.23 8.34±2.72 70.48±0.76 5.37±1.14 7.69±4.52 1/0.7 80.64±0.47 5.33±1.47 6.41±3.08 66.10±7.71 4.30±2.74 4.90±5.27 1/1 76.65±9… view at source ↗

**Figure 6.** Figure 6: Parameter sensitivity with different α and γ on UCI dataset strength provides a good balance between compactness and preserving informative deviations in the residual space. In contrast, the optimal weight of LBO is dataset-dependent, which is expected given that anomaly characteristics differ substantially across domains. On Wikipedia, a stronger bi-boundary term is beneficial: reducing its weight to λ1 =… view at source ↗

**Figure 7.** Figure 7: Visualization of anomaly score distributions on the MOOC (1) and UCI (2) test sets, respectively. Methods UCI Enron LastFM AUROC AP F1 AUROC AP F1 AUROC AP F1 CTDG-based DGAD Methods SAD 96.27±3.11 21.59±4.91 12.14±3.48 92.47±2.16 12.33±2.83 8.91±3.59 99.88±0.01 31.47±1.27 44.86±0.52 GeneralDyG 78.19±10.20 8.78±7.70 4.57±10.22 86.94±3.91 7.00±3.45 0±0 99.85±0.03 29.34±0.16 44.61±0.76 Representative CTDG Mo… view at source ↗

discussion (0)

Reference graph

Works this paper leans on

21 extracted references · 2 canonical work pages

[2]

Under 0≤n(x)≤1 , the normal violation magnitude is upper bounded by max(rmin−n(x),0)+max(n(x)−r max,0)≤max{r min,1−r max}·I[n(x)/∈[rmin, rmax]]≤ max{rmin,1−r max} log 2 Ln(x) (23) For an anomalous sample ( y= 1 ), if n(x)> r ′, then both the violation term and La(x) are zero. Otherwise let δ=r ′ −n(x)>0, La(x) = log(1 +e δ)e δ ≥log 2⇒I[n(x)≤r ′]≤L a(x)/lo...

2044
[7]

Flag: Adversarial data augmentation for graph neural networks.arXiv preprint arXiv:2010.09891,

Kong, K., Li, G., Ding, M., Wu, Z., Zhu, C., Ghanem, B., Taylor, G., and Goldstein, T. Flag: Adversarial data augmentation for graph neural networks.arXiv preprint arXiv:2010.09891,

Pith/arXiv arXiv 2010
[8]

Inflow: Robust out- lier detection utilizing normalizing flows.arXiv preprint arXiv:2106.12894,

Kumar, N., Hanfeld, P., Hecht, M., Bussmann, M., Gumhold, S., and Hoffmann, N. Inflow: Robust out- lier detection utilizing normalizing flows.arXiv preprint arXiv:2106.12894,

Pith/arXiv arXiv
[10]

Liu, Z., Dou, Y ., Yu, P

doi: 10.1109/ TKDE.2021.3124061. Liu, Z., Dou, Y ., Yu, P. S., Deng, Y ., and Peng, H. Al- leviating the inconsistency problem of applying graph neural network to fraud detection. InProceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval, pp. 1569–1572,

arXiv 2021
[11]

Postuvan, T., Grohnfeldt, C., Russo, M., and Lovisotto, G

doi: 10.1109/TKDE.2021.3118815. Postuvan, T., Grohnfeldt, C., Russo, M., and Lovisotto, G. Learning-based link anomaly detection in continuous- time dynamic graphs.Transactions on Machine Learning Research,

arXiv 2021
[13]

Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., and Bronstein, M

URL https: //openreview.net/forum?id=88tGIxxhsf. Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., and Bronstein, M. M. Temporal graph networks for deep learning on dynamic graphs.CoRR, abs/2006.10637,

Pith/arXiv arXiv 2006
[14]

doi: 10.24963/ijcai.2023/256

ISBN 978-1-956792-03-4. doi: 10.24963/ijcai.2023/256. Tian, Y ., Jiang, A., Huang, Q., Guo, J., and Qi, Y . Latent diffusion-based data augmentation for continuous-time dynamic graph model. InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 2900–2911, 2024a. Tian, Y ., Qi, Y ., and Guo, F. Freedyg: Frequency en- ha...

work page doi:10.24963/ijcai.2023/256 2023
[16]

doi: 10.1609/aaai.v39i20

ISBN 978-1-57735-897-8. doi: 10.1609/aaai.v39i20. 35508. URL https://doi.org/10.1609/aaai. v39i20.35508. Yu, L., Sun, L., Du, B., and Lv, W. Towards better dy- namic graph learning: New architecture and unified li- brary.CoRR, abs/2303.13047,

Pith/arXiv arXiv
[17]

doi: 10.1145/3510003.3510180

Association for Computing Machinery. doi: 10.1145/3510003.3510180. Zhang, S., Suzumura, T., and Zhang, L. Dyngraphtrans: Dynamic graph embedding via modified universal trans- former networks for financial transaction data. In2021 IEEE International Conference on Smart Data Services (SMDS), pp. 184–191,

arXiv
[18]

2021.00032

doi: 10.1109/SMDS53860. 2021.00032. Zhang, Y ., Sun, Y ., Cai, J., and Fan, J. Deep orthogonal hypersphere compression for anomaly detection. InThe Twelfth International Conference on Learning Represen- tations,

arXiv 2021
[19]

salience

Learning Discriminative and Generalizable Anomaly Detector for Dynamic Graph with Limited Supervision A. Discussion and Future Work In this section, we outline several practical directions for future work motivated by our empirical findings. First, it is necessary to revisit how synthetic anomalies are constructed and evaluated, especially in the limited-...

1980
[2006]

URL https://doi

doi: 10.1145/1143844.1143874. URL https://doi. org/10.1145/1143844.1143874. Dou, Y ., Liu, Z., Sun, L., Deng, Y ., Peng, H., and Yu, P. S. Enhancing graph neural network-based fraud detectors against camouflaged fraudsters. InProceedings of the 29th ACM international conference on information & knowledge management, pp. 315–324,

arXiv
[2010]

Hou, Z., Liu, X., Cen, Y ., Dong, Y ., Yang, H., Wang, C., and Tang, J

doi: 10.1109/ASONAM.2010.17. Hou, Z., Liu, X., Cen, Y ., Dong, Y ., Yang, H., Wang, C., and Tang, J. Graphmae: Self-supervised masked graph autoencoders. InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD ’22, pp. 594–604, New York, NY , USA,

work page doi:10.1109/asonam.2010.17 2010
[2015]

org/abs/1412.6980

URL https://arxiv. org/abs/1412.6980. Kirichenko, P., Izmailov, P., and Wilson, A. G. Why normal- izing flows fail to detect out-of-distribution data.Ad- vances in neural information processing systems, 33: 20578–20589,

Pith/arXiv arXiv
[2019]

TCL: transformer- based dynamic graph modelling via contrastive learning

Wang, L., Chang, X., Li, S., Chu, Y ., Li, H., Zhang, W., He, X., Song, L., Zhou, J., and Yang, H. TCL: transformer- based dynamic graph modelling via contrastive learning. CoRR, abs/2105.07944, 2021a. Wang, Y ., Cai, Y ., Liang, Y ., Ding, H., Wang, C., Bhatia, S., and Hooi, B. Adaptive data augmentation on temporal graphs.NeurIPS, 34:1440–1452, 2021b. W...

Pith/arXiv arXiv
[2020]

and Goadrich, M

Davis, J. and Goadrich, M. H. The relationship be- tween precision-recall and ROC curves. In Cohen, W. W. and Moore, A. W. (eds.),Machine Learning, Proceedings of the Twenty-Third International Confer- ence (ICML 2006), Pittsburgh, Pennsylvania, USA, June 25-29, 2006, volume 148 ofACM International Con- ference Proceeding Series, pp. 233–240. ACM,

2006
[2021]

ISBN 9781450384469

Association for Computing Machinery. ISBN 9781450384469. doi: 10.1145/3459637.3481955. Chen, N., Liu, Z., Hooi, B., He, B., Fathony, R., Hu, J., and Chen, J. Consistency training with learnable data augmentation for graph anomaly detection with limited supervision. InThe Twelfth International Conference on Learning Representations,

arXiv
[2022]

ISBN 9781450393850

Asso- ciation for Computing Machinery. ISBN 9781450393850. doi: 10.1145/3534678.3539321. Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. InInternational Conference on Learning Representations (ICLR),

arXiv
[2023]

Liu, Y ., Pan, S., Wang, Y

URL https:// arxiv.org/abs/2211.13123. Liu, Y ., Pan, S., Wang, Y . G., Xiong, F., Wang, L., Chen, Q., and Lee, V . C. Anomaly detection in dynamic graphs via transformer.IEEE Transactions on Knowledge and Data Engineering, 35(12):12081–12094,

Pith/arXiv arXiv
[2024]

Implementation Details.Following Postuvan et al

and additionally include some representative CTDG models originally developed for fundamental dynamic graph task (e.g., link prediction), which can be directly adapted to anomaly detection. Implementation Details.Following Postuvan et al. (2024), we apply a minimal modification when adapting general CTDG models: unlike standard link prediction that exclud...

2024
[2025]

Reha, J., Lovisotto, G., Russo, M., Gravina, A., and Grohn- feldt, C

doi: 10.1109/ TKDE.2025.3581578. Reha, J., Lovisotto, G., Russo, M., Gravina, A., and Grohn- feldt, C. Anomaly detection in continuous-time tem- poral provenance graphs. InTemporal Graph Learn- ing Workshop @ NeurIPS 2023,

arXiv 2025

[1] [2]

Under 0≤n(x)≤1 , the normal violation magnitude is upper bounded by max(rmin−n(x),0)+max(n(x)−r max,0)≤max{r min,1−r max}·I[n(x)/∈[rmin, rmax]]≤ max{rmin,1−r max} log 2 Ln(x) (23) For an anomalous sample ( y= 1 ), if n(x)> r ′, then both the violation term and La(x) are zero. Otherwise let δ=r ′ −n(x)>0, La(x) = log(1 +e δ)e δ ≥log 2⇒I[n(x)≤r ′]≤L a(x)/lo...

2044

[2] [7]

Flag: Adversarial data augmentation for graph neural networks.arXiv preprint arXiv:2010.09891,

Kong, K., Li, G., Ding, M., Wu, Z., Zhu, C., Ghanem, B., Taylor, G., and Goldstein, T. Flag: Adversarial data augmentation for graph neural networks.arXiv preprint arXiv:2010.09891,

Pith/arXiv arXiv 2010

[3] [8]

Inflow: Robust out- lier detection utilizing normalizing flows.arXiv preprint arXiv:2106.12894,

Kumar, N., Hanfeld, P., Hecht, M., Bussmann, M., Gumhold, S., and Hoffmann, N. Inflow: Robust out- lier detection utilizing normalizing flows.arXiv preprint arXiv:2106.12894,

Pith/arXiv arXiv

[4] [10]

Liu, Z., Dou, Y ., Yu, P

doi: 10.1109/ TKDE.2021.3124061. Liu, Z., Dou, Y ., Yu, P. S., Deng, Y ., and Peng, H. Al- leviating the inconsistency problem of applying graph neural network to fraud detection. InProceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval, pp. 1569–1572,

arXiv 2021

[5] [11]

Postuvan, T., Grohnfeldt, C., Russo, M., and Lovisotto, G

doi: 10.1109/TKDE.2021.3118815. Postuvan, T., Grohnfeldt, C., Russo, M., and Lovisotto, G. Learning-based link anomaly detection in continuous- time dynamic graphs.Transactions on Machine Learning Research,

arXiv 2021

[6] [13]

Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., and Bronstein, M

URL https: //openreview.net/forum?id=88tGIxxhsf. Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., and Bronstein, M. M. Temporal graph networks for deep learning on dynamic graphs.CoRR, abs/2006.10637,

Pith/arXiv arXiv 2006

[7] [14]

doi: 10.24963/ijcai.2023/256

ISBN 978-1-956792-03-4. doi: 10.24963/ijcai.2023/256. Tian, Y ., Jiang, A., Huang, Q., Guo, J., and Qi, Y . Latent diffusion-based data augmentation for continuous-time dynamic graph model. InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 2900–2911, 2024a. Tian, Y ., Qi, Y ., and Guo, F. Freedyg: Frequency en- ha...

work page doi:10.24963/ijcai.2023/256 2023

[8] [16]

doi: 10.1609/aaai.v39i20

ISBN 978-1-57735-897-8. doi: 10.1609/aaai.v39i20. 35508. URL https://doi.org/10.1609/aaai. v39i20.35508. Yu, L., Sun, L., Du, B., and Lv, W. Towards better dy- namic graph learning: New architecture and unified li- brary.CoRR, abs/2303.13047,

Pith/arXiv arXiv

[9] [17]

doi: 10.1145/3510003.3510180

Association for Computing Machinery. doi: 10.1145/3510003.3510180. Zhang, S., Suzumura, T., and Zhang, L. Dyngraphtrans: Dynamic graph embedding via modified universal trans- former networks for financial transaction data. In2021 IEEE International Conference on Smart Data Services (SMDS), pp. 184–191,

arXiv

[10] [18]

2021.00032

doi: 10.1109/SMDS53860. 2021.00032. Zhang, Y ., Sun, Y ., Cai, J., and Fan, J. Deep orthogonal hypersphere compression for anomaly detection. InThe Twelfth International Conference on Learning Represen- tations,

arXiv 2021

[11] [19]

salience

Learning Discriminative and Generalizable Anomaly Detector for Dynamic Graph with Limited Supervision A. Discussion and Future Work In this section, we outline several practical directions for future work motivated by our empirical findings. First, it is necessary to revisit how synthetic anomalies are constructed and evaluated, especially in the limited-...

1980

[12] [2006]

URL https://doi

doi: 10.1145/1143844.1143874. URL https://doi. org/10.1145/1143844.1143874. Dou, Y ., Liu, Z., Sun, L., Deng, Y ., Peng, H., and Yu, P. S. Enhancing graph neural network-based fraud detectors against camouflaged fraudsters. InProceedings of the 29th ACM international conference on information & knowledge management, pp. 315–324,

arXiv

[13] [2010]

Hou, Z., Liu, X., Cen, Y ., Dong, Y ., Yang, H., Wang, C., and Tang, J

doi: 10.1109/ASONAM.2010.17. Hou, Z., Liu, X., Cen, Y ., Dong, Y ., Yang, H., Wang, C., and Tang, J. Graphmae: Self-supervised masked graph autoencoders. InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD ’22, pp. 594–604, New York, NY , USA,

work page doi:10.1109/asonam.2010.17 2010

[14] [2015]

org/abs/1412.6980

URL https://arxiv. org/abs/1412.6980. Kirichenko, P., Izmailov, P., and Wilson, A. G. Why normal- izing flows fail to detect out-of-distribution data.Ad- vances in neural information processing systems, 33: 20578–20589,

Pith/arXiv arXiv

[15] [2019]

TCL: transformer- based dynamic graph modelling via contrastive learning

Wang, L., Chang, X., Li, S., Chu, Y ., Li, H., Zhang, W., He, X., Song, L., Zhou, J., and Yang, H. TCL: transformer- based dynamic graph modelling via contrastive learning. CoRR, abs/2105.07944, 2021a. Wang, Y ., Cai, Y ., Liang, Y ., Ding, H., Wang, C., Bhatia, S., and Hooi, B. Adaptive data augmentation on temporal graphs.NeurIPS, 34:1440–1452, 2021b. W...

Pith/arXiv arXiv

[16] [2020]

and Goadrich, M

Davis, J. and Goadrich, M. H. The relationship be- tween precision-recall and ROC curves. In Cohen, W. W. and Moore, A. W. (eds.),Machine Learning, Proceedings of the Twenty-Third International Confer- ence (ICML 2006), Pittsburgh, Pennsylvania, USA, June 25-29, 2006, volume 148 ofACM International Con- ference Proceeding Series, pp. 233–240. ACM,

2006

[17] [2021]

ISBN 9781450384469

Association for Computing Machinery. ISBN 9781450384469. doi: 10.1145/3459637.3481955. Chen, N., Liu, Z., Hooi, B., He, B., Fathony, R., Hu, J., and Chen, J. Consistency training with learnable data augmentation for graph anomaly detection with limited supervision. InThe Twelfth International Conference on Learning Representations,

arXiv

[18] [2022]

ISBN 9781450393850

Asso- ciation for Computing Machinery. ISBN 9781450393850. doi: 10.1145/3534678.3539321. Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. InInternational Conference on Learning Representations (ICLR),

arXiv

[19] [2023]

Liu, Y ., Pan, S., Wang, Y

URL https:// arxiv.org/abs/2211.13123. Liu, Y ., Pan, S., Wang, Y . G., Xiong, F., Wang, L., Chen, Q., and Lee, V . C. Anomaly detection in dynamic graphs via transformer.IEEE Transactions on Knowledge and Data Engineering, 35(12):12081–12094,

Pith/arXiv arXiv

[20] [2024]

Implementation Details.Following Postuvan et al

and additionally include some representative CTDG models originally developed for fundamental dynamic graph task (e.g., link prediction), which can be directly adapted to anomaly detection. Implementation Details.Following Postuvan et al. (2024), we apply a minimal modification when adapting general CTDG models: unlike standard link prediction that exclud...

2024

[21] [2025]

Reha, J., Lovisotto, G., Russo, M., Gravina, A., and Grohn- feldt, C

doi: 10.1109/ TKDE.2025.3581578. Reha, J., Lovisotto, G., Russo, M., Gravina, A., and Grohn- feldt, C. Anomaly detection in continuous-time tem- poral provenance graphs. InTemporal Graph Learn- ing Workshop @ NeurIPS 2023,

arXiv 2025