DR-GGAD: Dual Residual Centering for Mitigating Anomaly Non‑Discriminativity in Generalist Graph Anomaly Detection
Authors: Changlong Fu
Zhenli He
Xiong Zhang
Cheng Xie
Xin Jin
Yun Yang
Venue: ICLR 2026 Poster (2026)
Keywords: Graph Mining
Social Network Analysis
Graph Anomaly Detection
Primary area: learning on graphs and other geometries & topologies
TL;DR: This paper proposes DR-GGAD, a framework that addresses Anomaly non-Discriminativity in generalist graph anomaly detection.

Abstract: Generalist Graph Anomaly Detection (GGAD) seeks a unified representation learning model to detect anomalies in unseen graphs, but cross-domain transfer often entangles the learned anomalous and normal representations. We formalize this degradation as Anomaly non-Discriminativity (AnD) and define a normalized score to quantify it. We present DR-GGAD, which avoids direct comparison between anomalous and normal nodes via two residual modules: 1) a multi-scale Hyper Residual (HR) Center measuring node-to-center distances, yielding a compact normal residual structure with margin-pushed anomalies; 2) an Affinity-Residual (AR) module enforcing local residual directional consistency to recover structural separability. With frozen parameters (no target fine-tuning), DR-GGAD fuses both signals into a unified score. On 8 benchmark target graphs, it achieves new SOTA: mean AUROC +5.14% over the best prior GGAD, with large gains on high-AnD datasets (ACM +9.96%, Amazon +7.48%) and strong AUPRC boosts (Amazon +17.12%, CiteSeer +17.77%). Ablations confirm complementary roles of the two modules. DR-GGAD thus establishes AnD as a measurable bottleneck and delivers robust cross-domain anomaly detection.

Published as a conference paper at ICLR 2026
DR-GGAD: DUAL RESIDUAL CENTERING FOR MITI- GATING ANOMALY MON-DISCRIMINATIVITY IN GEN-
ERALIST GRAPH ANOMALY DETECTION
Changlong Fu; Zhenli He, Xiong Zhang, Cheng Xie! Xin Jin, Yun Yang
School of Software Engineering Yunnan University, Kunming, China
(hezi, xi xiecheng, xinjin, (anggunn@ynu...mm edu..ceeducc (fuchanglong, shangxiong)esttee ynu. enu.edu.co
ABSTRACT
Generalist Graph Anomaly Detection (GGAD) seeks a unified representation learning model to detect anomalies unseen graphs, but cross-domain transfer often entangles the learned anomalous and normal representations. We formalize this degradation as Anomaly non- Non-Diseriminativtty (AnD) and define a normal- ized score quantify it. We present DR-GGAD, which avoids direct compari- son between anomalous and normal nodes via two residual modules: 1) multi- scale Hyper Residual (HR) Center measuring node-to-center distances, yielding a compact normal residual structure with margin- margin-pushed anomalies; 2) an Affinity- Residual (AR) module enforcing local residual directional consistency to recover structural separability. With frozen parameters (no target fine-tuning), DR-GGAD fuses both signals into unified score. On 8 benchmark target graphs, it achieves new SOTA: mean AUROC +5. 55.4%% over the best prior GGAD, with large gains high-An'D datasets (ACM +9.96%, Amazon +7.48% and strong AUPRC boosts (Amazon +17.12%, CiteSeer +17.77%) Ablations confirm complementary roles of the two modules. DR-GGAD thus establishes AnD as measurable bottleneck and delivers robust cross-domain anomaly detection.
INTRODUCTION
Learning robust representations graphs is central to many mission-critical services. Effective representations allow social-media platforms to trace fake accounts and rumor cascades Duan et al. (024);; Yu et al. (2024), enable banks to uncover fraudulent transfers in massive ledgers Li et al. (2022a). and support security teams in blocking stealthy intrusions within corporate networks Jacob et al. (2022); Ghosh (025). All of these tasks depend on Graph Anomaly Detection (GAD), whose goal is to pinpoint the few vertices whose attributes or links reveal malicious or abnormal behavior. Missing even a single anomaly can be costly; high-frequency trading bot can distort prices in milliseconds, and a misinformation campaign can sway public sentiment before moderators react. Accuracy and timeliness are therefore essential.
Limitations of domain-specific training. Most GAD pipelines are trained on one graph at a time. They master the quirks of single citation network, social platform, or e-commerce site and achieve strong in-domain accuracy. However, each new graph demands fresh labels, a parrmme search, and additional compute. security operations center that monitors many evolving networks soon faces prohibitive retraining costs, and models may become obsolete just as adversaries pivot to a new domain.
The promise of generalization. Generalist Graph Anomaly Detection (GGAD) aims break this cycle by learning one detector that transfers to unseen graphs without further tuiig. Recent work has taken encouraging steps: contextual residual learning in ARC et (2024) and neighborhood
"These authors contributed equally.
1 Corresponning author

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Published as a conference paper at ICLR 2026
Source Domain (Yelp) CelpChi Graph)
Target Domain (Amazon Graph)
Rommal
Cress-domain Anomaly
Anomaly
non-Bisrriminativity
Anomaalia
Amomaal mon- Derrrriiiiiiiiillly Soire:
Animaly mone Dirriiiiiiis Soaret
Anomaly are slightly separable
Lower accuracy
Anomaly and
entangled
AnD Score: 0.4128
AnD Score: 0.5163
(a)
(b)
Figure 1: Anomaly non- DonDiicriminattivty (AnD). A GCN trained on YelpChi transfers to Amazon; the AnD score rises and AUC falls.
prompting in UNPrompt Niu et al. (2025) both improve zero-shot performance. A critical obstacle, however, continues to limit progress.
The Anomaly non-Disrriminativity (AnD) Bottleneck. AnD measures how much the latent representations of normal and anomalous nodes overlap; higher values indicate weaker separability. Figure Ta) shows a Graph Convolutional Network (GCN) trained on the YelpChi review graph. Its embeddings already partly entangled, yielding an AnD score of 0.41. After transfer Amazon's larger co-review graph, differences in feature statistics and neighborhood patterns blur the decision boundary. The AnD score climbs to 0.52, and the area under the ROC curve (AUC) falls from 0.58 to 0.46 [Figure| [b)..
Practical consequences. Imagine the opening morning of a holiday sale. Trust-and-safes engineers rely on this detector to intercept coordinated fake-review rings. Thousands of five-star posts arrive within hours. Because the elevated AnD score hides abnormal users among legitimate shoppers, roughly one in five fraudulent accounts slips through automated screening until manual audit. By that point, product rankings are distorted, and purehasing decisions affecting millions of dollars have already been influenced.
Our solution: compare with a center rather than with each other. Direct comparison between anomalies and normals is fragile under domain shift. We instead measure how both groups deviate from two residual centers. Concretely, it comprises two components: (1) Hyper Residual (HR) Center. Multi-scale residuals from successive graph neural network layers form a
invariant reference. Normal nodes cluster tightly around this center, while anomalies are pushed outward, restoring feature-space separability. (2) Affinity Residual (AR) Center. Residual vectors aligned within structural neighborhoods, revealing anomalies that hide primarily in topology rather than attributes. With parameters frozen after source training, DR-GGAD fuses HR and AR signals into a single score that transfers to target graphs without tuning.
Impact in practice. Across eight public benchmarks, DR-GGAD raises mean AUC by 5.14% over the previous GGAD best. Gains are especially large on high-AnD graphs: ACM (+9.96%), and Amazon (+7.48%). The area under the precision- recall curve (AUPRC) improves in paral- lel, climbing 17.12% Amazon and 17.77% on CiteSeer. These gains correspond to many more fraudulent users and compromised hosts being caught before damage occurs.
Contributions of this work. (1) We isolate and quantify AnD and release normalized AnD score for reproducible benchmarking. (2) We introduce Dual Residual Centering: the HR center mitigates feature-space entanglement, and the AR center restores structural alignment, yielding detector that needs no target-domant tuning. (3) We conduct extensive experiments that establish new state-of-the-art results eight benchmarks, demonstrating both the importance of addressing AnD and the effectiveness of DR-GGAD. These advances move GGAD closer to deployment-reade, reliability, allowing practitioners monitor emerging graphs without continual retraining.
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2 RELATED WORK
2.1 GRAPH ANOMALY DETECTION
Early GAD research framed node-level detection as a reconstruction or similarity task. Autoen- coder variants rebuild graph structure and attributes to highlight large reconstruction errors as anomalies Ding et al.] 2019); [Zheng et al. (2023); He et al.] (2024). Deep SVDD Ruff et al.] (2018) and Deep SAD Ruff et al.J (2020) perform anomaly detection by compressing the repre- sentations of normal samples into a hypersphere, making them suitable for single-domain tasks. However, their performance may be affected when facing domain shifts, limiting their application in cross-domain tasks. Distance-based methods compute local or global affinity scores; examples include OCGNN Wang et al. (2021) and the reinforcement-guidee strategy in [Bii et al. (023))
Edge-truncation models such as TAM Qiao & Pang (2023) and GCTAM [Zhang al. (2025) prune heterophilous edges, improving normal homophily. Contrastive learning further sharpens de- cision boundaries by sampling positive and negative node pairs Liu et al. b; Kim et al. 2023)
Spectral and propagation-awe aware designs -Higgns-GRRN Gao et al. (2023). BW BWGNN Tang et al. 2022),
and SmoothGNN Dong et al. (2025) (1155-ti trace the flow of high-frequency signals to flag outliers. Re-
cent adversarial and semi-supervised methods generate pseudo-anos anomalies or perturbations, raising
robustness and data efficiency Ding et al. (2021a) Meng al. (2023): Qiao al. (2024): Li et al.
2022b) Xiao et al. (2023).
Limitations. Most existing methods assume similar train-test distributions, so their representations degrade on unseen domains-a failure captured by our AnD metric. They further rely on labeled anomalies or domain-speetiee tuning, conflicting with the zero-tuning goal of GGAD.
2.2 GENERALIST GRAPII ANOMALY DETECTION
GGAD seeks single detector that generalizes across graphs. Previous cross-domain methods like COMMANDER Ding et al.] (2021b). ACT Wang et al. (2023), and CDFS-GAD [Cen et al. al.. (2024) align node representations or anomaly patterns to handle cross-domain tasks effectively. How- ever, they rely on target-domain data or fine-tuning, limiting their applicability in cases of data scarcity unknown target domains. Recent works, such as ARC Liu al. (2024) sorts node fea- tures by smoothness and employs multi-hop residual encoder to extract transferable signals under few-shot settings. UNPrompt(Nin
al. (2025) introduces unified neighborhood prompts that guide zero-shot model without any fine-tuning AnomalyGFM Qiao et al. (2025) pre-trains aagnssig prototypes for normal and abnormal classes, enabling both zero-shot and few-shot use.
Our distinction. Although these methods improve transferability, none explicitly tackle the rep- resentation overlap we term AnD. DR-GGAD mitigates this bottleneck through Dual Residual Centering: the Hyper Residual center reduces feature-space entanglement, and the Affinity Resid- ual center restores structural separability, together delivering a frozen model that remains effective across a wide range of unseen graphs
Method
Cros-Domainn
Addresses
Needs Few Samples
Key Idea
TAM TAMiQiao & Pang 2023
No
No
Yes
Edge truncation
GHR Gioo i 2035
No
No
Yes
High-freq signals
UNPrompt Niu
2025
Yes
No
No
Neighbothood prompt
LRC ala 2014
Yes
No
Yes
Contextual residual
AnomalyGFM et
2025
Yes
No
No
Prototype matching
DR-GGAD (Ours)
Yes
Yes
No
Dual residual centers
Table Comparison with representative GAD and GGAD methods.
Innovation Highlight. Table contrasts DR-GGAD with prior art. Our method is the first to (1) quantify AnD, (2) address it jointly in feature and structure space, and (3) achieve oate-of-the-an transfer without any target-domain tuning.
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3 PROBLEM FORMULATION
3.1 NOTATION AND PRELIMINARIES
Let AV. be an attributed graph with node set {ur, U2 ....... uN adjacency matrix
A E {0, 10,11 where Aij = =1 if and only if an undirected edge connects v, and ej, and feature matrix X E RNxd whose i-th row X; is the d-dimensional attribute of uz. A frozen encoder H F + Rh maps each x; to an embedding z Hxx:). We assume I 2 and |N 2 whenever the quantities below are defined.
3.2 GENERALIST GRAPH ANOMALY DETECTION TASK
We are given ni labeled source graphs Trrain = (D (mmin....... D(n..) }. each ((#) train (g(k), (60) with node labels (()) (0, 1>ID(*9) (1 anomaly). A detector fo is learned all sourees and then frozen. At deployment, fo applied without fine-runing to every unseen targer graph in Teaa = (G ................................ ................................
..... For each target node Us, the goal is output a score 84 E RR that reflects its anomaly likelihood.
3.3 ANOMALY NON- DISCRIIIINTTIVITY (AnD)
Unnormalized score. Let N and N denote the of normal and anomalous nodes. Their average pairwise Euclidean distances are
(+))
Σ Σ IEN+JEN+
2;ll2, d
-
Σ Σ 2z
2il12:
N-
JEN-JEN
(1)
d
Σ
Σ
12 22
JEN+JEN-
Then, define
AnD = d
(2)
Note. We use V-statistics; the corresponding U-statistic versions asymptotically equivalent for our purposes.
Normalization. Fix evaluation suite 3 of graphs used for cross-dataset comparison. To compare across graphs, we linearly rescale over S:
AnD (G) ming'es AnD"
AnD(G) maxg'es AnD' (g') ming'es es An""
where AnD E [0, 1] is the normalized AnD score. A higher AnD(g) score indicates greater overlap and weaker separability, while a lower score reflects clearer separation and stronger discrim- inability.
3.4
THEBRETICCA PROPERTIES OF AnD
We record two minimal properties justify AnD separability surrogate before presenting DR- GGAD.
Proposition 1 (Range & Calibration), Let m ming AnD and M maxs AnD* with Ml Then for any g E S, AnD(G) = ((AnD* (g) (M m)) E [0. 1], with AnD(g) = + AnD (g) = m and AnD(g)
> AnD* M; if m, set AnD
Lemma (Lipschitz scoring gap). For any L-Lipschitz score g Ig E. applied to embeddings, if (i, j) is drawn uniformly from N+ x N then
B(,,)) + (lg(2)))) - - t
Proof. By Lipschitz continuity, lg(2,) - g(z,)]= < Li|z, 2il12 for any (1.5) E N X N Taking expectations over (i,j) Uni x N-) yields the claim.
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Source Domain
Sode Residual Eacediig
Amumaly
H
L AR
Nermal
Exp (10)
Allisity Residial
Hyper Resiial
Auodiaty
LH Fgy 69)
Residual Calculation
Nurual
Graph Eacoder
Pre-traniiag
Target Domaain
H
R
Hyper Residaal Souring
KRS(F)
(q)(1
ARS(
Fig. (13)
Graph Encoder
Figure 2: Overview of DR-GGAD.
Remark. When the class-conditional embedding distributions coincide, AnD* typically lies near the upper end on given suite S; conversely, well-separated embeddings tend to the lower end. Whether such extremes realized depends on S.
3.5 KEY CHALLENGES
C1: Distribution shift. Feature statistics, degree profiles, and homophily ratios vary widely across graphs, eroding the margin learned in the source domain. C2: No adaptation budget. Target graphs arrive without labels, and the detector is not allowed to update its parameters. C3: Embedding overlap. When CI and C2 coincide, normal and anomalous embeddings overlap, which reflected by high AnD score.
Design Objective. DR-GGAD combats C3 by introducing two residual centers that provide a sta- ble, graph-agnostic reference in both feature and structure space, thereby counteracting C1 while respecting the no-adaptation constraint C2. In DR-GGAD, HR compresses d' + di-) while AR enlarges d(--); by equation 2 these jointly decrease AnD". Collectively, the above properties support AnD as a useful surrogate for separability: lower values coincide with reduced class over- lap and, empirically, correlate with stronger cross-domain generalization. To further investigate the AnD challenge, we conduct a quantitative analysis of both AnD* and normalized AnD scores, with detailed results provided in Appendix A
4 METHODOLOGY
To address Anomaly non-Discriminativtty (AnD) from direct node comparisons, DR-GGAD shifts to analyzing self-residuals. We propose dual residual centering with Hyper Residual and Affinity Residual, anchoring each node two domain-invarian centers and replacing fragile normal-to- abnormal contrast with more stable self-to-self discriminability. This section details how we (1) extract multi-layer residual embeddings, (2) build the Hyper Residual (HR) center, (3) enforce lo- cal Affinity Residual (AR) coherence, and (4) fuse both signals into single anomaly score. An overview is provided in Figure 2
4.1 NODE RESIDUAL ENCODING
The encoder transforms features into residual embeddings that capture cross-layer varia- tions tions-signals known to transfer well across graphs.
Node attribute alignment. Heterogeneous input dimensions unified by linear random projection, i.c., X T(X) E xxd, where T(-) preserves discriminative information while enforcing unified dimension d,,
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Shared graph encoder. Aligned features propagate through é light graph convolution layers with shared parameters:
1 D AD AD-
2X, X = D ---
(5)
followed by projections
H o ox* ERN t= 1...,.
(6)
Residual calculation. Layer-wise differences highlight how each node reacts to wider receptive fields:
M = 1 ! <ISE Ti n=
(7)
Stacking all r; yields R E R- not only reveals the differences between the ego node and neighbors but also effectively captures high-frequency signals and local heterophily. This enables the model to capture consistent residual representations shared across domains, which is crucial for anomaly detection Qiao Pang (2023). Liu et al. (2024). At the same time, preserves the ability identify more complex anomaly patterns within the graph structure.
4.2 HYPER RESIDUAL LEARNING
Instead of contrasting normal and abnormal residuals directly, we summarize normal patterns into compact set of centroids and measure each node against them.
Center construction. Across all source graphs, k-means clusters normal residuals into t groups. Each cluster C, contains normal residuals assigned to the i-th group. At iteration the centroids update as
(1+1))
W
Σ (1 EC
") c(0 = -Clustering R (t-1) ,r), Ce Ce (T)
(8)
forming the global HR center set R = (r and the centers are constructed based on the normal node residuals rj. reflecting the typical patterns of normal nodes.
Center- loss. Normal residuals are drawn toward the centers, while anomalies are repelled:
N CHR Σ> Fx
max(0., e -l|r, -Fxlly)
(9)
where n,th and r; denote the residuals of the normal and anomalous node, respectively. By min- imizing CHR, encourage the residuals of normal nodes be close to the HR center, thereby enhancing their semantic consistency, while forcing the residuals of anomalous nodes to exceed the boundary ensuring clear separation between normal and anomalous nodes. This ensures clear separation between normal and anomalous nodes, consequently amplifying the anomalous semantic information of anomalous nodes in the graph.
4.3 AFFINITY RESIDUAL LEARNING
While the HR center enforces global alignment, local structures may still diverge. AR learning, therefore, aligns residual directions within each neighborhood.
Affinity Score and Consistency Loss. To promote structural consistency in residual space, define the affinity-based consistency loss as:
N
CAR = Σ (1 -1- AR()), AR(i) = I.
T Iral
T |rlll
(10)
JEN;
where AR(i) measures the average cosine similarity between node and its neighbors in the resid- ual representation space. Minimizing LAR strengthens local structural semantics by ensuring that neighboring nodes with regular structural patterns remain aligned in the residual space, while nodes

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Published as a conference paper at ICLR 2026
with structural anomalies semantic inconsistencies exhibit deviations. By imposing this straint, it helps model capture meaningful local structural features, enabling it to detect anomalies without relying reconstruction-bet based supervision, thus alleviating the structural entanglement underlying the AnD problem.
Joint objective. Both losses combined to learn transferable residual representations and defined as LHR + LAR-
4.4 ANOMALY SCORING AND PREDICTION
After training on sources, parameters are frozen. For each target graph, we compute two com- plementary scores.
Hyper Residual score (HRS). Feature-level deviation from the HR centers
HRS(()
Σ
|r
Fall2-
(11)
k=
where larger values indicate stronger abnormality in residual space.
Affinity Residual score (ARS). We quantify how much node i deviates from its neighborhood:
ARS(1)
1 N
E JEN,
Ti Ira Irl
+ l1, rrlll))
(12)
Unified score. The final anomaly score aggregates both perspectives:
S(1) XHRS(()
ARS()), X [0.1)
(13)
Threshold selection. We choose the threshold that maximizes separation between predicted normals and anomalies:
Σ I(S(i) 2 7)
Σ I(S(s)
2 n)
arg
max (E(S)))EEN)
NN++
IN
iEN+
JEN
(14)
S(1) 24" 10. S(1) <T
1,
0:
This dual-center strategy directly targets anomaly non-discriminatiity by shrinking residual overlap both feature and structure spaces, enabling robust zero-shot detection on unseen graphs.
EXPERIMENTS
We now demonstrate that DR-GGAD converts the theoretical gains promised by dual residual cen- tering into tangible improvements eight heterogeneous target graphs.
5.1 EXPERIMENTAL SETUP
Datasets. We follow ARC's cross-domain protocol Liu et al. 2024). The four source graphs are Tuain (PubMed, Flickr, Questions, YelpChij, and the eight target graphs are Tee {Cora, CiteSeer, ACM, BlogCatalog, Facebook, Weibo, Reddit, Amazon). Each tar- get mixes synthetically injected and naturally occurring anomalies, ensuring a rigorous evaluation of cross-graph generalization.
Baselines. We compare DR-GE DR-GGAD against sixteen strong methods: (1) GAD methods and Super- vised Pre-Train--ee GCCN Kipf & Welling (2016). GAT Veličković et al. (2017). DOMINANT Ding
et al.
(2019). BGNN Ivanov & Prokhorenkova (2021). BWGNN Tang et al. 2022) ) GHRN Gao
al.
2023);
GAD methods and Unsupervised Pre-Train CoLA Liu et al. (202)) 1b. HCM-A Huang
et al.
(2022), TAM Qiao & Pangl (2023), SmoothGNN Dong et al. (2025). GCTAM [hhag et al.
(2025
CAGAD Xiao al. (2024), and Semi-GGAD Qiao al. (2024); (2) GGAD methods and

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Supervised Dye-Train-UNPrompp UNPrompt Niu et al. (2025), AnomalyGFM Liu et al. (2024).
Qiao et al. (2025). and ARC
Metrics and implementation. AUROC and AUPRC reported with mean = std over five seeds Tang et al. (202)) All runs use an RTX A6000 GPU and a 12th-Gen Intel i7-12700 CPU. Unless noted, the learning rate is 10-5, weight decay 5 x 10-5, dropout 0.2, unified feature dimension d, = 64, residual dimension d = 1024, GCN layers = 3, separation margin c = 1, and 60 training epochs.
Table 2: Anomaly detection performance (AUROC, %, mean + std). "Rank" is the average rank over eight targets; A is the absolute AUROC gain over the second-best method. The best, second, and third results are colored first, second, and third, respectively. Results tagged "*" are reproduced with the authors' code and default configures; all others are copied from ARC's Liu et al. (0224) leader-board.
Mathad
Facebook
ACM
Amazon
Cam
CiteSeer
Rod
Weiho
BlogCanaiog
Rank
GAD Methods
Supervised
Pre-
GCN(2917)
29.51-4866
60.49+99.65
46.63+3.47
50 64.4..330
60..77+8.1
50.4444.41
26.64+17.66
56. 19+69+663
10:00
20T12018)
5188-2116 16
48,79+2.75
50.52=17.22
50.06+22.65
51.78+4004
53,06+7.488
50.40=200
DOMINANT(2019)
51.01-0788
70.08:12.34
48 28.04:22669
53:1111
69.47:2.00
02.8810.55 32
6.88
BGNNN22211
$4.74=25:29
14.00:13.69
52:26:33:11
12.45
42.5211182
50274384
32,75
47.6728.52
13,02
BWGNN(2122)
45.41.497
67.59.10.70
55.26_.16.55
54.06.13.27
52.112288
48.9715774
53.38.11.1
16.3111121
10.31
GHRN(2023)
4481-8006
55.65:6.37
49.48=17.133
59 598996657
56,04+9.99
46 2.233333
1188714.188
57.64=3.48
11.00
GAD Method & Unsupervised
Pre Train
CoLAA/2021)
12,99:11.6
66.85144443
47 7.7977797
89.2888888
62.84-9935
62.811669
16.2745.64
50.04::.25
11:00
NCM-A/22022
35.94
53.70144.64
54.2814.73
48.12.5..00
48.791275
65.52&12.58
55.31.00.7
TAM(2023)
65.88_.666
7,.59
56 16.0611.19
62.0211..39
72.2710.83
55.4310.33
71.5110.188
19.36.10.33
5.60
CA24DD2024
4..4
39 39,80=9991
46 46.06
50.11=3.411
40.13:25.1
54.774389
58.9943422
49.4-12..37
13.44
40mi-6GAAD202244
$5.9988099 09
2.66
53. 11:992
50 401:4::441
38. 18:18:24.21 21
55 39
65.73433355
50.70:77334
11:38
SmockENNN
4881-600
49,02+7.37
51,77-36.49
S1 52+55.3
49.61+5.50
51 13+2.76
37,14+21.32 32
49.51-58.6
12:75
CCTAM(2025)'
19.57_1411
$1.2110.11
55,7410.00
58.7812.17
70.31
59.3210.773
70.6110.10
67.60.0.77
4.62
GGAD Methods & Supervical Pre-Train
UNitomptt 20025"
09.1=1128
56.0=11.09
54.1++1500
39.80:3311
18+1.44
45.56+3.75
00
AromssyyFM(10255
58.4477114
60,79:1148
60:65:007
54.1743.08
$4.71
99.9911.69
19.48:11111
37.77
6,62
ARC(2024)
1.65
79.88+00.88
6167+181
87 45+0777
90.95+0..99
6004+0.69
88.85+0.14
74.76-00066
2.38
Our & Supervised Train
DR-GGAD
82.16-1.98
91.17+0.78 9.961
88.15=2.11
93.20=0.56
95.00-0.441
66.6000.62
93,31
75.06-0.09
1.00
A
12.59
7.48*
5,751
4,051
0,561
0,431
0.30
5.2 OVERALL PERFORMANCE
As summarized in Table 2 DR-GGAD posts the top AUROC on every one of the eight target graphs, Facebook (+12.59%). ACM (+9.96%),
yielding perfect average rank of 1.0. Its largest and Amazon (+7.48%) coincide with the datasets that exhibit the greatest AnD. Traditional super- vised detectors (GCN, GAT, BGNN, GHRN) collapse once the deployment graph drifts away from the training distribution; unsupervised methods (c.g.. DOMINANT, GCTAM) thrive under strong homophily but falter on heterogeneous structures. Earlier GGAD designs, such as UNPrompt and ARC transfer better, yet they still compare nodes directly and thus lose separation when residual overlap is high. DR-GGAD instead anchors normal residuals to a global Hyper Residual center and restores local coherence through the Affinity Residual module, so its decision boundary remains wide even as both attributes and topology shift. The model's robustness is underscored by standard deviations below 2.5% on every dataset and by additional gains on relatively easy benchmarks like Cora and CiteSeer, confirming that dual residual centering helps in favorable settings without hurt- ing elsewhere. Complete AUPRC results, which show the same trend, are provided in the Appendix
5.3 ABLATION STUDY
To quantify how each component of DR-GGAD mitigates AnD, we disable the Hyper Residual (HR) and Affinity Residual (AR) modules individually and jointly. Table aablersssmmarizss the AUROC of four variants: Backbone: only the shared GCN encoder and residual extraction. Backbone+ adds the HR center but removes AR. Backbone+A R: adds AR but removes the HR center. Full: the complete DR-GGAD with both HR and AR.
Key findings. (1)HR addresses feature divergence. On Amazon and CiteSeer, whose attribute statistics differ most from every source graph, adding HR lifts AUROC by +19.47 and +36.79 points, respectively. By contracting within-class residuals toward domain-invariant center, HR
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reduces d(+) + d and thus AnD via Eq. equation 2 aligning with the observed AUROC gains. (1)AR addresses topology divergence. Cora and Facebook undergo the strongest topology shift; replacing HR with AR yields the larger boost (+44..23 and +32.59 points). Enforcing local residual alignment enlarges d(+-), which (by Lemma 2 relaxes the Lipschitz ceiling score separation and, empirically, correlates with higher AUROC, (2)HR and AR are complementary. The full model outperforms each single-module variant by non-trivial margins (e.g.. 26.36 on Amazon Backbone+ARR +16.78 on ACM vs. Backbone+HR). Acting on both sides of equation Sasaationnnssniiiiiinnnna shrinking d(+)+d(=) and enlarging d((-)_drive, AnD* down further and yields consistently higher AUROC. (3)Stable improvements. Standard deviations remain under 3% across five seeds, indicating robust gains rather than lucky initializations. The trend is consistent across datasets and fusion weights (Figure
AUROC Performance Across All Datasets
Table 3: AUROC (%) of DR-GGAD variants. Best per row in bold.
50.0
00
Dataset
Backbone
+HR
+AR
Full
Facebook
49 42
65.30
82.01
82.16
Amazon
68.57
88.04
61.79
88.15
00.0
ACM
53.02
74.39
90.85
91.17
500
CiteSeer
53.87
90.66
94.03
95.00
Cora
47.43
84.77
92.66
93.20
Weibo
47.02
88.61
88.35
93.31
BlogCatalog
60.29
74.31
74.43
75.06
Reddit
50.56
56.04
58.04
60.60
Figure 3: AUROC versus fusion weight À on all target graphs.
5.4 FUSION WEIGHT SENSITIVITY
We vary the fusion weight À in Eq. 13 from 0 to 1 and plot AUROC on all targets in Figure 3 Two clear regimes emerge: doomindd (A 0.6). Amazon, BlogCatalog Reddit, and Weibo reach their maxima here. These graphs suffer mainly from attribute shift, relying more the Hyper Residual score- A2S-dmnniant (A = 0.2). Cora, CiteSeer, ACM, and Facebook peak when the Affinity Resid- ual score has higher weight. Their performance limited by topology drift; ARS restores local structural coherence, aligning with the design goal of the AR module.
HR center contracts feature-space overlap- best mitigates AnD.
Takeaway. Figure confirms that dual residual centering offers a tunable trade-off:: HRS counters feature-level divergence, ARS counters structural divergence, and À lets practitioners bias the detec- tor toward the dominant source of AnD in a given graph-exactly exactly as intended by our framework. An extended analysis on À available in Appendix F.I
Table 4: Relationship between residual overlap (AnD*) and AUROC. Columns are sorted by our improvement A. Best and Second AUROC are color-coded.
Dataset
Facebook
Amazon
Cora
CiteSeer
Reddit
BlogCatalog
ACM
Weibo
AnDD Score
0.5272
0.5163
0.5190
0.5294
0.5964
0.4408
0.41.59
0.2745
AND Score
0.7850
0.7512
0.7596
0.7919
1,0000
0,5166
0.4393
0.0000
DOMINANT
51.01
48.90
66.53
69.47
50.05
74.25
70.08
92.88
GCTAM
69.57
55.74
58.78
70.31
59.32
67.60
81.21
70.61
AnomalyGPM
58.64
60.65
54.17
54.71
59.99
57.77
60.79
69
ARC
67.56
80.76
87.45
90.95
60.04
74.76
79.88
88.85
Our
82.16
88.15
93.20
95.00
60.60
75.06
91.17
93.31
12.591
7.481
5.75t
4.05t
0.56"
0.301
9.961
0.431
5.5
IMPACT OF AnD
Table 4 juxtaposes each target's AnD* score with AUROC obtained by DR- GGAG and four strong baselines. Three concise observations emerge: (1)Positive correlation with the performance gap.

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The larger the residual overlap, the larger improvement. Facebook and Amazon possess the highest AnD" (0.5272 and 0.5163) and see gains of +12.59 % and +7.48 %, respectively. (2) lapse of prior art under extreme overlap. When AnD* 0.5 (Facebook), ARC, DOMINANT, and GCTAM lose up to 20 AUROC points, whereas DR-GGAD still surpasses 80 %. Dual resid- ual centering prevents the decision boundary from vanishing. confirming our design motivation. (3)iiinis headroom when overlap is small. On Weibo (AnD* 0.2745) and BlogCatalog (0.4408), all models already separate anomalies well, so the attainable gain is modest (+0.43 and +0.30 %). This ceiling effect is consistent with Proposition | which states that AUC saturates as AnD- -.
Summary. Higher AnD" leads to wider gaps between DR-GGAD and prior methods, while lower overlap narrows the gap-direct non-discriminativity in both feature and structure spaces, fulfilling the paper's core objective without any target-domain tuning.
direct empirical evidence that dual residual centering neutralizes anomaly
LIMITATION
Despite its strong empirical results, DR-GGAD is not a panacea. We summarize the most salient limitations, each pointing clear avenue for future work. (1)Weak anomaly signals. On graphs where anomalies barely deviate (e.g.. Reddir), residuals overlap and margins shrink. In- jecting subgraph-leve! reconstruction or contrastive amplification could surface such subtle outliers. (2)Sparse or noisy attributes. Missing or adversarial features weaken the Elyper-Residun branch. structure-only fallback or lightweight denoising encoder would improve robustness. (3)Scalabil- ity. Global clustering and wide residual vectors add memory and pre-processing costs; hierarchical or quantized centers can reduce this footprint on billion-nok -ode graphs. (4)Fusion weight Choos- ing À still needs minimal validation. An unsupervised, drift-aware estimator would remove this final knob.
Outlook. These limits reflect open challenges for the entire GGAD field. By isolating and mitigating AnD under strict zero-shot constraints, DR-GGAD offers solid step forward while outlining clear paths for future research.
7
CONCLUSION
This paper advances representation learning for cross-domain graph anomaly detection by introduc- ing DR-GGA DR-GGAD, zero-shot framework that mitigates Anomaly non- non-Discriminativity by comparing each node to two overlap, and the complementary Hyper Residual and Affinity-Resdual Residual modules shrink that overlap from the feature and structure perspectives. Without any target-side tuning, DR-GGAD sets new state of the art eight benchmarks, lifting mean AUROC by 5. 5.14% and up to 12.59% on high-An:D graphs.
invariant residual centers. The new AnD metric quantifies representation
ACKNOWLEDGEMENTS
This paper is the result of the research project funded by the National Natural Foundation of China (Grant No. 62106216, 62362068, and 62162064), the Open Foundation of Yunnan Key Laboratory of Software Engineering under Grant No. No.2023SE104 and No.2023SE200 and Innovation Project for Postgraduate Students of Yunnan University (Grant No. KC-252511575), and the Project of Yunnan Provincial Department of Education Science Research Fund (Grant No. 2026Y0106).
the Scientific Research
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APPENDIX
A EXPERIMENTAL ANALYSIS OF AnD
Table 5: AnD scores of source domain and target domain.
Source Domain
Dataset
PubMed
Flickr
Questions
YelpChi
Averuge
AnD* Score
0.4061
0,4389
0.4079
0.4197 0.4473
0.4181
AnD Score
0.0000
1.0000
0.0592
0.3766
Target Domain
Dataset
Facebook
Amazon
Cora
CiteSeer
Reddit
BlogCatalog
ACM
Weibo
Average
AnD* Score
0.5272
0.5163
0.5190
0.5294
0.5964
0.4408
0.4159
0.2745
0.4774
AnD Score
0.7850
0.7512
0.7596
0.7919
1.0000
0.5166
0.4393
0.0000
0.6305
To further understand how DR-GGAD alleviates Anomaly non-Discriminattvity (AnDD* under do- main shifts, We perform dual analysis: we first examine the unnormalized AnD" and normalized AnD scores to quantify embedding overlap across domains; Building upon the results shown in Table 5 we proceed to analyze the role of the dual residual centering mechanism under different AnD problem. AnD* score quantifies the absolute overlap between normal and anomalous em- beddings within single graph, whereas AnD rescales these scores to the range [0, 1] to enable cross-domain comparability. These metrics provide a systematic characterization of the challenges in cross-domain separability.
A.1 AnD SCORE ANALYSIS
Cross-domain AnD problem Comparison. In the source domains (PubMed, Flickr, Questions, YelpChi), AnD" remains at moderate level (0.4061-0.4389), with an average AnD* score of 0.4181. This indicates that although source domain training alleviates AnD problem to some extent, feature overlap remains prevalent. In contrast, average AnD* of target domains rises sharply to 0.4774. In particular, Reddit (AnD* = 0.5964) and CiteSeer (AnnD 0.5294) exhibit severe entanglement between normal and anomalous embeddings, underscoring the amplification of AnD problem under cross-domain transfer.
High- AnD domains (AnD* >> 0.5). Facebook (0.5272), Amazon (0.5163), Cora (0.5190), Cite- Seer (0.5294), and Reddit (0.5964) exhibit pronounced embedding overlap, where anomalies are nearly indistigguishable from normal nodes, making detection highly challenging.
Facebook/Reddit: densely connected social networks with complex community structures; anomalous nodes often mimic normal interaction patterns, aggravating feature overlap.
Amazon: e-commerce review network with high-dimensional sparse attributes, where anomalous behaviors are easily confounded with normal user ratings.
Cora/CiteSeer: citation networks with highly similar semantic distributions; cross-domain transfer further introduces label semantics drift, reducing separability.
Low-AnD' domains (AnD) < 0.5). Weibo (0.2745) and ACM (0.4159) yield relatively low scores, indicating that anomalies in these datasets remain more distinguishable and cross-domain detection comparatively easier.
anomalies exhibit social behavior patterns that differ significantly from normal users, making anomalous nodes more salient in attributes and connectivity.
Weibo:
ACM: as co-authorship and publication network, anomalies often correspond to atypical collaboration or citation links, which stand out against the otherwise community-driven structure.
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A.2 THE SOLUTION OF AnD CHALLENGE.
To address the Anomaly non-Disriminnatiity (AnD) problem across domains, DR-GGAD intro- duces dual residual centering that integrates the Hyper Residual(HR) and Affinity Residual(AR). Empirical evidence (Table 4) shows that the level of AnD strongly relates to the contributions of HR and AR. high-Ani domains such as Facebook (AnD> 0.5272) and Amazon (0.5163), where residual overlap is severe, both components are indispensable: HR enhances semantic sepa- rability, while AR captures structural irregularities. In contrast, in low-AnD domains such as Weibo (0.2745) and BlogCatalog (0.4408), where anomalies remain comparatively more distinguishable, the score fusion strategy adaptively adjusts the weights HR and AR, avoiding redundant com- plexity while maintaining stable performance. These results demonstrate that DR-GGAD flexibly adapts to varying levels of AnD problem, achieving robust zero-shot cross cross-domait domain generalization without any target-domain tuning.
A.2.1
B ALGORITHM AND COMPLEXITY
B.I ALGORITHMIC DESCRIPTION
The overall workflow of OR-GGAD consists of a training and an inference phase (refer to Algo- rithm | and Algorithm 2 During training, the model aligns node features, extracts multi-layer GCN embeddings. and computes residuals across layers. It then jointly optimizes hyper residual clustering and affinity-based residual consistency to learn discriminative representations. In the ference phase, DR-GGAD operates without fine-tuning, leveraging pre-trained residual encoders to compute anomaly scores based on distances to hyper residual centers and local residual coherence, enabling efficient and transferable anomaly detection across graphs.
Algorithm Training of DR-GGAD
1: Input: Source domain graphs Tiain {D)
(1)
(m+)
}: training epochs E; cluster number 7.
train esin
2: Output: Trained model parameters; hyper residual centers (Fi,....
train E Tuain do 4: Project node features into unified representation space to ohtain X(
3: for each graph (A)
5: end for
6: for L...,, do
7: for each graph ((*)) E Timin do
8:
Compute multi-layer GCN embeddings via Eq.
66
9:
Calculate residual features R via Eq.
10:
Compute and update hyper residual centers [F using k-means Eq. 8
11:
Compute hyper residual loss CH via Eq.
12:
Compute affinity-residual loss CAR via Eq.
10
13:
Update model by minimizing joint loss C
ZAR + CaR-
14:
end for
15:
end for
B.1.1 COMPLEXITY ANALYSIS
Training Phase. The training time cost of DR-GGAD arises from five principal modules, each contributing to the total complexity as follows:
Node Attribute Alignment: Given node features X Raxd the dimensional projection to unified space of dimension d,, (e.g., via PCA Gaussian Projection) incurs a cost of (nddd.).
Graph propagation and representation encoding: For l layers of light GCN propaga- tion, each layer involves sparse matrix multiplications O(md,), where is the number of edges. The post-layer projection into hidden space d, has cost Ondd, dr.) per layer. Total complexity: Ol(mmd, + nd),
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Algorithm 2 Inference of DR-GGAD
1: Input: Testing graphs Tist = {Died
Dist ): frozen model parameters; hyper residual centers
(Fi, Fr); fusion weight X.
2: Output: Anomaly scores S(i) for all test nodes.
3: for each graph Dist Tix do
4: Project node features into a unified representation space to obtain X
5: Compute multi-layer GCN embeddings via Eq. (
Calculate residual features ( via Eq. (7)
7: Calculate the hyper residual score (RS(() ()) of node via Eq.
8: Compute the affinity-resduual score (R) of node i via Eq.
9:
Fuse scores to obtain final anomaly score S(t) of node via Eq.
10: Predict node anomalies Eq. (14)
11: end for
Residual computation: Residuals calculated via pairwise subtraction across e layers and concatenated, leading to cost (n((E - 1)d,).
Hyper residual clustering and updating: K-means clustering is applied to the normal node residuals form T centers in R(c-1)dn, requiring O(nr - 1)dn) per iteration (as- suming a constant number of iterations).
Affinity-residual computation: Cosine similarity is computed between each node and its neighbors in residual space, yielding O(n((E 1)dd), where d is the average node degree.
Hence, the overall training complexity becomes:
o Ondd, + L(md, + nd,,da) + n(e 1)d, + nT (T 1)d, + nnd(f - 1)da
(15)
In our experiments, the total training time across all source-domain graphs was approximately 46 seconds under a single seed (60 epochs, = 3, T = 4), measured on a single NVIDIA RTX A6000
GPU.
Testing Phase. The inference complexity includes aligned projection, feature encoding, residual generation, and score computation:
Node Attribute Alignment: Same training, projection into d, dimeennnsoo space: Onddd.).
Embedding and residual computation: Multi-layer GCN encoding and residual compu- tation: O((mmd, + ndddd) + n(E 1)dx).
Hyper residual scoring: Distance computation to r pre-trained hyper residual centers: (wr 1)da).
Affinity-residual scoring: Same as training: O(nd(e - 1)da).
Therefore, the total inference complexity is:
Ondd, + E(md, + nd,d,) + n(( 1)d, + nT - 1)d, + ndd(f - 1)da
(16)
In our experiments, DR-GGAD completes inference on each target-domain graph in approximately 0.35 seconds on RTX A6000 without any fine-tuning.
To further evaluate the computational feasibility of DR-GGAD, we compare its computational cost and detection performance against representative GGAD baselines, shown Table 6 The key findings are follows:
1. Training Time and Memory: DR-GGAD requires more training time and memory than ARC (46.06s vs. 10.26s; 35.58GB vs. 888GG)) but the additional cost is justified by improved performance, while achieving the highest average AUROC (84.83), particularly excelling in high AnD domains like Facebook and Amazon.
2. GPU Memory Usage: UNPrompt and AnomalyGFM use more GPU memory (46.45GB and 47.42GB, respectively) compared to DR-GGAD (35,58GB), with DR-GGAD outper- forming both methods.
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Table Comparison computational cost and detection performance across representative GGAD methods. Average AUROC(%) is com- puted as the mean across target datasets.
Metric
UNPrompt
AnomalyGFM
ARC
Our
Training Time(s)
9.62
299.19
10.26
46.06
Inference Time(s)
76.32
0.58
0.26
0.35
GPU Memory(GB)
46.45
47.42
8.18
35.58
Average AUROC(%) (%)
56.07
53.28
78.77
84.83
3. Inference Speed:
DR-GGAD maintains competitive inference speed (0.35s vs. 0.26s for ARC), ensuring efficient testing despite higher training costs.
4. Future Optimizations: Future optimizations, like parallel computing, can further enhance both training and inference speed.
In conclusion, DR-GGAD offers practical and efficient solution with significant performance gains, making it worthwhile trade-off in cross-domann anomaly detection.
C DESCRIPTION OF DATASETS
Following the experimental protocol of ARC Liu et al. 2024), Tang al. (2023). we benchmark DR-GGAD on a suite of twelve graph datasets, organised into four domain specific categories:
Citation Networks: Injected Anomalies
Social Networks: Injected Anomalies
Social Networks: Real-World Anomalies
Co-Review Networks: Real-Worle Anomalies
Within each category, the largest graph is designated the source dataset for training, while the remaining graphs serve as target datasets for testing. This trii--n-larrget,, test-on-rest paradigm imposes stringent evaluation of DR-GGAD's cross-graph generalisation capacity. Table 7 sum- marises the principal statistics all datasets. Spanning diverse application domains, the collection comprises both synthetic and naturally occurring anomalies, thereby exposing DR-GGAD to broad spectrum of abnormal patterns during evaluation-an an essential prerequisite for assessing robustness on unseen graphs. Detailed dataset descriptions are provided as follows:
Cora, CiteSeer, PubMed Sen et al. (2008), and ACM Tang et al. 2008 are four represen- tative citation network datasets, where nodes denote academic papers and edges represent citation links, covering diverse domains such computer science and biomedicine. Node features are constructed using bag-of- oo-words representations derived from textual content, and the structural and semantic variations across datasets facilitate comprehensive evalu- ation of model's cross-domain generalization capability.
BlogCogalog and Flickr Ding et al. (2019): Tang Liu (2009) are representative social network datasets, where nodes represent users and edges represent their social connec- tions. Node features are derived from aser-generated content such as blog texts or image tags, offering rich semantics and structural diversity for evaluating model performance complex graphs.
Amazon and YelpChi Rayana Akoglu (2015): McAuley Leskovec (2013) are graph- structured datasets built upon user review behaviors, primarily used for detecting deceptive activities and opinion spam. Amazon focuses on uncovering users involved in review ma- nipulation through shared product interactions, while YelpChi targets suspicious reviews that distort business reputations. In this work, we utilize two specific graph constructions: Amazon UPU, where users are linked via co-reviewed products, and YelpChi- RUD, where edges connect reviews authored by the same user, enabling the detection of subtle and coordinated anomalies.
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Facebook Xu et al. (2022) and Reddit Kumar et al. (2019) originate from real-world social networks and online community platforms, respectively. In the Facebook dataset, nodes represent users and edges denote friendship connections, reflecting localized community structures in human social graphs. Reddit models posts as nodes connected via user in- teractions, with node attributes derived from textual content; posts associated with banned users are labeled as anomalies for detecting malicious or disruptive behavior.
Weibo Kumar al. (2019) a dataset derived from the Weibo platform, which modeled as heterogeneous graph consisting of users and their associated hashtags. It focuses on detecting abnormal behavior characterized by high-frequency posting within short time windows. Node features incorporate geolocation data and bag-of-words representations, enabling the identification of suspicious users based on both behavioral and textual patterns.
Questions Platonov et al. 20233 dataset is collected from the Yandex Q platform, repre- sents users as nodes, and encodes question-ansee answer interactions within a one-year window edges. Node features computed by averaging FastText embeddings of user descrip- tions, with an additional binary indicator for missing descriptions, enabling effective mod- eling of semantic relations and interaction behaviors among users.
Anomaly Injection. For datasets with injected anomalies, follow the strategies introduced in Ding et al. (2019);]]] Liu et al. 2021 to generate both structural and attribute anomalies. Structural anomalies are created by injecting small cliques, each consisting of fully connected nodes labeled as anomalies. A total of x q such nodes are generated per dataset, with 15 fixed and q set to 10, 15, 20, 5, 5, and 20 for BlogCatalog, Flickr, ACM, Cora, Citeseer, and PubMed, respectively. Attribute anomalies are injected following the method in [Song et al. (2007). For each target node V/ we randomly sample = 50 nodes from the graph and identify the one with the largest feature deviation from Us denoted ety. The feature of vj is then assigned to v4 i.e.. X2 +- Xj, forming camouflaged anomaly. The number attribute anomalies is kept equal to that structural anoma- lies for consistency.
Table 7: The statistics of datasets.
Dataset
Train
Test
#Nodes
#Edges
#Features
Avg. Degree
#Anomaly
%Anomaly
Citation network with injected anomalies
Cora
2,708
5,429
1,433
3.90
5.53
CiteSeer
3,327
4,732
3,703
2.77
150
4.50
ACM
v
16,484
71,980
8,337
8.73
597
3.62
PubMed
19,717
44,338
500
4.50
600
3.04
Social network with injected anomalies
BlogCatalog Flickr
5,196
171,743
8,189
66.
300
5.77
7,575
239,738
12,047
63.30
450
5,94
Social network with real anomalies
Facebook
1,081
55,104
576
50.97
25
2.31
Weibo
8,405
407,963
400
48.53
868
10.30
Reddit
10,984
168,016
64
15.30
366
3.33
Questions
48,921
153,540
301
3.13
1,460
2.98
Co-review network with real anomalies
Amazon
10,244
175,608
25
17.18
693
6.76
YelpChi
/
23,831
49,315
32
2.07
1,217
5.10
D DESCRIPTION OF BASELINES
To ensure a fair and comprehensive evaluation of DR-GGAD, we compare it against sixteen rep- resentative baseline methods, covering three learning paradigms: supervised, unsupervised, and GGAD approaches. These categories represent common methodological frameworks in graph anomaly detection and include several state-of-the-ar (SOTA) models, providing a broad basis for performance comparison under different assumptions and settings.
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D.1
SUPERVISED METHODS:
GCN Kipf Welling (2016) is a neural network that extends convolution operations to graph-structured data and enables efficient feature aggregation from nodes and their neigh- bors.
GAT Veličković et al. (017) is graph neural network that introduces an attention mech- anism to assign different weights to neighboring nodes, enabling more flexible feature ag- gregation.
BGNN Ivanov & Prokhorenkova (2021) is novel end-to-end architecture, integrates Gra- dient Boosted Decision Trees (GBDT) with Graph Neural Networks to handle graph- structured data with node features, significantly improving performance on node prediction tasks.
BWGNN Tang et al. (022 leverages spectrally and spatially localized band-pass pasddppsssss filters; the model mitigates the right-shift phenomenon caused by anomalies, thereby enhancing its ability to identify and detect anomalous nodes.
GHRN Gao et (2023) mitigates the heterogeneity problem in graph anomaly detection by precisely pruning inter-class edges through the capture of high-freet frequency signals in the graph.
D.2 UNSUPERVISED METHODS:
DOMINANT Ding et al, 2019) combines graph convolutional networks with deep au- toencoders to jointly reconstruct graph structure and node attribute information, effectively enabling the detection of anomalous nodes in attributed networks.
CoLA Liu et al. 202 performs anomaly scoring by sampling contrastive instance pairs between nodes and their neighborhood substructures, combined with GNN encoding and anomaly-aware consistency evaluation.
HCM-A Huang al. (2022) formulates hop count prediction self-supervised task, integrates local and global information, and performs anomaly scoring based on prediction error and uncertainty.
TAM Qiao Pang (2023) enhances anomaly detection and homophily modeling by lever- aging local affinity scoring and truncated graph optimization to mitigate the interference of heterophilous edges.
CAGAD Xiao et al. (2024) method that combines counterfactual data augmentation with graph pointer network identify potential anomalies and construct abnormal neighbor- hoods, thereby generating more distinguishable node representations.
Semi-GGAD Qiao et al. (0244) cemi-supervised anomaly detection method that gen- erates pscudo-anomalour nodes with prior abnormal characteristics and leverages a small set of normal nodes train one-class classifier.
SmoothGNN Dong et (2055) leverages the unsmoothable nature of anomaly nodes to build multi-level modeling framework and anomaly scoring strategy, effectively distin- guishing anomaly nodes from normal ones.
GCTAM Zhang et al. (2025) adopts an anomaly truncation method that integrates con- textual mechanisms with global affinity, effectively overcoming the misjudgment issues caused by fixed-threshold truncation in traditional methods.
D.3 GGAD METHODS:
UNPrompt Niu et al. (0255) proposes a zero-shot graph anomaly detection method based on neighborhood prompts, achieving cross- cross-graphe graph generalization with single model through attribute predictability and cross-graph alignment.
AnomalyGFM Qiao et al. (2025) introduces a foundation model for graph anomaly de- tection, which aligns residuals with prototypes through pre-training to enable cross-graph generalization under zero-shot and few-shot settings.
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ARC Liu et al. (2024) is the first generalist graph anomaly detection method that supports few-shot inference, achieving cross grash generalization without retraining through feature alignment, residual encoding, and context-aware scoring modules.
E DETAILS OF IMPLEMENTATION
E.I HYPER- SYPEE-PPRRAMTERS
We present the key hyperparameter settings of DR-GGAD, selected ensure stable training and robust cross-domain generalization. The configurations below summarize the specific values used our experiments.
Hidden layer dimension: {64, 128, 265, 512, 1024]
Number layer of Graph Encoder: {1, 3,
Dropout rate: {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)
Learning rate: floats between 10 and 10-2
Weight decay floats between 10 and 10
Number of hyper residual center T: {2, 4, 6, 8, 12, 16, 20)
E.2 EVALUATION METRICS
We evaluate model performance using two widely adopted metries: Area Under the Receiver Operat- ing Characteristic Curve (AUROC) and Area Under the Precision-Recal Curve (AUPRC), AUROC reflects the model's overall discriminative capability, while AUPRC particularly informative un- der class imbalance. Higher values indicate better performance. All results are reported as the mean and standard deviation over five independent runs.
E.3 EXPERIMENTAL ENVIRONMENT
All experiments were executed on Linux server configured with Ubuntu 20.04. The system was powered by 13th Gen Intel(R) Core(TM) 17-12700 CPU, 64GB RAM, and NVIDIA GeForce RTX A6000 GPU with 48GB of memory. The software environment was managed using Ana- conda3, with PyCharm as development interface. Experiments were conducted under Python 3.8.14. CUDA 11.7, and PyTorch 2.0.1 Paszke et al. (2019).
E.4 MULTI-GRAPHI TRAINING PIPELINE
To ensure that the model learns residual patterns that generalize across source graphs, we adopt a coordinated multi-graph training pipeline. First, all source-domain graphs projected into uni- fied feature space using PCA, which provides consistent input dimensionality and reduces dataset- specific noise. During training, graphs processed sequentially within each epoch: for every source graph, the model performs an independent forward pass, computes the residual-based loss, and executes one optimizer update. As result, an epoch contains multiple updates-ead driven by a different graph domain.
This alternating optimization strategy prevents the model from overfitting to any single graph and gradually guides the parameters toward a Nomain--nvariann region that is compatible with diverse structural and attribute distributions. Through repeated cross-domain updates, both the encoder and the residual modules learn residual deviation patterns that are stable across datasets, forming the basis for reliable zero-shot anomaly detection on unseen graphs.
F SUPPLEMENTARY EXPERIMENTS
F.1 FUSION WEIGHT ANALYSIS
We conduct a systematic evaluation of the fusion weight À E [0.01, 0.99] to investigate the col- laborative effect between the proposed Hyper Residual (HR) and Affinity (AR) modules
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(a) AUROC acEOss
(0) AUFRC pcross
0.7
Facebook
StopCotalog
Reddi:
Figure 4: AUROC and AUPRC scores under different values of A.
Table 8: Anomaly detection performance (AUPRC, %, mean + std). "Rank" is the average rank over eight targets; The best, second, and third results are colored first, second, and third, respectively. Results tagged "* reproduced with the authors' code and default configures; all others are copied from ARC's Liu et al. (2024) bader--oard.
Method
Facebook
ACM
Amazon
Cora
CheSeer
Reddit
Weibo
BlogCatalog
Rank
GAD Metheds
GCN(2017)
1.59.0.11
5.27=1112
6.9611204
7.411:555
6.4011140
3.3910.39
11.22
7,4411007
11.75
GATY2018)
1.70-0055
15.74117.85
6.491084
5,5810.62
3.7310.51
DOMINANT/2019)
2.5-0006
15.5412269
6.11::029
12.75:071
13.8512.34
3.4910.44
81,47:0,32
35:22:0087
6.50
2C1N)(2021)
181-2.12
1.38-1.33
7.51+00.8
490++1.27
3.1++1.0
3.52+0.50
30.26+29 9M
5.75+1.47
12,88
20G2
2.54-063
1.14-0200
13:12+11.2
1,25+0300
6.35+0.73
3.69+0881
12.13+0.71
8.99+1.12 1,12
11.00
GHRN(2023)
2.4100622
5.61=031
7.54+2.01
9.56::2.40
7.79::2.01
3.24
28.53+77.38
10.9422..56
10.63
CaLA(2021)
1.31
11.0614445
HCM-A(2022)
0.08-0.00
1.0110611
5.87.00077
5,78.10.76
4,1810.75
3.1810023
2191111178
6.8910.34
14,63
TAM(2023)
8.40-097
23.20:12.36
10,7511.00
11.18:10755
11.5510.44
3.94110.13
16.46.10009
10.57
7.25
CAGAAD(2024)
161-077
7.97-467
7.49+0.73
5.11+3.20
385+1160
13.56+18911
2095+18.34
6,40+-3.066
11.88
Semi GGAD(2024)
1.4
9.72-2.18
7.37.0..6
4.6510.50
3,7210,30
4.2510.21
$2.4214.13
22.9516.54
10.00
Smmvk6GNN/20255
17.35
7.2311.96
5.611.71
3.4010.24
28.81200688
GCTAM(3025)*
9.61-096
08.09:0
13.71:0.11
9,52:0069
10.2920.78
4.3420.17
16887:1.1
27.7::0.54
GGAD Methools
UNPrompit 2015y"
261-045
10:45+1.55
10,277704
6,02+00300
4.4+00322
5.154665
1866+4431
24.89+3
9.25
AnomaycFPMr20255
5.48-343
5.410009
11.0243.59
8.65+1006
7,11#0.77
5.0400399
37.15#16.41
10.44+3.38
ARC12024)
8.38-2.39
44.25%7.41
45.77
64.1840.55
Our 16.77:1136
51.4511.04
61.37:6334
58.1811.70
63.5412.13
533310.4
70.0610..55
36.56::0.2
1.25
across diverse graph domains, As a key hyperparameter, À controls the balance between HRS and ARS, thereby directly influencing the model's 's capacity to address the Anomaly non- Discriminattivtty (AnD) problem in both feature and structure spaces.
Empirical results from AUROC and AUPRC scores reveal a consistent unimodal trend across datasets, with peak performance often concentrated along the diagonal, as shown in Figure 4 This indicates a strong alignment between the optimal and the intrinsic structure-featue of each graph. Specifically, graphs with strong structural homophily (e.g.. Facebook, Cora) favor smaller values (A < 0.3), where AR effectively captures local affinity residuals. In contrast, graphs characterized by citibbute-riiven or cross doos-dd heterogeneity (e.g., Amazon, Weibo) benefit from larger values (A E [0.6, 0.9),, which amplify the generalization capacity of HR in capturing trans- ferable feature residuals. These results highlight the necessity of adaptive À scheduling align with the structural or attribute dominance of the input graph, enabling optimal synergy between HRS and ARS for robust cross-domain anomaly detection.
F.2 PERFORMANCE COMPARISON OF AUPRC
As shown in Table our method achieves the highest average AUPRC across all eight target graphs, consistently outperforming all baselines. Compared to the strongest existing GGAD method, ARC, approach yields substantial improvements feature-structure entanglement such as Facebook (+8.39%), and Amazon (+17.12%) demonstrat- ing superior diseriminative capability under challenging anomaly non-separability. Traditional
all datasets, especially domains with severe
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pervised models (e.g., GCN, GAT, BGNN exhibit limited generalization due to their reliance domain-specific labels. Even recent variants like CAGAD and GHRN show significant performance variance under structural shifts. Among unsupervised baselines, methods such DOMINANT and GCTAM perform well on selected datasets but degrade under noisy features or heterogeneous struc- tures. ARC performs competitively on graphs like Cora and CiteSeer, benefiting from residual con- textual modeling, but suffers on structurally diverse graphs such as Reddit and Amazon. In contrast, our method integrates the strengths of the HR and AR modules: HR promotes transferable feature residual encoding, while AR enforces local structural alignment, resulting in more robust and adap- tive anomaly detection. Moreover, our approach maintains low variance across datasets, indicating strong stability even on complex graphs like BlogCatalog and Weibo, and further substantiating the robustness of our framework under diverse anomaly distributions and graph structures.
62-
32
-0- Zora
-0 Olesser
<di Bf Bryyatall
-0-
ACN
Tacebooc
Seddt Amazin
16
Figure 5: Sensitivity analysis of
F.3 SENSITIVITY ANALYSIS OF HR CENTERS
As illustrated in Figure BRAGGA exhibits clear and consistent sensitivity pattern with respect to the number of residual centers т. When increases from 1 to around 4-6, most datasets show a noticeable AUROC improvement, suggesting that normal nodes indeed occupy multiple residual modes and that a small set of prototypes is sufficient to characterize their multi-scale variation. Beyond this range, however, the performance quickly stabilizes: for r 2 8, all curves enter a plateau with fluctuations generally below 0.5%, indicating that the residual structure is already well captured and additional centers only over-segment existing clusters without introducing new information. This stability across eight diverse graphs demonstrates the robustness of the prototype mechanism and supports our choice of T = 4, which provides strong performance while avoiding unnecessary redundancy and computational overhead.
F.4 ABLATION VISUALIZATION
To validate the contribution of different modules to anomaly detection performance, conducted ablation experiments with histogram visualizations on the ACM and Weibo datasets, comparing the anomaly score distributions of the AR module, HR module, and the complete DR-GGAD model. The results show that AR and HR modules have complementary advantages in detecting different types of anomalies, as shown in Figures to II (1) On the ACM dataset, the AR module effectively distinguishes between normal and anomalous nodes, with a small overlap area of 0.0490, demon- strating strong structural anomaly detection capability. In contrast, the HR module shows weaker discrimination, with an overlap area of 0.6016. When combined, the complete model reduces the overlap area further to 0.0287, significantly enhancing anomaly separability and showcasing the performance improvement from module synergy. (2) On the Weibo dataset, due to more complex features, the AR module performs significantly worse (overlap area of 0.6283), and the HR mod- ule also struggles to distinguish normal from anomalous nodes (overlap area of 0.2803). However, the complete model reduces the overlap area to 0.2124, demonstrating that dual-residual modeling can still effectively restore good anomaly separability even in complex scenarios. In summary, the AR and HR modules each excel at detecting structural and feature- anomalies, respectively. Their collaboration significantly reduces the overlap between normal and anomalous nodes, allevi-
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ating the Anomaly non- non- Discrmminaaaiiity (AnD) problem and improving the model's cross- domain generalization ability.
Figure 6: AR
Figure 7: ACM HR
Figure 8: ACM Full
Figure 9: Weibo AR
Figure 10: Weibo HR
Figure 11: Weibo Full
These findings confirm that multi-layer residuals provide complementary structural and semantic signals, and the concatenation strategy significantly improves anomaly detection performance.
Table 9: Comparison of K- MeMas and Spectral Clustering with AUROC.
Method
Facebook
ACM
Amazon
Cora
CiteSeer
Reddit
Weibo
BlogCatalog
Time(s)
K-means
50.06
72.77
57.75
57.71
55.44
41.85
93.90
72.81
Our (Spectral Clustering)
82.53
91.11
88.14
93.14
95.06
60.59
93.25
74.08
1239.0
(K-means)
82.16
91.17
88.15
93.20
95.00
60.60
93.31
75.06
5.36
F.5 COMPARISON OF K-MEANS AND SPECTRAL CLUSTERING FOR HR CENTER CONSTRUCTION
To compare the performance of K-means and Spectral Clustering in constructing Hyper Residual (HR) centers, we conducted an in-depth analysis of their differences in terms of performance, com- putational feasibility, and scalability.
K-means directly minimizes the Fuclidean distance in the residual feature space, making it distance-driven clustering method. On the other hand, Spectral Clustering requires constructing the graph Laplacian and performing cigen-decomposition to map the nodes into the spectral space before applying K-means. It emphasizes structural information but comes with higher computational costs.
Method Difference:
Experimental Results: As shown in Table D. both K-means and Spectral Clustering achieve nearly identical performance in the HR module. The differences in AUROC are minimal (e.g.. Cora: 93.20 vs. 93.14 ACM: 91.17 vs. 91.11), indicating that both methods capture the same dominant normal modes in the multi-scale residual space.
Computational Cost: Spectral Clustering requires dioopoieconooiitionn of the n Laplacian matrix, which has a computational complexity of O(n'), resulting in much higher running time than K-means. In our experiments, spectral clustering took 1239 seconds, while K-means took only 5.36 seconds. Moreover, as the graph size increases, the stability of spectral clustering declines, mak- ing unsuitable for large-scale or cross-domain scenarios. Despite similar performance, Spectral Clustering is computationally expensive and lacks scalability for large- scale datasets. Therefore, K- means is preferred due to its stability, efficiency, and practicality in constructing the Hyper Residual centers.
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G DISCUSSION
G.1 ANALYSIS OF AnD Vs. MMD IN ANOMALY DETECTION
To investigate the relationship between class overlap and anomaly detection performance, we compare our proposed Anomaly non-Discriminativity (AnD) with Maximum Mean Discrepancy (MMD). While both metrics measure distributional differences, they capture distinct aspects of the embedding space. AnD quantifies the class-conditional overlap between normal and anomalous nodes, reflecting the difficulty of distinguishing these two classes within a single embedding space. In contrast, MMD measures the global distribution shift between two sets of embeddings, but it does not directly capture class separability.
Empirically, we analyze Inter-domain MMD, Intra-domain MMD, and AnD" across eight datasets, correlating them with AUROC (Table [T). Inter-domain MMD measures the distribution shift be- tween different domains (source and target domains), while Intra-domain MMD measures the dis- tribution shift within the same domain, specifically between normal and anomalous nodes. AnD* shows the highest Pearson correlation with AUROC (0.7508), far surpassing MMD, which has only moderate or weak correlation. For example, the Amazon dataset. Intra-domain MMD is high, but AUROC is low, with MMD failing to capture this discrepancy. However, AnD* reaches 0.5163, accurately reflecting the class overlap and aligning with the observed performance decline.
global distribution shift and class separability. Since anomaly detection performance is driven by separability, AnD provides a more robust and consistent indicator.
These results highlight that MMD and AnD measure orthogonal concepts:
Table 10: Comparison of distribution-shift metrics and the correlation with AUROC.
Dutuset
Cora
CiteSeer
ACM
BlogCatalog
Facehook
Weibo
Reddit
Amazon
Correlation
Inter-domain MMD
0.8545
1.0002
0.5933
0.5421
0.8077
0.9478
0,5189
0.3416
-0.7246
Intra-domain MMD
0.0115
0.0092
0.0454
0.1911
0.0382
0.1362
0.0002
0.1758
-0,3302
AnD
0.5190
0,5294
0.4159
0.4408
0.5272
0.2745
0,5964
0.5163
0.7508
AUROC
59.64
60.27
60.49
58.91
$5.68
70.56
42.02
45.49
G.2 DISCUSSION OF CLUSTERING-BASED METHOD
Clustering- based methods usually enhance anomaly detection by leveraging two core strategies: strengthening intra-cluster compactness while expanding inter-cluster separation, and aligning fea- ture or cluster distributions to discriminate anomalous instances from normal ones better Aytekin ctt al.] (2018). Kulatilleke et al. (2025), (Shnn et al. (2023). For instance, CARE Zheng et al. (2025) integrates soft membership assignments into the adjacency matrix and uses contrastive learning to capture affinities among nodes. Similarly, discDC Cai et al.] (2025) explicitly optimizes intra- and inter-cluster separability to enhance deep clustering performance, ensuring compact within- cluster structure and clear separation between clusters. ClusterQ Gao et al. (2022) focuses on feature-distribution alignment, addressing the issue of model quantisation without access to orig- inal data. By clustering the generated data and aligning its feature distribution to mimic real data, ClusterQ improves the inter-class separability and maintains high-quality anomaly detection even in data-limited scenarios.
DR-GGAD adopts Dual Residual Centering, introducing the innovative Hyper Residual (HR) center and Affinity Residual (AR) module. Unlike existing methods such as CARE and discDC, we opti- mize the compactness and separability of the source domain's clustering, performing optimization in both the feature and structural spaces during training. This approach overcomes the performance degradation caused by feature overlap and structural changes in traditional methods, while simulta- neously improving the robustness of cross rross-domain transfer. Additionally, our method eliminates the need for labels in the target domain and avoids the necessity for re-clustering, further minimizing the dependency on the target domain.
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Published as a conference paper at ICLR 2026
G.3 ANALYSIS OF AR MODULE'S EFFECTIVENESS
To explore the effectiveness of the AR module in revealing structural anomalies, conducted experimental validation.
The AR module works by measuring the consistency of node residuals with respect to their neighborhood structure. Normal nodes typically maintain stable residual directional consistency, while structural anomalies cause significant changes in the residual direction. AR pri- marily focuses on:
Design Motivation:
Neighborhood Structure Consistency: The alignment of a node's residual with its neigh- bors.
Topological Deviation: Deviations caused by irregular neighborhood connections or struc- tural anomalies that deviate from normal patterns.
As such, AR is highly sensitive to anomalies caused by topological deviations, such as motif anoma- lies and anomalous crossccommunity edges.
Experimental Verification: We conducted structural anomaly injection experiments based on pre- vious work Ding al. 2019), Liu al. ) where fully connected small cliques (size p) were injected into anomalous nodes to simulate strong structural anomalies. As p increases, the strength of the structural anomaly increases, and the experimental results are shown in Table
Structural Perturbations: As the structural anomaly increases (from p = 2 to p = 6). AR's AUROC improves significantly, indicating that AR has monotonic response topo- logical anomalies.
Sensitivity to Topological Changes:
The improvements are most pronounced on datasets with relatively homogeneous structures, such Cora, CiteSeer, and ACM, showing that AR is particularly sensitive to topological perturbations.
Robustness Across Diverse Datasets: Even in datasets with high noise levels (such as Reddit and Weibo), AR still shows stable improvements, demonstrating its robustness in various topological conditions.
The experimental results show that Affinity Residual (AR) is highly responsive to structural anoma- lies, with its performance positively correlated with the intensity of the anomalies, especially when there are changes in the topological structure. AR's effectiveness in topology- based anomaly detec- tion has been validated, particularly when anomalies arise primarily from changes in graph structure rather than node attributes.
Table 11: Performance (AUROC) of AR with varying structural noise injection across different datasets.
Method
Facebook
ACM
Cora
CiteScer
Reddit
Weibo
BlogCatalog
Amazon
AR-Only
82,16
90.85
93.20
94.03
58.04
88.35
74.43
61.79
AR Structural noise (p = 2)
82.48
92.17
94.63
95.19
61.77
91.21
74.60
$9.03
AR Structural noise (p = 4)
83.28
93.88
94.58
95.93
68.10
92.47
74.76
57.33
Structural (p 83.62
94.11
95.32
96.51
69.84
92.86
75.42
57.15
H DECLARATION OF LLM USAGE
We used Large Language Models (LLMs) solely as auxiliary for polishing certain parts of the manuscript, including grammar correction and fluency improvement. LLMs had no role in the study conception, method design, experimental implementation, data analysis, generation of scientific conclusions. All technical content, results, and conclusions in the manuscript are the sole responsi- bility of the authors. The authors take full responsibility for all content in this manuscript.
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git, covering the model's core Published as a conference paper at ICLR 2026
I REPRODUCIBILITY STATEMENT
We believe that reproducibility is essential for validating our research. To ensure that our work can be reproduced, have made the following efforts:
Code Availability: The source code for the model and experiments is available at the http://gthuu..oomff//////////// components and main experiment flows.
GitHub repository:
Data Processing: A detailed description of the data processing steps, including data clean- ing, feature extraction, and transformation procedures, is included in the GitHub repository. This will help replicate the datasets used in our experiments.
Experiment Setup: The experimental setup, including hyperparameter configurations, training procedures, and evaluation protocols, is described in detail in both the main text and the appendix to ensure that the experiments can be faithfully reproduced.
By making these resources publicly available and providing comprehensive explanations, we aim to support reproducibility and enable other researchers validate and extend work.
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Reviews:
[{"review_id": "Rz3a9RrjSj", "reviewer": "Reviewer_ozsE", "summary": "The paper introduces $\\mathcal{A}n\\mathcal{D}$, a graph anomaly detection framework that leverages multi-scale residual representations derived from successive graph neural network layers to detect anomalous nodes and substructures. It constructs domain-invariant reference centers and measures affinity residuals between node embeddings and these references to identify deviations indicative of anomalies. The method aims to capture both feature-level and topological irregularities in graphs without relying on labeled anomalies or reconstruction losses.", "questions": "Please refer to Weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1.\tThe paper is easy to follow.\n2.\tThe performance seems improved a lot.\n3.\tThe statistical results are comprehensive.", "weaknesses": "1.\tIs the dimensionality of the visualized embeddings in Figure 1 directly set to 2? Since t-SNE projects data into a 2D space, the resulting distribution differs from the actual data distribution.\n2.\tThe authors should provide a discussion comparing $\\mathcal{A}n\\mathcal{D}$ with existing distribution-level metrics such as MMD. While MMD measures distributional distances, what advantages does $\\mathcal{A}n\\mathcal{D}$ offer?\n3.\tThe authors should clarify the technical differences between the proposed method and clustering-based approaches.\n4.\tThe paper claims that multi-scale residuals from successive GNN layers form a domain-invariant reference, but no theoretical justification or citation is provided to support this statement.\n5.\tThe authors state that the Affinity Residual component can reveal anomalies primarily hidden in the topology. However, no experimental evidence supports this claim. It is also recommended to compare with subgraph anomaly detection methods to substantiate this advantage.\n6.\tThe authors mention that no existing methods explicitly address representation overlap. However, representation overlap appears related to clustering operations that aim to increase inter-class separation, such as works [1], [2]. Please discuss how the proposed method differs from or improves upon those clustering-related works.\n7.\tThe paper lacks one-class classification baselines such as OCSVM. The authors claim their method remains effective across various unseen graphs. If the decision boundary tightly encloses the normal data, one-class models may also generalize well. Please include a comparison or discussion on this point.\n8.\tAn ablation study comparing the concatenation of residuals from all layers versus using only the final-layer residual is missing. The authors should explain why concatenation was chosen instead of alternative fusion strategies (e.g., addition or averaging).\n9.\tIt remains unclear how the proposed method extracts semantically meaningful embeddings without the guidance of a reconstruction or logits-based loss.\n10.\tWhy was K-Means chosen for center initialization instead of Spectral Clustering? Please include comparisons and also provide results using K-Means directly for anomaly detection.\n11.\tThe problem definition is unclear. Does the center construction step rely solely on normal data?\n12.\tWhat is the meaning of $\\epsilon$, and what value is used in the experiments?\n13.\tMore visual comparisons for the ablation studies should be presented to illustrate their effects intuitively.\n14.\tHow does the proposed method handle source data with inconsistent feature dimensions?\n15.\tThe dataset name in Figure 3 is inconsistent with that in the experimental table; please correct it.\n16.\tPlease analyze why the proposed method achieves lower AUPRC on the Reddit and Weibo datasets.\n17.\tThe manuscript contains multiple formatting issues. Please proofread carefully for consistency and correctness.\n\n**Reference:**\n\n [1] \"discDC: Unsupervised discriminative deep image clustering via confidence-driven self-labeling.\" Pattern Recognition (2025): 112382.\n\n[2] \"Towards feature distribution alignment and diversity enhancement for data-free quantization.\" 2022 IEEE International Conference on Data Mining (ICDM). IEEE, 2022.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WbyNvqnOWZ", "reviewer": "Reviewer_CXFF", "summary": "This work presents DR-GGAD, a generalist anomaly detection framework that introduces two residual modules for centre-based scoring. Specifically, the two residual modules focus on attribute and structural normality separately. A GAD statistic, Anomaly non-Discriminativity (AnD), is proposed to quantify the overlap between normal and anomalous representations, which serves as a measurable indicator of cross-domain separability. Experiments on eight benchmark datasets demonstrate the competitive performance of the proposed method for generalist graph anomaly detection.", "questions": "Please refer to my weaknesses", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper is well written and easy to follow.\n2. Clear visualisations are provided to enhance understanding.\n3. Theoretical analysis is presented to support the proposed Anomaly non-Discriminativity (AnD) score.", "weaknesses": "1. Centre-based scoring is used in this paper. However, deep hypersphere-based AD methods Deep SVDD (Ruff et al., 2018) and Deep SAD (Ruff et al., 2020) are not discussed. A discussion comparing the proposed scoring approach with these methods would be essential to highlight the differences and advantages.\n2. The paper mentions that cross-domain transfer often entangles anomalous and normal representations. Previous works such as COMMANDER (Ding et al., 2021) and ACT (Wang et al., 2023) have explored cross-domain evaluation, and discussing their relevance would help clarify this limitation. \n3. In Figure 3, the curve for BlogCatalog appears almost flat, suggesting that the synergy between the two residual terms may be limited in some cases. It would be good to provide more details on this.\n4. It would be helpful to elaborate on how the dominant factor for abnormality can be determined in practice for unseen graphs.\n5. Some datasets are from GAD Benchmark (Tang et al. 2023). Could the author provide some justifications on why they are selected over the rest?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3ragAeOC71", "reviewer": "Reviewer_cnZP", "summary": "This paper addresses the generalist graph anomaly detection (GGAD) problem. The authors quantify the anomaly-normal separability of different datasets by a new metric termed anomaly non-discriminativity. Based on this, a new GGAD method is introduced, with hyper residual and affinity residual modules for anomaly scoring. Experiments are conducted to show the effectiveness of the proposed method DR-GGAD.", "questions": "Please refer to the issues discussed in the Cons section above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The motivation of this paper (i.e., quantifying the discriminatively ability of cross-dataset GAD models) is interesting. It would be useful to measure the separability of different datasets in terms of graph anomaly detection.\n\n2. The performance of the proposed method is competitive compared to other baselines. \n\n3. The paper is well-written and easy to follow.", "weaknesses": "1. The motivation of designing HR and AR should be better clarified. It is not clear why these designs can help address the AnD bottleneck.\n\n2. In the \"node attribute alignment\" part, only a linear/random mapping is used here. In this case, how to ensure the semantic alignment of features across different datasets?\n\n3. No discussion is given about the running efficiency of the proposed method. More evidences, including complexity analysis and empirical efficiency comparison, are expected.\n\n4. In table 1, ARC is described as \"needs Few fine-tuning\". However, according to the paper I think ARC doesn't need fine-tuning (but requiring few-shot samples). It's better to fix this.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tQc28xMZyP", "reviewer": "Reviewer_XcC9", "summary": "This paper introduces a new evaluation metric, AnD, which analyzes anomaly scores by defining two types of residuals: the hyper-residual center and the affinity residual, corresponding to feature and structural aspects, respectively. The difference between these two residuals is used to compute the anomaly score. The proposed method is evaluated on eight datasets and achieves the best performance under a zero-shot setting.", "questions": "See above **Weakness**", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) This dual-center strategy effectively addresses the non-discriminative nature of anomalies by reducing residual overlap in both feature and structural spaces, thereby enabling robust zero-shot detection on unseen graphs.\n\n(2) They propose AnD to quantitatively measure representation overlap and visualize the dual residuals, making the paper well-motivated and conceptually clear.", "weaknesses": "(1) The hyperparameters in the clustering module have not been thoroughly investigated. How does the performance of DR-GGAD vary with different values of $\\tau$ and the number of clusters? The results seem to become stable once the number of prototypes exceeds 20. Please provide an explanation for why around 20 prototypes are appropriate for a two-class anomaly-detection setting across various datasets.\n\n(2) Since multiple graphs are used for training, the paper should clearly explain how the pre-trained model is optimized across these graphs. Please describe the detailed training pipeline, including how samples from different graphs are organized and how parameter updates are coordinated across them.\n\n(3) ARC, UNprompt, and AnomalyGFM employ supervised pre-training, whereas the proposed method appears to follow an unsupervised paradigm. To ensure a fair and transparent comparison, the main results table should explicitly indicate the differences in supervision settings among the compared methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)