Topological Anomaly Quantification for Semi-supervised Graph Anomaly Detection
Authors: Ting Guo
Yangrui Fan
Caixia Cui
Jiye Liang
Jiao Zhao
Da Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Graph neural network
graph anomaly detection
semi-supervised graph anomaly detection
Primary area: learning on graphs and other geometries & topologies

Abstract: Semi-supervised graph anomaly detection identifies nodes deviating from normal patterns using a limited set of labeled nodes. This paper specifically addresses the challenging scenario where only normal node labels are available. To address the challenge of anomaly scarcity in real-world graphs, generative-based methods synthesize anomalies by linear/non-linear interpolation or random noise perturbation. However, these methods lack a quantitative assessment of anomalies, hindering the reliability of the generated ones. To overcome this limitation, we propose a generative graph anomaly detection model based on topological anomaly quantification (TAQ-GAD). First, we design a topological anomaly quantification module (TAQ), which quantifies node abnormality through two topological metrics: The node boundary score (NBS) quantifies the boundaryness of a node by evaluating its connectivity to labeled normal neighbors. The node isolation score (NIS) assesses the structural isolation of a node by evaluating its connection strength to other nodes within the same category. This anomaly measurement module dynamically screens nodes with high anomaly scores as pseudo-anomaly nodes. Subsequently, the topological anomaly enhancement (TAE) module generates virtual anomaly center nodes and constructs their topological relationships with other nodes. Finally, the method integrates normal and pseudo-anomaly nodes on the enhanced graph for model training. Extensive experiments on benchmark datasets demonstrate TAQ-GAD’s superiority over state-of-the-art methods and effectively improve anomaly detection performance.

Published as a conference paper at ICLR 2026
TOPOLOGICAL ANOMALY QUANTIFICATION FOR SEMI-SUPERVID GRAPH ANOMALY DETECTION
Ting Guo', Yangrui Fan", Caixia Cui Jiye Liang" Jiao Zhao Da Wang
1 School of Computer Science and Technology, North University of China, Taiyuan, 030051, Shanxi, China
2 College of Computer Science and Technology, Taiyuan Normal University, Taiyuan, 030619, Shanxi, China
3 Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University. Taiyuan, 030006, Shanxi, China
E-mails: gt gtingenuc edu, en (Ting Guo);
1 yj sxu. edu, on (Jiye Liang, corresponding author)
ABSTRACT
Semi-supervised graph anomaly detection identifies nodes deviating from normal patterns using limited set of labeled nodes. This paper specifically addresses the challenging scenario where only normal node labels are available. To address the challenge of anomaly scarcity in real-world graphs, generative-basee methods synthesize anomalies by linear/non-lincat interpolation or random noise perturba- tion. However, these methods lack quantitative assessment of anomalies, hinder- ing the reliability of the generated ones. To overcome this limitation, we propose a generative graph anomaly detection model based on topological anomaly quantifi- cation (TAQ-GAD) First, we design topological anomaly quantification module (TAQ), which quantifies node abnormality through two topological metrics: The node boundary score (NBS) quantifies the boundaryness of node by evaluat- ing its connectivity to labeled normal neighbors. The node isolation score (NIS) assesses the structural isolation of a node by evaluating its connection strength to other nodes within the same category. This anomaly measurement module dynamically screens nodes with high anomaly scores sseudo-anomaly nodes. Subsequently, the topological anomaly enhancement (TAE) module generates vir- tual anomaly center nodes and constructs their topological relationships with other nodes. Finally, the method integrates normal and annmmly nodes on the enhanced graph for model training. Extensive experiments on benchmark datasets demonstrate TAQ-GAD's 's superiority over state-of-the oo-t-h--rtttttttooo methods and effectively improve anomaly detection performance.
INTRODUCTION
Graph anomaly detection (GAD) is technique that aims identify abnormal nodes in graphs that deviate from normal behavioral patterns Qiao et al. (2025); Tang et al. 2: Liang et al. (2024).
This technology is widely applied in critical domains such financial fraud detection Liu al. (2023), network intrusion prediction Wang et al.] (2023a), and failure prediction Li et al. 2022).
playing an important role in ensuring data security and improving system reliability. Despite signif- icant progress in unsupervised GAD methods Ma et al. (2025): Li et al. (202)); Dong et al. (2025); Lin et al. (2024), their lack of labeled guidance confines them to intrinsic graph information, thus introducing fundamental ambiguity in identifying true semantic anomalies. In contrast, the semi- supervised GAD framework leverages limited labeled data (including both normal and anomalous nodes, or only labeled normal nodes) offers more promising research direction. In vanilla semi- supervised GAD Ma et al. (2024): Chen et al. 2024); Liu et al. (2022a): : Huang et al. (2022a); Gao et al. (2023); Shi al. (2022), the availability of both labeled normal and anomalous node frames the problem as a binary classification task. However, obtaining reliable anomalous node labels is often impractical due their rarity and the high cost of annotation. The semi-supervised setting

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with only normal labeled nodes presents more challenging yet realistic scenario, better reflecting real-world constraints where labeled anomalies are searce or unavailable QQio et al. (2024). The key advantage of this paradigm lies in its ability to leverage easily attainable normal nodes liable anchors, shifting the objective from identifying global outliers to detecting deviations from learned normal profile. This transition not only markedly reduces the false positive rate and en- hances robustness against sophisticated camouflaged attacks, but also aligns well with the practical constraints of real world labeling costs. Therefore, this work focuses on this more challenging and practical setting, aiming to explore how limited normal prior knowledge can be utilized to achieve more reliable anomaly detection. In order to alleviate the problem of scarce labels, generative- based methods learn latent distribution features of normal data and synthesize diverse anomaly samples to augment training data, thereby effectively improving model detection performance.
Existing generative-based methods mainly fall into two categories: feature interpolation methods and noise perturbation methods Qiao et al. (2024). Feature interpolation methods enhance distribu- tion modeling and generalization by generating synthetic samples through linear/non-linee interpo- lation between node features [ernández et al. (2018); Zhou et al. (2024). However, the generated samples are often overly smooth, not only lacking the complexity of real anomalies and thus fail- ing to capture boundary cases effectively, but also introducing additional computational overhead. Noise perturbation methods construct anomaly samples by adding random noise to the labeled nor- mal nodes Cai et al. 22025); Chen et al.] (2024): Liu et al.] (2022a); Qiao et al. (2024). The core assumption underlying these methods is that anomalous samples exhibit significant deviations from the normal data distribution in either feature or structural space. Consequently, they typically simu- late anomalous patterns by artificially injecting random perturbations into the feature space or graph structure of normal nodes. Despite their contributions, both strategies face inherent limitations in ensuring the quality of generated anomalies. A fundamental issue lies in the lack of quantitative mechanism for assessing node anomaly degrees. The injected perturbations are largely stochastic and unguided, leading to generated pseudo-anomalous nodes that suffer from low representativeness and reliability. Consequently, these synthetic samples ultimately fail to simulate the complex and meaningful anomalous patterns observed in real-world scenarios.
Therefore, this paper proposes a topology-based pseudo-anomaly generation approach that selects by deeply mining graph structural information. Specifically, we de-
high-quality pseudo-anomale sign two metrics: node boundary score (NBS) and node isolation score (NIS). NBS quantifies the boundaryness of a node by evaluating its connectivity to labeled normal neighbors. The connec- tion density between anomalous nodes and normal nodes is substantially sparser than that observed among normal nodes themselves. The node isolation score (NIS) quantifies a node's isolation by measuring its connection strength to other nodes within the same category. We harness these com- bined metries to select nodes topologically akin to anomalies from labeled normal data, leveraging them as pseudo-anomalies to improve the model's discriminative capability. Additionally, we fur- ther adopt topological anomaly enhancement (TAH) module that dynamically generates virtual anomaly center points based on node prediction confidence and constructs their topological rela- tionships with other nodes. Finally, the method integrates normal nodes and pseudo-anomaly nodes on the enhanced graph structure for joint training to achieve more accurate anomaly detection. The main contributions of this paper are follows:
We propose TAQ-GAD, a generative GAD model based on topological anomaly quantifi- cation, effectively addressing the low quality of generative nodes.
We propose the node boundary score (NBS) and the node isolation score (NIS), two topo- logical metrics that characterize a node's 's anomaly degree from the perspectives of boundary proximity and structural isolation, respectively.
TAQ-GAD incorporates a TAE module that dynamically generates virtual anomaly center nodes and establishes their topological relationships with other nodes, significantly enhane- ing model anomaly identification performance.
Extensive experiments on several datasets demonstrate that TAQ-GAD outperforms state- of-the-art methods, confirming its effectiveness for GAD.
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2 RELATED WORK
2.1 GRAPH ANOMALY DETECTION
Unsupervised GAD. Unsupervised GAD methods detect anomalies by modeling the intrinsic struc- ture of graphs without labeled data Qiao & Pang (2023). Reconstruction--assee models are widely used e.g.. DOMINANT al. (2019) employs graph autoencoders, while AnomalyDAE Fan
et al. (2020) enhances reconstruction with attention. Contrastive methods are also prominent: CoLA
Liu et al. (2022b) compares nodes with local substructures, and GCCAD Chen et al. (2023) and ANEMONE Jin et al. [02I)) learn from positive-negativy pairs.
Semi-supervised GAD. Semi-supervised GAD leverages a limited amount of labeled data along with unlabeled nodes to improve detection performance. Existing methods can be categorized into two main paradigms: Semi-supervised GAD with labeled normals and anomalies, and semi- supervised GAD with labeled normals only. In the former category, methods exploit anomalies
both the feature and structural levels Ma et al. (2024); Liu et al. (2022a); Zhou et al. (2024); Tang
(022g):uanngg Huang et al. (022a)); Gao et al. (2023). On the feature side, CGenGA Ma et al. (2024) establishes design principles for denoising networks tailored to anomaly generation; gADAM Zhou
al. (2022):
al. (2024) augments training data via adaptive interpolation in the embedding space; and BWGN Tang et al. (2022) employs spectral filters to capture high- feeg-ffyyynccy anomaly signals. Structurally, AO-GNN Huang et al. (2022a) incorporates an AUC-oriented reinforcement learning module to optimize edge pruning policies; OffeteroGGHR [Ga et al. (2023) trims inter-class edges by em- phasizing high-frequency graph components to handle heterogeneity. In the latter category, where only normal labels are available, GGAD Qiao et al. (2024) proposes generative framework that constructs ppeudo-anomaln nodes to provide effective negative samples for training.
2.2 GENERATIVE GAD
To address the anomaly scarcity problem, generative-based methods synthesize pseudo-anomaly nodes to augment training sets. Based on synthesis strategies, existing methods are categorized into feature interpolation and noise perturbation approaches Qiao et al.) (2025). Feature interpolation methods generate synthetic nodes by mixing features from normal instances Zhao et al. (2021): Wu eet al. (2022). For example, GraphENS Park et al. (2022) introduced adaptive interpolation rates, and AuGAN Zhou et al. (023) uses feature interpolation to generate synthetic anomaly nodes, aug- menting training data for improved detection performance. Noise perturbation methods generate pseudo-anomaly nodes by injecting noiseChen et al. (2020). Representation permutation approaches include: DAGAD Liu et al. (202a)) employs the permutation and concatenates on the representa- tion learned from limited number of labeled instances generate the anomalous sample, thereby enriching the knowledge of anomalies captured in the training set, GGAD et al. (2024) aims to generate outlier nodes that assimilate anomaly nodes in both local structure and node representations by leveraging the two priors of anomaly nodes, including asymmetric local affinity and egocentric closeness, impose constraints the representations.
PRELIMINARIES
Semi-supervised GAD. We focus on semi-supervised GAD on graphs. Given an attributed graph g = (V. A, X) with N nodes, where A E N is non-negative adjacency matrix and X E Nxd represents the node feature matrix. In the sumi-supervised setting. we have access to a limited set of labeled normal nodes Vi C V, while the remaining nodes V. V V; remain unlabeled. The goal of semi-supervised GAD is to learn an anomaly scoring function f V + such that for any normal node and abnormal node v', we have f(v) < f(r'), thereby effectively distinguishing normal nodes from abnormal ones. Following semi-supervised GAD settings, our method leverages normal labels and graph topology to identify high-confidence pseudo-anomalies.
Graph neural networks. We employ graph neural networks (GNNs) to learn node representations by aggregating structural and attribute information Guo al. (202)) Liang et al. (2023). The layer- wise propagation is formalized as:
O = GNN (A, ((-1) w(o),
(1)
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NBS PIS
Scurh
node
node 2
GNN
node n
G
select 2-hop neighbors
node score
pseudo-anomat nodes generation
Norma Nodes
Unlabeled Nodes
NBS(
PIS(N)]
(2)
lod
0.B
0.1
low-iisk
0.2
0.7
goor
Nightisk
anomaly score
label flipping stretegy and topology enhancement
node risk estimation
pseudo- Jabel generolion
Pseudo anomaly Nodes
Anomaly /Normal High-risk Nodes
Anomaly/Normal Center Nodes
Figure 1: The overall framework of TAQ-GAD.
where ( X. and H E Nxx(() denotes node representations layer f. The final represen- tations (L) = (hi...., hv) with h, e IRd are used for downstream tasks.
4
OUR METHOD
In this section, we first explore the correlation between graph topological structure information and node anomaly properties. We introduce the topological anomaly quantification module (TAQ). The TAQ module precisely quantifies the degree of node anomaly using NBS and NIS metrics. Then, the topological anomaly enhancement module (TAE) is designed to generate virtual anomaly center nodes and construct their topological relationships with other nodes. Finally, we theoretically analyze the rationality and the effectiveness of the proposed anomaly measurement metrics. Figure 1 Iillustrates the overall framework of TAQ-GAD.
4.1 TOPOLOGICAL ANOMALY QUANTIFICATION MODULE
In this section, examine the relationship between graph topological structure and node anomaly properties. We introduce the TAQ module, which provides a precise quantification of node anomaly levels through the NBS and NIS metries. Subsequently, the TAE module is designed to generate virtual anomaly centers and construct their topological relationships with other nodes. We further present theoretical analysis demonstrating the validity of the proposed anomaly metrics and offer insights into the effectiveness of the TAQ-GAD. The overall architecture is illustrated in Figure
Let Vi represent the labeled normal node set. For node v; E Vi, we define the distance path( (e; 0y) as the shortest path length between nodes U; and Uy in graph G. We also construct the K K-hopp neighborhood e; as: (u; = (u, V path(v;, vt) < K}.
Definition 3.1. (Node boundary score, NBS). The node boundary score (NBS) of node ;; quan- tifies its proximity to the boundary of the normal region by measuring the proportion of labeled normal nodes among its neighbors:
NBS(w;) =1 (V(
(2)
[V(x;)
where | denotes the number of nodes in a set. A higher NBS value indicates that the node has fewer connections to the labeled normal class and is therefore more likely reside the decision boundary, suggesting a higher degree of anomalousness. This is illustrated in Figure 2 where node Y2 exhibits higher NBS value than U/ consistent with its sparser connections to normal nodes.
Definition 3.2. (Node isolation score, NIS). The node isolation score (NIS) of node v; quantifies its structural isolation within its category by measuring the mean shortest-path distance to other
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nodes sharing the same category label:
1
NIS( (a((v)
path 2z),
(3)
by (ox)
where where.Ng(vs) {u, E NN(;)) ye, = Ne, denotes the set of nodes within the K Khhop neighborhood of o that belong to the same category as v;- A higher NIS value indicates that the node more topologically isolated from other nodes in its category. As illustrated in Figure 2 node es exhibits a higher NIS value than Uj reflecting its weaker connections to other nodes of the same category, while v, maintains stronger topological associations with its peers. This suggests that U, has higher likelihood of being an anomaly compared to U/.
In the absence of genuine anomaly labels, we introduce the proxy isolation score (PIS), topology-basee metric designed to quantify node isolation. The PIS score is defined as:
MALN - 2/1 WRROO (N)())
1 [E((( +E
log(d, +e)
PIS( = =1 1
D+1
Mi8e] - WoGn) > Male]
(4)
NIS: node isolation soore
where di denotes the degree of node Vi. [E(((,))) is the number of edges among its neighbors, D is the maximum degree in the graph, > 0 a small constant to avoid divi- sion by zero, and is the Euler's number. This formulation integrates two complementary as- pects of topological sparsity: the first term captures the local clustering density, while the second term penalizes high-degree nodes to highlight structural sparsity. A higher PIS value indicates that the node has fewer neighbors and those neighbors are poorly interconnected, reflecting the "few and scattered" structural pattern characteristic of anomalous nodes. Although PIS is not mathematically equivalent to the supervised NIS metric, both capture the same underlying topological principle: anomalous nodes tend to be structurally isolated. Thus, in settings where anomaly labels are un- available, PIS serves as a robust and practical surrogate. Its ability to leverage purely local structural information makes it especially suitable for large-scale graph-based anomaly detection.
normal users
fraudulent users
NBS: node boundary score
Figure 2: NBS and NIS metrics for quantifying the degree of node anomaly. The ((vx) is defined as the 2-hop neighborhood of node e4.
Based on the Score(u:), we rank all labeled nodes and select the top 7-proportion highest-scoring nodes as pseudo-anomaly nodes for model training, where E (0, 1) is predefined ratio parameter.
Score(u;) = (BS + AePIS(t;).
(5)
where A and A2 are hyperparameters. After obtaining pseudo-anomalous nodes, we train the GNN model by integrating the remaining normal nodes and unlabeled nodes, subsequently generating prediction probability vectors for all nodes. NBS and NIS indicators are theoretically grounded in the structural characteristics of anomalous nodes in semi-supervised networks. We establish two key theoretical results that justify their effectiveness.
Theorem (NBS separability):: Under network homophily and labeling bias assumptions, anoma- lous nodes exhibit systematically higher NBS values than normal nodes, i.e., EE[BS((;;) A, > E[: Ni). Anomalous nodes at the network periphery have fewer labeled neighbors, so a higher proportion of their neighbors are unlabeled.
Theorem 2 (PIS anomaly indication): A high value of PIS (representing extreme topological isolation) significantly increases the posterior probability of node being anomalous, i.e., P(A; PIS(c;) 1) P(A.). This phenomenon arises from the topological isolation of anomalous nodes, which are more likely to lack direct connections to labeled normal nodes.
These theoretical insights demonstrate that NBS captures the boundary characteristics of nodes (through neighborhood labeling density), while PIS captures their topological isolation (through complete disconnection from normal label support). Together, they provide a principled approach to identify pseudo-and anomalous candidates from labeled normal nodes. The formal proofs, including detailed mathematical derivations and validity conditions, provided in Appendix
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4.2 TOPOLOGICAL ANOMALY ENHANCEMENT MODULE
The TAE module refines graph structure by strengthening connectivity between anomalous nodes and anomaly centroids, leading to improved anomaly detection performance. It operates in two stages: first, it estimates risk coefficients for nodes to derive pseudo-labels; then, it generates pseudo- class centroids based on the refined pseudo-labels and constructs topological relationships between the centroids and other nodes. By augmenting the graph with pseudo-labels and pscudo-anomal centroids, the TAE module reinforces the topological connections of anomalous nodes, thereby en- riching their informational context for more disceriile detection.
For node risk estimation, let P.. [pt. Pe. denote the predicted probability distribution of (1) (0) and Pe; representing the probabilities of belonging to the normal and anomalous
node vs, with pe, classes, respectively. Based on this probability, we derive the initial pseudo-labels for nodes. The
prediction uncertainty is quantified as: u(e;) = 1-11-mm m- Pi; where e indexes the class labels. This metric captures the model's confidence in its prediction for node U, with higher values indi- cating greater uncertainty. To mitigate selection bias arising from inter-class uncertainty disparities, we compute a risk score relative to the class-wise average uncertainty:
r(us) = max (0, u(v.) ūgg.) x Wig.
(6)
where ú; is the predicted class of U;, Tg. denotes the average uncertainty across nodes predicted as class hi. and Wgg is a class weight based on inverse frequency calculated the ratio of the smallest class size to the current class size. Wg. tends to assign higher importance to the minority (anomalous) class. A high risk score r(v:) indicates that the node's uncertainty substantially exceeds its class average, flagging it as potentially misclassified or ambiguous.
Subsequently, we leverage the graph's 'ss topological structure to compute the class distribution within each node's 's neighborhood posterior probability:
Ku, E (w,) : c3l [N(x:)]
po p
CE (0,
For high-risk nodes (where r(u:) 0), we implement a label flipping strategy: if the node's neighbors show high confidence in the opposite class (i.e., p post(1 1-))) >> p we flip the node's pseudo-label from its current prediction ÿi to the opposite class - St. This approach is based on the topological consistency principle. When neighbor information strongly supports the opposite class, it indicates the original prediction may be incorrect and should be corrected through label flipping. By applying label flipping strategy, we generated the refined pseudo-labels.
Based on the current labeled nodes, we compute class centroids for each category. The connection probability between node 2 and centroid e defined as:
P(us, Plus, vinual) r(v:) pe.
ve
peea(()) [I-I[ [1];=c) cc).
(8)
Through probabilistic sampling, we generate virtual edges between nodes and centroids, construct- ing an augmented graph gnew (ynew A new
X
4.3 TRAINING OBJECTIVE
To effectively leverage both the topological structure learning and pseudo-anomaly classification capabilities, we design a joint training objective that combines regularization loss and classification loss. The overall loss function is formulated as:
Listal = a Logg + B- Less
where a and 3 are hyperparameters that balance the contributions of regularization and classification losses. The purpose of the regularization loss Lreg = ||Z 1 is to prevent overfitting by penalizing the model for learning node embeddings Z with excessively large values, where Z represents the node embeddings learned by the encoder and || denotes the Frobenius norm. The classification loss is computed using a combination of the ground -tuth labels and the refined pseudo-labels: Cas- = BCE( (X)ew) Y Ynow), where BCH(.) is the binary cross-entropy loss function.

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Table I: Performance comparison of different GAD methods. We report GGAD and TAQ-GAD results under different label rates, with the highest scores bolded.
Datasel
Setting
Method
AUROC
AUPRC
Amazon
T-Pinance
Reddit
Elliptic
Photo
Amazon
T-Pinance
Reddit
Elliptic
Photo
DOMINANT
0.7025
0.6087
0,5105
0,2960
0.5136
0.1315
0.0536
0,0380
0.0454
0,1039
Unsupervised
Anomaly DAE
0,7783
0,5809
0,5091
0,4963
0,5069
0.1429
0.0491
0,0319
0,0872
0,0987
OCGNN
0,7165
0,4732
0.5246
0.2581
0.5307
0.1352
0.0392
0,0375
0.0616
0,0965
AEGIS
0.6059
0.6496
0.5349
0.4553
0.5516
0.1200
0.0622
0,0413
0.0827
0,0972
GAAN
0,6513
0.3091
0.5216
0.2590
0.4296
0.0852
0.0283
0.0348
0.0436
0.0767
TAM
0.8303
0.6175
0.6062
0.4039
0.5675
0.4024
0.0547
0.0437
0.0502
0.1013
DOMINANT
0.8867
0.6167
0.5194
0.3256
0.5314
0,7289
0.0542
0.0414
0.0652
0.1283
AnomalyDAE
0.9171
0.6027
0,5280
0,5409
0,5272
0.7748
0.0538
0.0362
0.0949
0.1177
OCGNN
0,8810
0,5742
0,5622
0.2881
0.6461
0.7538
0.0492
0.0400
0.0640
0.1501
ABGIS
0,7593
0.6728
0,5605
0,5132
0.5936
0,2616
0.0685
0.0441
0.0912
0,1110
Semi-supervied
GAAN
0.6531
0,3636
0,5349
0,2724
0,4355
0,0856
0.0324
0,0362
0.0611
0,0768
TAM
0.8405
0.5923
0.5829
0.4150
0,6013
0.5183
0.0551
0,0446
0,0552
0,1087
CHRN
0,9346
0,7581
0.5731
0.7315
0.6223
0.7865
0.0970
0,0500
0.2101
0,1420
SpaceGNN
0.8616
0.8326
0.5010
0.6245
0.6314
0,5674
0,1942
0.0329
0.1257
0.1744
GGAD
0.9443
0,8228
0.6354
0.7290
0.6476
0.7922
0.0610
0.2425
0.1420
TAQ-GAD
0.9474
0.8675
0.6682
0.7453
0.7107
0.7973
0.2255
0.0780
0.3573
0.2073
Table 2: Performance comparison on DGraph dataset. We report GGAD (G) and TAQ-GAD (T) results under different label rates, with the highest scores bolded.
Baseline Methods
GGAD (G) vs TAQ GAD (T)
Metric
Unsupervised
Semi-supervised
0.05%
0.2%
0.35%
0.5%
DOMINANT AnomalyDAE ABGIS DOMINANT AmemaayDAE ABGIS
0.5892
0.5943
G: 0.5902
0.5949
AUROC
0.5738
0.5763
0.4509
0.5K51
0.5866
0.4450
0.6327
0.6569
T: 0.6581
0.6623
G: 0.0080
G: 0.0082
G: 0,0080
0.0083
AUPRC
0.0075
0.0070
0.0053
0.0076
0.0071
0.0058
T: 0.0126
T: 0.0151
T: 0.0158
T: 0.0162
5
EXPERIMENTS
Dataset and baseline methods. We conduct experiments on six real-world graph datasets, including
Amazon Dou et al. 2020). T-Finance Tang et al. (2022), Reddit/Kumal et al. (2019). Elliptic Weber
(201)), Photo McAuley et al. 2015), and DGraph Huang et al. (202b)). More details about the datasets can be found in Appendix B We adopt the semi-supervised learning scenario from GGAD Qiao et al. 2024), where ratios of the normal nodes in the training set are randomly sampled as labeled data, and the remaining ones are kept unlabeled. All anomaly nodes remain unlabeled during training. The data split and label rates are strictly consistent with those used in GGAD. To comprehensively evaluate the performance of TAQ-GAD, we select several representative GAD methods (DOMINANT) Ding et al.] (2019), AnomalyDAE Fan al. (2020), TAM Qiao & Pang (2023). OCGNN Wang et al. (2021). AEGIS Ding et al. (2021), GAAN Chen et al. (2020). CHRN Gao et al. (2023), generative method GGAD Qiao al. (0024) as basclines. More details about the methods can be found in Appendix C
Evaluation metries. Our evaluation employs two standard metrics: AUROC and AUPRC/Chai al. (222)); Pang et al.] 22221;; Wang et al. (2023b). The AUROC score assesses the model's 's ability to distinguish between normal and anomalous instances overall. Given the inherent class imbalance in anomaly detection datasets, we also report AUPRC, which provides a more critical assessment of how well the model identifies true anomalies amidst the majority of normal nodes. For both metrics, the score ranges from 0 to 1, and a higher value signifies better detection performance.
Implementation details. We implement TAQ-GAD using PyTorch 1.10.0 and PyTorch Geometric within Python 3.8 environment. The Nv;);) is defined as the K K-hop neighborhood of node v;. In TAQ-GAD, K = 2 for all datasets. The model employs a consistent embedding dimension of 300 across all datasets and is trained with the Adam optimizer. We rank all labeled nodes and select the top proportiio of highest-scoring nodes as pseudo-anomaly nodes. A detailed analysis of key hyperparameters, including the pseudo-anoman selection threshold 7, the loss coefficients and ,
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Table 3: Ablation study results on different components of TAQ. We bold the highest scores.
Dataset
Component
AUROC
AUPRC
Amazon
T-Finance
Reddit
Bliipiic
DGraph
Amazon
I-Fmance
Reddit
Ellipic
Photo
DGraph
Baseline
0.7262
0.6055
0.3228
0.4198
0.5500
0.1595
0.0453
0,0448
0.0279
0.0889
0.0074
+NBS
0,8579
0.6931
0.6169
0.5022
0.7305
0.6047
0.6338
0.0540
0.0463
0.0368
0,2599
0.0157
+PIS
0,9033
0.7251
0.5754
0.6422
0.6114
0.5995
0.7277
0.1028
0,0422
0.0625
0.1386
0.0109
+NBS + PIS
0.9261
0.8261
0.6489
0.7159
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Psoudo anomaly rado
(a) Amazon
(b)
Reddit
(c)
Elippo
(d) T-fnance
Figure 3: Effect of T.
the normal node sampling ratio p. and the neighborhood hop count K, the \1 and X2 are provided in Section 5.3 and Appendix D The source code of TAQ-GAD has been available on GitHut
5.1 MAIN COMPARISON RESULTS
To evaluate the effectiveness of TAQ-GAD, we compare performance against multiple baseline methods across various datasets. Following the experimental setup of GGAD, we randomly sample 5% of the normal nodes as labeled normal data for training, where p E {10, 15, 20, 25, 30). The results of semi-supervised methods reported in the [ based on 15. Under this setting, our method outperforms all competing approaches.
To further validate the effectiiveness of our approach, compare TAQ-GAD with GGAD under different normal label rates across multiple datasets. At the p = 30, TAQ-GAD achieves significant performance improvements on several datasets. This performance advantage persists even as the label rate decreases. Under the p = 20, although GGAD demonstrates competitive performance on the T-Finance dataset (AUROC: 0.8560). TAQ-GAD still shows better comparable results other metrics and datasets. More importantly, under low-rate (15% and 10%), TAQ-GAD continues stably outperform GGAD. At the p 10, TAQ-GAD achieves higher AUROC scores on Ama- zon (0.9365 vs. 0.8796), T-Finance (0.8501 vs. 0.7252). Reddit (0.6367 vs. 0.6344), and Elliptic (0.7485 vs. 0.7301), while maintaining competitive AUPRC scores. Furthermore, on the challenging DGraph dataset with an extremely low anomaly rate (as shown in Table 2). TAQ-GAD consistently surpasses GGAD across all label rates (0.05% 0.5%). At the 0.5% label rate, TAQ-GAD achieves an AUROC of 0.6623 and AUPRC of 0.0162, compared to GGAD's 0.5940 and 0.0083, demon- strating its superior capability in detecting rare anomalies under class imbalance. The consistent superiority of TAQ-GAD over GGAD across varying label rates and diverse dataset characteristics validates the effectiveness of our topological quantification approach.
5.2 ABLATION STUDY
To evaluate the contribution of each component in TAQ-GAD, we conduct an ablation study com- paring the full model against several variants, with results summarized in Table First, we examine the impact of the topological quantification modules. Using only GCN as the baseline, we ob- serve that incorporating either the NBS or PIS module individually leads to notable improvements in both AUROC and AUPRC across most datasets. When both modules are combined (+NBS+PIS), performance is consistently and significantly enhanced over the single-module configurations, con- firming their complementary roles in capturing topological anomalies. Furthermore, the addition of the TAE module results in substantial gains across all datasets, achieving the highest scores in
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(b) Amazon AUPRC
(c) Reddit AUROC
(d) Reddit AUPRC
Figure 4: Effect of and B.
every case. This demonstrates that TAE plays critical role in strengthening anomaly connectivity through virtual anomaly centers, ultimately pushing the model to its optimal performance. More importantly the classification loss Lets serves as the primary objective, while the regularization loss Ligg constrains the node embeddings prevent overfitting by penalizing excessively large values. Empirical results confirm that Ley plays a critical role in the effectiveness of TAQ-GAD.
5.3 SENSITIVITY ANALYSIS
ratio (varied from 0.05 to 0.9) is shown in Figure 3 For Amazon, Elliptic, and T-Finance, performance peaks at T = 0.05 and declines with larger ratios, implying that excessive pseudo-anomalies introduce detrimental noise. This is particularly evident on the Elliptic dataset, where the AUROC exhibits sharp decline from 0.7 0.4 as 7 increases from 0.05 0.6, highlighting its pronounced susceptibility noise inter- ference. Conversely, Reddit's performance improves up to 0.5, indicating that its anomalous patterns require a broader pseudo-anomaly set for effective capture. Overall, a low of 0.05 generally optimal, with performance degrading due to noise higher values.
The effect of The sensitivity analysis of the
The effect a and B: evaluate the robust- ness of TAQ-GAD, we systematically vary the loss coefficients (ar, 3) from (0.1, 0.9) to (0.9, 0.1) across all datasets. The results, visualized in Figure 4 reveal a significant insensitivity to these hyperparameters. For instance, the Ama- zon dataset maintains robust performance under most weight combinations, indicating that our method does not require precise loss balancing achieve optimal results. Similarly, Reddit hibits minimal performance fluctuation.
D20 0OmB
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Figure 5: The effect of p.
The effect of p: As shown in Figure we evaluated TAQ-GAD with different proportions of labeled normal nodes {(10, 15, 20, 25, 30). The results demonstrate that our model maintains excellent anomaly detection performance across all p values. Notably, even with only & = 10, TAQ-GAD still outperforms all baseline methods. We believe this robust performance under limited supervision val- idates that our anomaly quantification module can reliably identify high-quality pseudo-anomalies. anomalies,, thereby enabling effective detection with minimal labeled data.
The effect of \ and Az: TAQ-GAD, A and X2 are hyperparameters for the NBS and PIS, respec- tively. NBS is assigned higher weight as it captures behavioral patterns in local neighborhoods. PIS evaluates the structural isolation of nodes by measuring their connection strength. Setting an ex- cessively high weight for PIS may introduce structural noise and interfere with the model's ability detect genuine anomalies. To validate the robustness of parameter configuration. we systematically conducted sensitivity analysis of λ and A across six datasets. As shown in Figure 6 experimen- tal results demonstrate that our model maintains stable performance across four datasets, showing particular insensitivity variations in A2 when > is fixed 1.
5.4 COMPARISON WITH NAÎVE PSEUDO-LABELING STRATEGIES
To validate the effectiveness of the pseudo-label generation module in our proposed method, we present detailed ablation study. TAQ-GAD is designed to select high-quality pseudo-anomalous

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Figure 6: The effect of X1 and X2
nodes based on topological properties, which are subsequently used to train a model for obtaining sample-level pseudo-labels. We compare TAQ-GAD against two naive baseline strategies:
(1) Random:
This baseline serves fundamental reference by randomly selecting a subset of nodes from the graph as pseudo- -eoumlanno samples, without leveraging any structural or semantic information. These randomly selected nodes are then used to train the TAE module.
(2) Low-degree: This baseline selects nodes with relatively low degrees as pseudo-anomalous sam- ples, based on the heuristic that anomalies often exhibit sparse connectivity or isolation from the majority of the graph. These low-degree nodes are subsequently used to train the TAE module.
Table 4: Performance comparison of different sampling strategies
Reddit
Photo
Amazon
AUROC
AUPRC
AUROC
AUPRC
0.0352
0,5953
Low dewreegree
0.5579
0.0480
0.6359
0.1346
0.9084
0.6940
TAQ-GAD
0.6682
0.0780
0.7107
0.2073
0,9474
0.7973
T T_finance
Elliptic
Dgraph
AUROC
AUPRC
AUROC
AUPRC
AUROC
AUPRC
Random
0,7483
0.0907
0.6946
0.2228
0.4287
0.0101
Low-degree
0.7565
0.1119
0.7266
0.3423
0.3766
0.0092
TAQ-GAD
0.8675
0.2255
0.7453
0.3573
0.6693
0.0178
Experiments are conducted across six standard benchmark datasets, with the results reported in Table shown in Table the proposed appoloyy-giides pseudo-label generation strategy (TAQ-GAD) significantly outperforms both baseline methods on the majority of datasets and evaluation metrics. For instance, on the Reddit dataset, TAQ-GAD improves AUROC by 22.8% and 19.8% over ran- dom selection and lew-degree selection, respectively. These results demonstrate that TAQ-GAD's pseudo-label generation can more accurately identify potential anomalous instances. Besides, the low-degree selection strategy outperforms random selection on certain datasets (e.g., Elliptic), indi- cating that simple structural features do carry some discriminative information regarding anomalies, its performance remains substantially lower than that of method. This validates that the compre- hensive topological quantification employed in our approach exhibits stronger discriminative power compared to relying solely on node degree.
CONCLUSION
We propose TAQ-GAD, a generative graph anomaly detection framework designed to tackle the challenge of limited anomaly labels by leveraging topological strueture analysis. The framework begins with a topological anomaly quantification module that employs two heuristic NBS and PIS metrics to identify high-quality pseudo-an useudo-anomalies. Building upon this, the framework incorporates a TAE module. Importantly, the TAE module does not simply memorize these heuristic scores. Instead, starting from the pseudo-anomalous samples selected by NBS and PIS, rectifies them through risk-based pseudo-label generation mechanism and a label-flipping strategy. This pro- cess creates virtual anomaly centers and strengthens the topological connections among anomalies, enabling the module to learn more fine-grained node representations. Extensive experiments on six benchmark datasets demonstrate the superiority of TAQ-GAD over existing methods in terms of AUROC and AUPRC, highlighting its effective anomaly detection capabilities. Future research will develop priors for complex topological patterns, design scalable augmentation techniques, and extend the framework dynamic graph anomaly detection with temporal modeling.
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ACKNOWLEDGE
This work was supported by the National Natural Science Foundation of China (62376141), the Natural Science Foundation of Shanxi Province, China (Grant No. 202403021222153), the Shanxi Provincial Key Laboratory (CICIP2024002), the Shanxi Higher Education Institutions Science and Technology Innovation Project (2024L164).
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Reviews:
[{"review_id": "bvA59cJhiK", "reviewer": "Reviewer_Ad2j", "summary": "The paper introduces TAQ-GAD, a semi-supervised graph anomaly detection framework that quantifies node abnormality using two topological metrics: Node Boundary Score (NBS) and Node Isolation Score (NIS). These metrics guide pseudo-anomaly selection, while the Topological Anomaly Enhancement (TAE) module refines them through risk-based label flipping and virtual anomaly centres. The paper achieve significant performance improvement on the selected datasets.", "questions": "Please refer to my weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The proposed method is fairly easy to follow.\n2. The framework plot is informative, making it easier to understand the overall workflow.\n3. The proposed methods achieved competitive performance on the selected dataset.", "weaknesses": "1. My understanding is that the proposed method mainly achieves performance gain through pseudo labelling. However, I didn’t find (at least the paper not specifically mentioned) any comparison with training SOTA supervised GAD methods on pseudo labels generated by naïve pseudo labelling strategies. This is essential for evaluating whether the proposed pseudo labelling methods are more effective.\n\n2. The authors mentioned unsupervised methods, “their heavy reliance on intrinsic graph structures to define anomalies introduces fundamental ambiguity, often failing to distinguish genuine semantic anomalies from rare yet normal patterns.” However, the proposed method leverages node degree and graph homophily. Why are these graph properties more robust for GAD?\n\n3. In Eq. 9 the regularisation term is similar to weight decay. Why are two balancing parameters required?\n\n4. The baseline selection, including unsupervised and semi-supervised baselines, adapts some well-known unsupervised methods for semi-supervised evaluation. However, how they are adapted for semi-supervised GAD is not clearly discussed. This is important for fair comparison. In addition, some results appear to be missing in Table 1. Also, most of the baselines are unsupervised methods; it would make the evaluation stronger if supervised and more semi-supervised methods were studied.\n\n5. In the related work section, the semi-supervised methods part mixes methods that use labelled anomalies and those that only use labelled normal training data. They should be discussed separately. Other than BWGNN, there are a lot more recent supervised methods that are not discussed. Also, recent generalist methods have shown promising cross-dataset performance. The relationship of the paper’s setting with those methods' should be discussed.\n\n6. In the references, there are quite a few papers that were listed as arXiv preprints but are actually published papers in well-regarded conferences and journals.", "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": "KrvpiUAGzP", "reviewer": "Reviewer_DW3F", "summary": "This paper tackles semi-supervised Graph Anomaly Detection (GAD) with only normal node labels. The proposed framework, TAQ-GAD, introduces two topological metrics—Node Boundary Score (NBS) and Proxy Isolation Score (PIS)—to identify pseudo-anomalies and assign pseudo-labels. A Topological Anomaly Enhancement (TAE) module further generates virtual anomaly centers and their topological relations, improving the quality of pseudo-anomaly generation.", "questions": "1. In Table 2, the ablation study reports results for “+NBS”, “+NIS”, and “+NBS+NIS”. However, according to Equation (5), the pseudo-anomaly scoring in TAQ-GAD is actually based on NBS and PIS, rather than NIS. Could you clarify whether the ablation table contains a writing error, or if NIS was intentionally used instead of PIS in the ablation experiments?\n2. Although $\\alpha$ and $\\beta$ show robustness, the selection of $\\tau$ (pseudo-anomaly ratio) can heavily influence performance and may require dataset-specific tuning.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The logical flow of the paper effectively guides the reader through the proposed solution and its evaluation.\n2. Formal definitions and theoretical analysis of the proposed metrics enhance interpretability and reliability. \n3. The experimental evaluation is fairly comprehensive, covering multiple datasets and various baseline methods.", "weaknesses": "1. The proposed method is topology-centric, and performance may degrade on graphs with noisy or unreliable structure. Feature-level anomalies may not be captured when the detection relies solely on topology, which could limit robustness in cases where structural information is noisy or uninformative.\n2. While PIS is claimed to be a key component of TAQ-GAD, its weight in the scoring function is set almost negligibly compared to NBS. Specifically, the implementation fixes $\\lambda_{1} = 1$ for NBS and $\\lambda_{2} = 0.001$ for PIS across all datasets. This large imbalance (1000:1 ratio) raises doubts about whether PIS truly contributes to the model. Moreover, no sensitivity analysis on λ₁ and λ₂ is provided, making it unclear if PIS has any substantive impact on performance.", "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": "9J9mz3t01B", "reviewer": "Reviewer_AXae", "summary": "This paper proposes TAQ-GAD, a semi-supervised graph anomaly detection method designed for scenarios where only normal nodes are labeled. The approach introduces a Topology-Aware Quantification (TAQ) module to measure each node’s boundary and isolation scores, identifying potential anomalies based on structural characteristics. It further employs a Topology-Aware Enhancement (TAE) module that creates virtual anomaly centers and applies risk-aware pseudo-labeling to strengthen anomaly representation. Experiments on multiple benchmark datasets show that TAQ-GAD significantly outperforms existing methods, demonstrating strong robustness and generalization ability.", "questions": "Factually speaking, datasets in the graph domain often have their own particularities depending on the scenario and task. For example, in the datasets used in this paper, the clear separation between normal and anomalous nodes largely comes from the way researchers artificially define and split the data for different tasks. This setting is far from real-world conditions. Therefore, I believe the authors should consider developing a more general and realistic approach, rather than designing a method that only fits the specific characteristics of these benchmark datasets.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper tackles a challenging semi-supervised graph anomaly detection setting where only normal nodes are labeled; this is a realistic and underexplored problem.\n\nThe proposed TAQ-GAD framework is conceptually clear, combining structural quantification (NBS/NIS/PIS) with topology-aware data augmentation (TAE).\n\nThe TAQ module provides interpretable metrics that capture both boundary proximity and structural isolation, which are intuitive and effective.", "weaknesses": "1. Methodological Limitation — Not Realistic for True Anomaly Detection:\n\nThe proposed TAQ-GAD framework heavily relies on neighborhood label statistics, especially through its Node Boundary Score (NBS) and Node Isolation Score (NIS).However, in real anomaly detection scenarios:\n* Anomalies are inherently rare, often less than 1–5% of total nodes.\n* The assumption that “normal nodes cluster together and anomalies cluster together” is unrealistic — in many graphs (e.g., financial fraud, cybersecurity, IoT networks), anomalies are structurally mixed within normal communities.\n* Consequently, computing NBS or NIS using the local density of labeled normal nodes implicitly assumes a strong topological separation between normal and anomalous nodes, which may not exist in practice.\n\nTAQ-GAD is not learning “anomalousness” from data, but rather imposing a strong heuristic constraint that fits specific benchmark graphs.\n\n2. Label Dependency — Not Truly Semi-Supervised\n\nAlthough the paper claims to address the semi-supervised anomaly detection setting, its implementation contradicts this claim:\n\n* The paper uses 60% / 20% / 20% train/validation/test splits, meaning a large fraction of nodes (including many normals) are labeled for training.\n\n* In contrast, GGAD and other baseline works typically use only 15% labeled normal nodes to simulate a truly low-label semi-supervised scenario.\n\n* Furthermore, both works control labeled ratio via the same variable ρ, but ρ in TAQ-GAD refers to a much larger absolute label count, making the comparison unfair.\n\nTAQ-GAD’s strong performance likely stems from having access to far more label information, not from the novelty of its topology quantification.\n\n3. The definitions of NBS and NIS inherently bias the model toward datasets with: Clear community separation between normal and anomalous nodes, homogeneous degree distributions (since both metrics rely on K-hop neighbor density). This structural bias means the method may overfit to benchmark datasets like Amazon or Reddit, which have cleaner topologies, and fail on real-world heterogeneous graphs (e.g., fraud networks, financial transaction graphs).\n\n4. Because both TAQ and TAE modules are built upon graph topology and labeled-normal density, the framework is not agnostic to graph structure. The “topology-aware” quantification might work as a feature engineering trick in specific graphs, but lacks generalizability across: Dynamic or time-evolving graphs, Multi-relation heterogeneous graphs, or Graphs with partial/noisy labeling.", "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": "cwepWeufz7", "reviewer": "Reviewer_4ajr", "summary": "This paper proposes CER-GOD, a novel graph outlier detection framework to address the '' Homophily Trap'', which is a critical issue where graph convolutional operations blur the feature representations of normal and anomalous nodes that are neighbours. The proposed method synergistically integrates two main components: a self-discriminative masking spoiler that learns to reweight graph edges to suppress contaminating information flow from heterogeneous neighbours, and a clustering-based outlier detector that generates unsupervised pseudo-labels to guide this reweighting process. To ensure stable training and prevent clustering collapse, a diversity loss is introduced as a regularization term. The proposed CER-GOD method is jointly optimized as an end-to-end framework. Extensive experiments on multiple benchmark datasets demonstrate that CER-GOD significantly outperforms a wide range of state-of-the-art baselines.", "questions": "Please refer to the Weaknesses.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The paper addresses a critical and well-articulated problem in GNN-based anomaly detection: the \"Homophily Trap\". The authors provided clear motivation, supported by insightful empirical analysis (Figure 1), highlighting how neighbourhood aggregation can contaminate node representations and fundamentally hinder outlier identification.\n2. The proposed CER-GOD framework is methodologically sound and the idea is novel. The main innovation lies in the synergistic joint optimization of a self-discriminative masking spoiler and a clustering-based detector. This design creates a powerful feedback loop where pseudo-labels from clustering guide the edge reweighting, and the refined graph structure, in turn, yields more discriminative embeddings for improved clustering.\n3. The comparison against a comprehensive set of baselines fully validates the effectiveness of CER-GOD. Additionally, the authors provided convincing qualitative evidence, such as t-SNE and mask visualizations, to further enhance the  persuasiveness and interpretability of the approach.\n4. The authors provided the implementation code of the proposed method, which increases the reproducibility.", "weaknesses": "1. The choice of the Chebyshev distance for the MMD kernel calculation should be elaborated. While the intuition is provided, the paper would be strengthened by an empirical comparison against a more conventional Euclidean-based RBF kernel to justify this specific design.\n2. The diversity loss $l_{diversity}$ introduces a crucial hyperparameter $\\epsilon$ to control the minimum proportion of samples per cluster. However, there is no discussion regarding the setting of $\\epsilon$ or any corresponding parameter sensitivity analysis.\n3. The paper distinguishes the edge reweighting mechanism from graph rewriting methods. Could the authors further elaborate on the fundamental advantages of such learnable masks over heuristic-based hard edge removal or addition? A deeper discussion would be valuable.\n4. The framework relies on a feedback loop where pseudo-labels guide the mask optimization. In the early training phase, these pseudo-labels might be noisy, which potentially leads the model to a suboptimal solution. How does the model ensure stability during the training phase? Is there a warm-up phase, or does the joint optimization naturally navigate towards a good solution?", "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)