Escaping the Homophily Trap: A Threshold-free Graph Outlier Detection Framework via Clustering-guided Edge Reweighting
Authors: Yunhe Zhang
Jinyu Cai
Qi Hao
Pengyang Wang
See-Kiong Ng
Venue: ICLR 2026 Poster (2026)
Keywords: Outlier Detection
Graph Neural Networks
Clustering
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Graph outlier detection is a critical task for identifying rare, deviant patterns in graph-structured data. 
However, prevalent methods based on graph convolution are fundamentally challenged by the ''Homophily Trap'': the aggregation of features from neighboring nodes inadvertently contaminates the representations of normal nodes near anomalies, blurring their distinctions. 
To overcome this limitation, we propose a Clustering-guided Edge Reweighting framework for Graph Outlier Detection (CER-GOD), which jointly optimizes a self-discriminative masking spoiler with an adaptive clustering-based outlier detector. 
The masking spoiler learns to selectively weaken the influence of heterogeneous neighbors, preserving the discriminative power of node embeddings. 
This process is guided by the clustering detector, which generates pseudo-labels in an unsupervised manner, thereby eliminating the need for predefined anomaly thresholds. 
To ensure robust optimization and prevent class collapse—a failure mode exacerbated by the homophily trap—we introduce a diversity loss that stabilizes the clustering process. 
Our end-to-end framework demonstrates superior performance on multiple benchmark datasets, establishing a new state-of-the-art by effectively dismantling the homophily trap.

Published as a conference paper at ICLR 2026
ESCAPING THE HOMOPHILY TRAP: A THRESHOLD- FREE GRAPH OUTLIER DETECTION FRAMEWORK VIA CLUSTERING-GUIDER EDGE REWEIGHTING
Yunhe Zhang** Jinyu Cai Qi Hao' Pengyang Wang*1 Sec-Kiong Ng
'he State Key Laboratory of Internet of Things for Smart City, Department of Computer and Information Science, University of Macau, China Instiiute of Data Science, National University of Singapore, Singapore (zhangyhannie, jinyucail 1995) @ma com
Asteriaqq.xin@commm crin@conneet.. um edu. mo pywangeum. edu eed.dmmm. mo seekicngenus edu.
ABSTRACT
Graph outlier detection is critical task for identifying rare, deviant patterns in graph-structured data. However, prevalent methods based on graph convolution are fundamentally challenged by the "Homophily Trap": the aggregation of features from neighboring nodes inadvertently contaminates the representations of normal nodes near anomalies, blurring their distinctions. To overcome this limitation, we propose a Clustering-guided Edge Reweighting framework for Graph Outlier De- tection
which jointly optimizes a delf-discriminative masking spoiler and an adaptive clustering bbased outlier detector. The masking spoiler learns to selectively weaken the influence hetcrogeneous neighbors, preserving the dis- criminative power of node embeddings. This process is guided by the clustering detector, which generates pseudo-labed in an unsupervised manner, thereby elimi- nating the need for predefined anomaly thresholds. To ensure robust optimization and prevent class collapse-a failure mode exacerbated by the homophily trap-we introduce a diversity loss that stabilizes the clustering process. Our end-to-end framework demonstrates superior performance on multiple benchmark datasets, establishing a new state-of-the-se by effectively dismantling the homophily trap.
INTRODUCTION
Graph outlier detection, which aims to identify anomalous data (e.g., nodes, subgraphs) deviating from dominant patterns, is critical unsupervised learning task with significant real-world applications in areas like financial fraud detection (Kim al., 2024 Wang et al., 2019 ?), traffic monitoring
(Wawrowski et al. 2023 Le et al. 2011: Zhou et al.) 2009), and biological analysis (Zhou et al. 2025]] Xu et al. 2024), etc. Over past decades, variety of detection strategies have emerged,
achieving remarkable success, such as reconstruction--ant based measurements (Ding et al.. 2019 Fan
al. 2020), contrastive learning based strategies (Liu et al. 2021b Dillon et al. 2024), or statistical
characteristic-basee methods (Chen et al. 2020 Breunig et al. 2000).
Despite their diverse approaches, foundational component in many state-of ofate-of-it of-the-ar models the graph convolutional (GC) operation, which learns node representations by aggregating information from local neighborhoods (Xu et al. 2019: Welling Kipf 2016 Sun et al. 2019). However, the effectiveness of GC operations is rooted in the principle of homophily somophily-tie the assumption that nearby nodes are similar. This very principle creates a fundamental conflict in outlier detection. When normal and anomalous nodes neighbors, the convolution process blurs their distinctions, problem recently termed the "Homophily Trap" (He et al.) 2024). This contamination of node embeddings obscures the discriminative features essential for identifying anomalies, thereby undermining the performance of existing detectors.
'These authors contributed equally. Corresponning author.

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Published as a conference paper at ICLR 2026
Original Graph
Learnalee Mask
Reconsiructed Graph G
Decoder
Latent Embedding?
Topology A
Argt Canveittioal
Distribution Repuision Loss
Divesity
Horma Hodes
kaamell fodd
Promete
Meirie
Original Labert MMD Scors Diatrbution
Torght Labrent MND Scon Distibution
Pro Prediitton
Cluster
The architecture of the proposed CER-GOD framework for graph outlier detection. The model takes an input graph with its topology, applies learnable mask to suppress noisy or irrel- evant connections, and encodes the refined structure using graph convolutional layers. The latent embeddings are then used for graph reconstruction and clustering bestering-based anomaly prediction. Based on these predictions, normal and anomalous candidate groups are generated and optimized through distribution repulsion loss. The framework is jointly optimized with three objectives: reconstruction loss, clustering loss (with a diversity regularization term), and distribution repulsion loss.
Figure 1:
To facilitate the understanding of the adverse ef- feet of "Homophily Trap" in graph outlier detec- tion, here show empirical evidence in Figure 2] Formally, a 'normal node 1-hop away from anomalies' denotes normal node with direct edge (1-hop distance) to at least one anoma- lous node, while 'normal node multi-hop away from anomalies' is normal node at a distance of two or more hops from its nearest anoma- lous neighbor. The embeddings of neighboring normal nodes are noticeably altered after graph convolution, with minimal distinction between 1-hop normal and anomalous nodes. This illus- trates that: (1) anomalous neighbors weaken the discriminability of normal nodes; and (2) this contamination effect decreases with increas- ing path. For example, when normal nodes are surrounded by anomalous ones (or vice versa), the aggregation process can blur the distinction between them, thereby weakening the model's ability detect outliers. This issue is especially severe when the nodes are closely connected, as anomalous neighbors exert stronger influence through short-range paths. contrast, the contamination effect diminishes as the path length increases, suggesting that distant neighbors contribute less to the node's final representation.
100
boop Novial hati
Maxtmim Moon Discrepancy
(4)
Figure 2: The histograms of maximum mean dis- crepancy distances and the t-SNE visualization between standard Gaussian distribution A/0, L2) and three types of node embeddings (normal node multi-hop away from anomalies, normal node 1- hop away from anomalies, and anomalous nodes) for real-world anomaly on Email dataset. Note that the embeddings are obtained via a single-layer graph convolution operation.
To address this fundamental challenge, we propose a novel framework, termed CER-GOD ceastering-guided Edge Reweighting for Graph Outlier Detection), which dismantles the homophily trap through the joint optimization two synergistic components: 1) Discrmmmiiiaeeee Masking Spoiler, and 2) Clustering- based Outlier Detector, where the architecture is shown in Figure Specifically. the masking spoiler adaptively fine-tunes the edge weights of the original topology. thereby weakening strengthening the degree of information aggregation in GC operations. As result, the discriminability between the aggregated embeddings of normal and abnormal nodes is then enhanced. However, this becomes particularly challenging when node labels unavailable. Thus,
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further introduce a clustering- blusterrng-based outlier detector, which eliminates the need for predefined thresholds when identifying anomalies. This enables the identification of candidate normal and anomalous nodes, which are then jointly optimized with the masking spoiler to further prevent the aggregation of heterogeneous node types.
Nevertheless, the "Homophily Trap" may potentially lead to class collapse (f.e., all instances clustered into a single group) due to incomplete or suboptimal optimization in the early learning process. To counter this, we further develop diversity loss that triggered when class collapse occurs and gradually reallocates a portion of samples from the dominant cluster to another cluster. This ensures the anomalous candidate group remains populated. Finally, we design a new anomalous score according to the probability confidence learned via the clustering layer. We demonstrate the superiority of the proposed method over state-of-the-an graph outlier baselines through comprehensive experiments on multiple benchmark datasets. The main contributions of this paper are summarized as follows:
We provide a rigorous analysis of the "Homophily Trap" and introduce self-discriminative masking spoiler that adaptively re-weights the graph topology to mitigate the contaminating influence of heterogeneous neighbors.
A Novel Approach to Counter the Homophily Trap:
Threshold-Free Anomaly Detection: We propose an adaptive clustering- detector that generates pseudo-labels to guide the masking process in fully unsupervised manner, eliminating the reliance on arbitrary, predefined thresholds for outlier identification.
Robust Optimization with Diversity Loss: We introduce a diversity loss function that effec- tively prevents class collapse during clustering, ensuring the stability and reliability of the joint optimization framework.
METHODOLOGY
2.1 PRELIMINARY AND MOTIVATION
Given a graph G = &), where V = {vi, U2,...., uN) denotes the set of nodes and & denotes the set of edges, each node is associated with an attribute vector x E RRd, and the graph structure represented by adjacency matrix A E {0, NNNNN, where A,, 1 if there exists edge between node i; and node Vz. In graph outlier detection tasks, the objective to learn a discriminative embedding in latent space that effectively separates normal nodes from anomalous ones, which can
be initially formulated as follows:
0, 8; T
max (f(oona)))) (G s( =
11 otherwise,
where E(-, f()) and s(-) denote the distribution measurement, the graph representation learner, and the anomaly detector that assigns an anomaly score to each node, respectively. If s; exceeds the threshold v, the i-th node is classified as anomalous, and its label yı set to
To facilitate the learning of graph embeddings, an I--layer Graph Convolutional Network is utilized learn the node representation at L-th layer:
= Aggr(z) (1-1)
(1-1) Aggr(z z -/-111 : N()),
(2)
where where.V(i) (ii is the neighbor node set of the i-th node, Aggr(-) denotes the operation that updates the representation of a node by aggregating the information of its neighbors. z, E Ø² denotes the latent representation of node v, initialized as 2, graph structure has achieved success in all kinds of fields, for the outlier detection task, it still brings several challenges:
Although aggregating information along with the
The aggregation operation along graph edges may propagate anomalous information from anoma- lous nodes to neighboring normal nodes, thereby contaminating their representations.
According to the squashigg phenomenon (Topping et al. (022). as the shortest path distance between anomalous and normal nodes increases, the extent of information propagation (which is also known as the degree of contamination) diminishes.
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Towards illustrating these challenges, let the shortest distance between node and j be r, (x
Jacobian matrix "x. to quantify the influence of the node representation a to a specific input feature x; in the node i.
Proposition 1. Vo S and VAggri S for S S1ST. then the following holds
Oz (++1) $ (a:3)++( (A (A**))
(3)
The proof of Proposition can be found in Appendix A Given the implications of it, we recognize that as the shortest path distance increases, the upper bound on the influence exerted by the i-th node's attributes on the target node embedding 2 progressively diminishes. It indicates that the sensitivity between them exhibits an exponentially decreasing trend with respect to their shortest path distance.
In the challenging unsupervised context of outlier detection, the "homophily trap" issue severely hinders the separation of normal nodes from nearby anomalies. Our approach directly confronts this by integrating self-discriminative masking spoiler with an adaptive clustering- baaeedd detector. The masking spoiler encourages aggregation to perform primarily within intra-cluster samples and designs a penalty strategy resist cluster collapse. Different from existing methods (please refer to Section B). the proposed masking spoiler selectively weakens existing edges without altering the original message passing paths. This design preserves the structural integrity of the graph while encouraging the aggregated embeddings of the two clusters to become as discriminative as possible.
2.2 SELF-DISCRIMINATIVE MASKING SPOILER
We first present mathematical formulation of the proposed candidate filter strategy. To begin with, eeconstruction-based Graph Auto-Encoder (GAE) is utilized to learn low-dimensional embeddings for each node:
Σ & x xI2 Í -
Here, À sigmoid(Z" Z) denotes the reconstructed adjacency matrix, with Z rene [X, A) representing the node embeddings obtained from the graph encoder function (=ac(-) parameterized by W = [W,, by
Then we introduce learnable variable M, and constrain the new topology À at each epoch based on the original topology A and M:
Á M O A, subject to M [0, NxN
where @ denotes the Hadamard product and M is obtained through Mij- = sigmoid(M:;). Following this, the normalization operation of the adjacency matrix Å + IN is adopted to ensure that each node's ego-information preserved. We define I as the identity matrix of shape N N.
The objective of this spoiler is to let the distributions of predicted normal nodes and anomalous nodes be as discriminative as possible. Here we first collect all predicted normal instances with label y 0 into the normal candidate node set Poss and the remaining instances into the anomalous candidate node set Pusg. The maximum mean discrepancy (MMD) (Gretton et al., 2012) is then used measure the aggregated distribution distance between the two groups. Based this, we define the distribution repulsion loss as follows:
m
173
MMD? [F, Dpos: Doeg]
<(ZZ pos
22200)
m(m - 1)
i=1
j=1
(6)
R(2,
nog
pos
23
Dog
n j=ا.jهi
where x(...) represents a certain kernel function and = {z) (0) 1N
J==1 Note that D can be taken as the graph convolutional outputs of arbitrary layer when considering computational limits, though
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this may reduce the optimization strength. Besides, use the Gaussian kernel via the Chebyshev distance, which can be defined as:
dCctbbysbew 1/² ( 20²
(max, l2c 3El))
KChebyshev (I, y) exp
=xxp
exp
(7)
2a²
Since apply it to certain graph convolutional layer in high-dimensional space, focusing the maximum difference in any single dimension is more effective, as it reduces sensitivity to noise in the remaining dimensions, Then we define the distribution repulsion loss follows:
ta MMD (Dpos Docg).
(8)
Maximizing the separation between normal and anomalous points is straightforward in supervised setting, where labels are available. However, in the absence of labels, achieving this goal becomes significantly more challenging, obtaining reliable labels itself is difficult task. To assist in optimizing the mask M edge reweighting module, we design a clustering- based outlier detector to generate temporary predicted labels. Based these pscudo labels, raise new outlier score function to guide the optimization process. The entire architecture operates in an end-to-end manner, allowing the model to learn both the optimal connections and the superior detected results simultaneously.
2.3 CLUSTERING-BASEE OUTLIER DETECTOR
Learnable Clustering Layer. To preliminarily separate the normal cluster from the anomalous candidate cluster, introduce a clustering layer (Guo al. 2017) that incorporates learnable cluster centroids into our model. Specifically, the similarity between the latent representations Z {z..... 2x} } and the cluster centroids fa is measured using the Student's t-distribution, yielding the soft clustering assignment probabilities for each sample across all clusters:
+1+ + 2 - 11 Øs -1 (1 M. 12)-11
where we assume that the N samples are partitioned into classes. is set 2, our goal is to achieve binary separation between normal and anomalous nodes. The soft assignment probabilities dy form distribution matrix Q. To further refine the clustering process and improve the compactness of cluster assignments, the target distribution P is defined as follows:
23/ // 25
Pij
(10)
Ex=1
E 4y
Given the target distribution P and current distribution Q, we formulate the clustering loss follows:
Le (L(P)IQ)
Psj log
Pvi
(11)
This loss function serves to guide the clustering optimization process and encourages the learned embeddings to capture much discriminative information possible.
During the training stage, the predicted labels are computed via Ú; = arg max)(gis) for the i-th instance. Then we first designate the cluster containing a relatively larger number of samples the normal cluster, and temporarily treat all nodes within it as normal candidates. Conversely, the remaining cluster is considered the anomalous candidate cluster. This assumption is made based on the fact that, in most datasets for outlier detection tasks, normal data constitutes the majority. Generally, the learnable clustering module avoids the use of pre-defined threshold by generating pseudo labels directly for outlier identification, thereby improving the reliability and robustness of the detection process.
Diversity Loss.
However, the ceff-discriminative masking phase could encourage one cluster to contain no samples, resulting in a trivial solution, as this represents the easiest way to maximize the MMD value. We refer to this class collapse of clustering, iee, the optimization process collapses
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all nodes into single cluster, thereby undermining the clustering effectiveness and impeding the self-discriminative masking phase. To address this, we design regularization term:
diveesity
max (0, - úg),
(12)
where 0g = N Σ qik: represents the proportion of samples assigned to cluster k. & is minimum proportion threshold that ensures each cluster maintains sufficient number of samples. If úg is greater than or equal to E, the term becomes zero (i.e., no penalty). Otherwise, it would become positive and penalize the whole objective loss.
Inference. Let pox and D Dney in Eq. (8) denote the sets of normal candidate nodes and anomalous candidate nodes, respectively. We define the anomalous scores according to the predicted logits in the clustering layer. Denoting Mpos the centroid of the normal cluster, the anomaly score for node i defined as:
(1 ||z: Mpos 112)
8;
Qt.pos
(13)
E/-=1 (1 + Iz 11)
which means that the higher the scores of the nodes, the more anomalous they are. Combining all the above loss terms, we define the overall objective function as
= a le + 3 lar + ldiversity
(14)
The proposed objective function enables the ceff-discriminative masking spoiler and outlier detector to be jointly optimized, facilitating the learning of more discriminative latent representation. The reconstruction loss employed to retain essential information from the original data. Concurrently, the uuffdiscriminative loss encourages the nodes from the same cluster to strongly connect, thereby reducing anomalous information contamination. The detailed procedure of the proposed method and complexity analysis are summarized in Appendices B and respectively.
CONNECTION WITH PREVIOUS WORK
The concept of the "Homophily Trap" (He et al. 2024) crystallizes long-standing challenge in graph anomaly detection. However, it measures anomaly degree using pre-computed spectral property-based metric and then generates multi-level graph nodes, edges, and subgraphs accordingly, making the results heavily dependent the quality of this metric. Previous attempts to mitigate it have primarily focused on graph rewriting (Dou et al., 2020 Liu et al. 2021a Qiao & Pang 2023 Gasteiger et al.) 2019 Topping et al.) 2022). These approaches, however, often hende- they either risk destroying the graph's 's essential structure through complete reconstruction or rely on heuristics that require manually defined thresholds, raising concerns about reliability. A detailed
introduction to these works can be found in Appendix [
Our celf-discriminative masking spoiler offers a more effective solution. Rather than rewriting connections, it adaptively re-weights them, preserving the original graph structure while surgically suppressing the information flow that causes the homophily trap. This targeted re-weighting differs fundamentally from the attention mechanism in GAT (Veličković et al., 2018). While GAT weights edges based on local feature similarity for representation learning, our masking spoiler explicitly guided by a global, task-specific objective: maximizing the separation between clusters of normal and anomalous nodes. This guidance is a core component of our eeff-diseriminative paradigm, which employs a clustering detector to generate pseudo-labels, creating principled, end-to-end solution that is both adaptive and threshold-free
4 EXPERIMENT
In this section, we provide detailed the experimental settings, and conduct comprehensive experi- ments to answer the following research questions (RQs):
RQ1: Does the proposed model outperform state-of-the-art graph outlier detection baselines?

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Table 1: Average AUCs with standard deviation (10 trials) of different graph anomaly detection algorithms. The best and second-best results are bolded and underlined, respectively.
MetiodeThtiees
Fanill
Corn
Disncy
Flickr
CasSaerr
Farcon
Amssoc
LISUB Milker al. 2010
72.89-0.26
52.57+0000
50 800-0045 75
54.43-0.02
63.86 03
60.5++2.51
56.94 06.94-0.00
47.53-0.02
DESPPO Wang etal 2015
0:08
00.96:00000
02.25
50.00000000
51. 51.67.0.00
5000=:000
GAT+Clist AD Velionee ol.
2018
66.19-6.05
61 +8:0000000
67 07.544+3.47
51.19-0.8 0.80
53. 53.26+2.50
63.51+3361
54, 74438.111
65.4-99.0 60
DUMINANT Ding dtal
94.00= 12.00
52,000:
05.88:0445
00.36
Fan
X123
65.91155.41
72.52.5.77 5.772
56.9219221
26.54.10.00
28.72.0.01
48. 18.05.77.51
48.38.22.7
29,80 69,00
CONAD
15.000::25 50
45.62:20.19
59.50=10.1
51:87:00.4
12:1005
AS GAB
Zhang Zoas
2022
54.08_18..0 18.50
75. 21 79
54. 54.32.10.00
55.98.11.14
12.89.00995
61.7314.71
49.35
48,99 0.552
Pang
30.45.0001
30.51:0.00
65.19:10.8
46.75.1.40
44.75.:0.03
ADA-TAIT
H ai 11244
81 $1.85-11 11.85-10.700 10.76
71 1168++00.0
41 41.10+5525
55.99+0.02
68.08-0.00
50.94+4409 69
56.17-0.100 10
50.86-11 10
DOURNE
64.39.2.00
61.96.1211
45.10:88.59
66.2612281
57.48.2228
75.01::7.15
GADAM
Chinel
20/4
28.12:2..90
92.62-0.336
69 25-05-2222
61.46-0.22
93.91-0.13
33.91+0.47
58.44-0.26
57.15-1.50
AD-GCL
Xi
57.79=1.77
68.5420000
14
46.62=2.75
72.56=2.91
65.87=2.02
53, 53,94-0.79
24:94:3.52
SmoothNNN Dmgg
1025
51.09 11.09-3533
62. 72.72++8.1 14
54.40-8.64
50.26+4.26
52.82-110 1.09
52:35+33.00
58.38 13-38-6623
40, 49.96-0.08
CBR GOD
96,98.0.05
92.0911.26
72.13:1011
67.08.0.16
24.01:0.37
726313365
59.71
96.24.3.56
RQ2: How do the
of the proposed method affect its detection performance?
RQ3: Does the proposed method learn more effective and discriminative latent representations compared to other ofate-of-the-art methods?
RQ4: Does the learned mask hold meaningful relevance?
RQ5: What is the individual contribution of each component in the proposed method to graph anomaly detection?
4.1
EXPERIMENTAL SETTINGS
Datasets. We adopt eight datasets across five different types: citation networks, social networks, communication networks, organic and co-review, including Email, Cora, Flickr, CiteSeer, Disney, Enron, Reddit and Amazon. Detailed dataset descriptions are deferred to Appendix G
Implementation Details, The implementation details are provided in Appendix H due to page limitations. To evaluate the anomaly detection performance of each method, we utilize the widely used metric: Area Under the Curve (AUC). The experimental results are reported as the mean and standard deviation, calculated over 10 independent runs of each algorithm to ensure fair evaluation.
Compared Baselines. To evaluate the effectiveness of the proposed method, we compare it with two types of graph outlier detection baselines: ten node-level outlier detection methods, namely GAT+ClusterAD (Veličković et al.] (0188). DOMINANT (Ding et al. (019), AnomalyDAE (Fan et al. 2022)) CONAD (Xu et al. 2022), ADA-GAD (He et al. 2024), BOURNE (Liu al. 2024). AD-GCL (Xu et al., 2025). TAM (Qiao & Pang, 2023), SmoothGNN (Dong et al. 2025). and
GADAM (Chen et al. 2024); and three subgraph- levell outlier detection SOTAs: LISUB (Miller
ct al.
2010), DEEPED Wang et al. 2018), and AS-GAE (Zhang & Zhao
2022).
4.2
COMPARISON WITH STATE-OF-THE-AL BASELINES (RQ1)
Table | provides detailed evaluation of the proposed method against thirteen recent baselines across eight widely used graph datasets. CER-GOD consistently achieves competitive performance across all datasets, attaining the best second-best results in the majority of cases. For instance, on the Email dataset, our model surpasses the previous best (i.e., AS AS-GAE) by more than 12%, indicating exceptional capability in identifying anomalies in communication networks. Moreover, the proposed method maintains consistently high accuracy and stable performance without catastrophic failures, reflecting both its robustness and adaptability to diverse graph characteristics. is also worth noting that GAT+CCusterAD serves as strong competitor, as it is constructed by integrating GAT with clustering-bast based outlier detector. Nevertheless, CER-GOD achieves substantial improvements over it, further highlighting the effectiveness of the SD-MS module.
4.3 PARAMETER SENSITIVITY ANALYSIS (RQ2)
Impact of Key the anomaly detection performance of the proposed model, conduct sensitivity analysis on the
a, 3 and 7, To assess the influence of key
on
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60
AUG
33
0001 0.11 0.1
10
100
1060
0.001
0.1
70
100 1000
y
Figure 3: Parameter sensitivity of clustering loss coefficient a, distribution repulsion loss coefficient 3, and diversity loss 7
100
100
B2
00
80
AUC (%)
60
AUC (%6
60
AUC (%%)
Email
20
Dincy
Chetysheocbeed Kame
Erron
Email
Ozna Dataset
Dianey
0.45
50
Layer
Kernel Compuriscn
Impact of
Layer-wise Sensitivity ofDR Loss
Figure 4: Parameter sensitivities of 1) different kernel methods for MMD calculation; 2) impact of hyper-parameter that controls the minimum proportion samples per cluster; impact of applying distribution repulsion (DR) loss to different GCN layers.
syper-parameters a, 3, and y, which control the trade-off among the reconstruction loss, clustering loss, distribution repulsion loss, and penalty term. Figure prresents the AUC trends on the Flickr and Cora datasets across varying values [e 3, 1e3). The observations are shown as follows: (1) Too large syper--arameters may cause the clustering loss, self-discriminative loss penalty loss to dominate the reconstruction loss, which can lead to the learned embeddings losing their original semantic information, thereby increasing the difficulty of training: (2) Moderate values beneficial for preserving semantic information while achieving better performance, as the multiple objectives compete with each other during training. (3) When the trade-off values are too small, the model tends to prioritize oow-dimesiional reconstruction at the expense of discriminative features, resulting in poor separation between normal and anomalous nodes and an underdeveloped decision boundary. (4) Our model exhibits broad safe operating region (e.g., o, B E [0.01, 1)) with consistently stable performance, enabling a reliable fixed default configuration.
Impact of Different Kernel Methods for the MMD Calculation. The results in Fig. 4(a) show that the Chebyshev-basee kernel consistently outperforms the conventional RBF kernel across all three datasets. We attribute this improvement to the geometric properties of the metrics: the RBF kernel aggregates differences across all dimensions, which potentially dilutes anomalous deviations through a "smoothing" effect in high-dimennional spaces, while the Chebyshev kernel focuses exclusively on the maximum discrepancy along any single dimension. Given that anomalies generally exhibit as deviations in specific feature subsets rather than uniform global shifts, the Chebyshev kernel property enables the model capture critical outlier patterns more effectively.
Impact Trade-off Parameter c. We have included detailed sensitivity analysis of the diversity loss hyperparameter in Fig. 4b.. It can be observed that excessively small values may be overly permissive and further enable cluster collapse, thereby compromising performance across all datasets. Instead, 0.5 denotes the strictest setting, which may slightly hurt performance because forcing an exact 50:50 balance may be too rigid for the nature of the data.
Layer-wise Sensitivity Analysis for Distribution Repulsion Loss. We conduct a sensitivity analysis for the distribution repulsion (DR) Loss by imposing it different GCN layers (from 1st to
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DOMINANT
GOCONAD
AnorolyDAl
USASGAA
(BADA-GAD
HDURRE:
CHADOOL
Figure 5: The comparison of t-SNE visualizations on the Email dataset for all baseline methods and the proposed model. Normal nodes are depicted in blue, while anomalous nodes are shown red.
may fre
Pay fock
Original Graphi
Masked Graph
Original Graph
Maskel Graph
Figure 6: Visualization of the sampled subgraph topology on the Flickr and Cora datasets. The color bar represents the masking strength of edge connections.
5th) and compare the anomaly detection performance. Fig. F(c) shows that performance consistently decreases as the layer depth increases from the 1tt layer to the 5th layer, with the first layer yielding optimal results.
4.4 QUALITATIVE STUDY (RQ3&RQ4)
Embedding Visualizations. First, a more intuitive demonstration of the discriminative power of the learned embeddings is provided through t-SNE visualizations across eight baselines and the ablated model w/o Self- seff-Dscriminative Masking Spoiler (SD-MS), as shown in Figure Compared the baselines, the proposed model achieves significantly better separation between normal and anomalous nodes. The anomalies are tightly clustered and clearly isolated from the majority of normal nodes, indicating that our model learns more discriminative and structured embedding space. In contrast, most baseline methods, such as LISUB, DOMINANT, and AD-GCI. show scattered or overlapping distributions of anomalous nodes, making them harder to detect. Even models like AS-GAE and CONAD, which display relatively better anomaly grouping, still fail achieve the level of compactness and separation seen in our approach. The comparison with the degraded model (i) further confirms the effectiveness of the seff-diseriminative mask spoiler, removing the SD-MS component results in more dispersed and less distinguishable anomaly embeddings.
Mask Visualizations. intuitively illustrate the effectiveness of the learned mask, we display the masked graph structure (in Figure () and the learned mask (please refer to Appendix FF. The visualized subgraph consists of 30 randomly sampled nodes, colored according to their corresponding classes. The key observations are as follows: 1) The edge weights between inter-class nodes are significantly reduced, as indicated by edges predominantly colored in shades of blue. 2) Edges connecting intra-class nodes tend to appear red. For example, in Subfigure (b), all anomalous nodes are interconnected with red edges. Although some normal nodes are linked by blue edges, they can still aggregate information through other undrawn normal nodes.

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Ablation Visualizations of SD-MS. We also provide Figure to present histograms of the Ly- norm distances between the learned node embeddings and vectors sampled from a standard Gaus- sian distribution O0, Ig), comparing the cases with and without the proposed ceff-discriminative masking spoiler (SI-MMS) module on Cora dataset (results other datasets are presented in Appendix(F)das to page limitation). Here, the purple bars represent the distance distribution of normal nodes, while the blue bars correspond to anomalous nodes. This metric serves proxy to evaluate how well the embeddings of anoma- lous and normal nodes are separated in the latent space. The application of the SD-MS module significantly increases the separation between the distance distributions of normal and anoma- lous nodes. Specifically, in all datasets, SD-MS reduces the overlap between the two classes, re- sulting in more distinguishable and polarized score distributions: normal nodes cluster near lower distances, while anomalous nodes shift toward higher distances.
Proquency
Distance with SD-MS
wio SD-MS
Figure 7: Distribution histograms of embedding distances with w/o SD-MS Cora. The dis- tance is computed between learned embeddings and vectors sampled from standard Gaussian dis- tribution N N(0, Ix) through Lz-norm.
4.5 ABLATION STUDY (RQ5)
Here, we conduct an ablation study to demonstrate the effectiveness of each com- ponent in the proposed framework. Specif- ically, design three degraded mod- ules, including 1) w/o Reconstruction vari- ant (which applies the learnable cluster- ing directly to the GCN encoder), 2)
Table 2: Ablation Study on Email, Cora, and Flickr
(mean (t) (%)
Dethods/Datasets
Email
Cora
Flickr
w/o Reconstruction Reconstruction OD w/o SD-MS
50.80=3.10
12.20=11..3
49.24422.35 56.70++5.15
14.12+1.11
7.651+1.60
87.05=4.66
78. 78.8412..68
58.4016.66
Reconstrruction-based Outlier Detector (i.e., w/o Clustering based Outlier Detector); 3)
Ours
96.98=0.08
92,09=11266
67.08=+0.16
w/o Seff-Dicriminative Masking Spoiler (SD-MS). Note that we utilize the percentile filter strategy to get the pseudo labels for the degraded model Reconstruction OD, which is set to the actual anomaly ratio of all samples. The experimental results are shown in Table 2 which clearly demonstrate that the full model consistently outperforms all degraded variants across datasets, confirming the contributions of the clustering-bai OD as well as the SD-MS module. In contrast, replacing the detection mechanism with reconstruction error yields significantly inferior performance, underscoring the necessity of the proposed components for effective anomaly detection. The results also show that removing the reconstruction component leads to a significant performance drop, which suggests the necessity of this component in our method. Besides, please note that the diversity loss cannot be ablated, as it is essential for preventing class collapse in the clustering layer.
CONCLUSION
In this work, we addressed the "Homophily Trap", a fundamental challenge in graph outlier detection where message-passing mechanisms of graph convolution operation inadvertently blur the distinction between normal and anomalous nodes. Our proposed end-to-end framework successfully dismantles this trap by synergistically combining several key innovations. The core of our approach is self- discriminative masking spoiler that intelligently re-weights graph connections, effectively filtering out contaminating information from dissimilar neighbors without destroying the underlying graph structure. This masking process is guided in a fully unsupervised manner by an adaptive clustering- based detector, which provides crucial pseudo-labels and frees the model from relying on arbitrary thresholds. To maintain stability and prevent the common pitfall of class collapse during optimization, we integrated a diversity loss. The joint optimization of these elements allows our model to learn a powerfully discriminative latent space, culminating in state-of benchmark datasets. The limitation is that this work currently focuses on binary anomaly detection; multi-class extension remains a direction for future work.
performance wide range of
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ACKNOWLEDGMENT
The work is funded by the Science and Technology Development Fund (FDCT), Macau SAR (File No. 001/2024/SKL, 0072/2025/AMJ, 0123/2023/RIA2, CG2026-IOTSC), This research is also supported by the National University of Singapore, Institute of Data Science. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the National University of Singapore.
REFERENCES
Markus M Breunig, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander. Lof: identifying density- based local outliers. In Proceedings of the ACM SIGMOD International Conference on Manage- ment of Data, pp. 93-104, 2000.
Jinyu Cai, Yunhe Zhang, Jicong Fan, and See-Kiong Ng. Lg-fgad: An effective federated graph anomaly detection framework. In Proceedings of the International Joint Conference Artificial Intelligence, pp. 3760-3769, 2024.
Jinyu Cai, Yunhe Zhang, and Jicong Fan. Self-discriiinative modeling for anomalous graph detection. In Proceedings of the International Conference on Machine Learning, 2025a.
Jinyu Cai, Yunhe Zhang. Fusheng Liu, and See-Kiong Ng. Leveraging diffusion model as pseudo- anomalous graph generator for graph-level anomaly detection. In Proceedings of the International Conference on Machine Learning, 2025b.
Jinyu Cai, Yunhe Zhang, Pengyang Wang, and See-Kiong Ng. Moegad: A mixture-of-experts framework with pseudo-anomaly generation for graph-level anomaly detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2026.
Jingyan Chen, Guanghui Zhu, Chunfeng Yuan, and Yihua Huang. Boosting graph anomaly detection with adaptive message passing. In Proceedings of the International Conference Learning Representations, 2024.
Zhenxing Chen, Bo Liu, Meiqing Wang, Peng Dai, Jun Lv, and Liefeng Bo. Generative adversarial attributed network anomaly detection. In Proceedings of the ACM International Conference on Information & Knowledge Management, pp. 1989-1992, 2020.
Barry M Dillon, Luigi Favaro, Friedrich Feiden, Tanmoy Modak, and Tilman Plehn. Anomalies, representations, and superviiri..... SciPost Physics Core, 7(3):06, 2024.
Kaize Ding, Jundong Li, Rohit Bhanushali, and Huan Liu. Deep anomaly detection attributed networks. In Proceedings of the SIAM International Conference on Data Mining, pp. 594-602. SIAM, 2019.
Xiangyu Dong, Xingyi Zhang, Yanni Sun, Lei Chen, Mingxuan Yuan, and Sibo Wang. Smoothgnn: Smoothing- gnn for unsupervised node anomaly detection. In Proceedings of the ACM Web Conference, pp. 1225-1236, 2025.
Yingtong Dou, Zhiwei Liu, Li Sun, Yutong Deng, Hao Peng, and Philip S Yu. Enhancing graph neural network- based fraud detectors against camouflaged fraudsters. In Proceedings of the ACM International Conference on Information Knowledge Management, pp. 315-324, 2020.
Haoyi Fan, Fengbin Zhang, and Zuoyong Li. Anomalydae: Dual autoencoder for anomaly detection on attributed networks. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 5685-56899 IEEE, 2020.
Johannes Gasteiger, Stefan Weißenberger, and Stephan Günnemann. Diffusion improves graph learning, Advances in Neural Information Processing Systems, 32, 2019.
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf. and Alexander Smola. A kernel two-sample test. Journal of Machine Learning Research, 13(1):723-773, 2012.
11

---

Published as a conference paper at ICLR 2026
Xifeng Guo, Long Gao, Xinwang Liu, and Jianping Yin. Improved deep embedded clustering with local structure preservation. In Proceedings of International Joint Conference on Artificial Intelligence, volume 17. pp. 1753-1759, 2017.
Will Hamilton, Zhitao Ying. and Jure Leskovec. Inductive representation learning on large graphs. Advances in Neural Information Processing Systems, 30, 2017.
Junwei He, Qianqian Xu, Yangbangyan Jiang. Zitai Wang, and Qingming Huang. Ada-gad: Anomaly- denoised autoencoders for graph anomaly detection. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 8481-8489, 2024.
Yejin Kim, Youngbin Lee, Minyoung Choe, Sungju Oh, and Yongjae Lee. Temporal graph networks for graph anomaly detection in financial networks. In Proceedings of the AAAI Workshop on Al in Finance for Social Impact, 2024.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 1412.6:411.6880 69800, 2014.
Do Quoe Le, Taeyoel Jeong. H Eduardo Roman, and James Won-Ki Hong. Traffic dispersion graph based anomaly detection. In Proceedings of the Symposium Information and Communication Technology, pp. 36-44 41, 2011.
Jundong Li, Harsh Dani, Xia Hu, and Huan Liu. Radar: Residual analysis for anomaly detection in attributed networks. In Proceedings of the International Joint Conference on Artificial Intelligence, volume 17, pp. 2152-2158, 2017.
Jie Liu, Mengting He, Xuequn Shang, Jieming Shi, Bin Cui, and Hongzhi Yin. Bourne: Bootstrapped self-supervised learning framework for unified graph anomaly detection. In Proceedings of the IEEE International Conference on Data Engineering, pp. 2820-2833 IEEE, 2024.
Yang Liu, Xiang Ao, Zidi Qin, Jianfeng Chi, Jinghua Feng. Hao Yang. and Qing He. Pick and choose: gnn-based imbalanced learning approach for fraud detection. In Proceedings of the ACM Web Conference, pp.
2021a.
Yixin Liu, Zhao Li, Shirui Pan, Chen Gong, Chuan Zhou, and George Karypis. Anomaly detection on attributed networks via contrastive self-suuprvised learning. IEEE Transactions on Neural Networks and Learning Systems, 33(6):2378-2392 2021b.
Xuexiong Luo, Jia Wu, Amin Beheshti, Jian Yang. Xiankun Zhang, Yuan Wang, and Shan Xue. Comga: Community-aware attributed graph anomaly detection. In Proceedings of the ACM International Conference on Web Search and Data Mining, pp. 657-665, 2022.
Yuankai Luo, Lei Shi, and Xiao-Ming Wu. Can classic gnns be strong baselines for graph-level tasks? simple architectures meet excellence. In Proceedings of the International Conference on Machine Learning, 2025.
Benjamin Miller, Nadya Bliss, and Patrick Wolfe. Subgraph detection using eigenvector 11 norms. Advances in Neural Information Processing Systems, 23, 2010.
Seong Ho Pahng and Sahand Hormoz. Improving graph neural networks by learning continuous edge directions. In Proceedings of the International Conference Learning Representations, 2025.
Junjun Pan, Yixin Liu, Yizhen Zheng, and Shirui Pan. Prem: A simple yet effective approach for node-level graph anomaly detection. In Proceedings of the IEEE International Conference Data Mining, pp. 1253-1258. IEEE, 2023.
Junjun Pan, Yixin Liu, Rui Miao, Kaize Ding, Yu Zheng, Quoe Viet Hung Nguyen, Alan Wee-Chung Liew, and Shirui Pan. Explainable and fine ane-grained safeguarding of Ilm multi-agent systems via bi-level graph anomaly detection. arXiv preprint arXiv:2512.1873. 2025.
Mathilde Papillon, Guillermo Bernardez, Claudio Battiloro, and Nina Miolane. Topotune: A frame- work for generalized combinatorial complex neural networks. In Proceedings of the International Conference Machine Learning, 2025.
12

---

Published as a conference paper at ICLR 2026
Hezhe Qiao and Guansong Pang. Truncated affinity maximization: One-class homophily modeling for graph anomaly detection. Advances in Neural Information Processing Systems, 36:49490-4995 2023.
Hezhe Qiao, Hanghang Tong, Bo An, Irwin King, Charu Aggarwal, and Guansong Pang. Deep graph anomaly detection: A survey and new perspectives. IEEE Transactions on Knowledge and Data Engineering, 2025.
Michael Scholkemper, Xinyi Wu, Ali Jadbabaie, and Michael T Schaub. Residual connections and normalization can provably prevent oversmoothing in gnns. In Proceedings of the International Conference on Learning Representations, 2025.
Fan-Yun Sun, Jordan Hoffmann, Vikas Verma, and Jian Tang. Infograph: Unsupervised and semi- supervised graph-level representation learning via mutual information maximization. arXiv preprint arXiv:/908. 01 000,, 2019.
Yan Sun and Jicong Fan. Mmd graph kernel: Effective metric learning for graphs via maximum mean discrepancy. In Proceedings of the International Conference on Learning Representations, 2024.
Ziheng Sun, Chris Ding, and Jicong Fan. Lovász principle for unsupervised graph representation learning. In Advances in Neural Information Processing Systems, 2023.
Ziheng Sun, Xudong Wang, Chris Ding, and Jicong Fan. Learning graph representation via graph entropy maximization. In Proceedings of the International Conference on Machine Learning, 2024.
Jake Topping, Francesco Di Giovanni, Benjamin Paul Chamberlain, Xiaowen Dong, and Michael M Bronstein. Understanding over-squahhin and bottlenecks on graphs via curvature. In Proceedings of the International Conference on Learning Representations, 2022.
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. Proceedings of the International Conference on Learning Representations, 2018.
Daixin Wang, Jianbin Lin, Peng Cui, Quanhui Jia, Zhen Wang, Yanming Fang, Quan Yu, Jun Zhou, Shuang Yang, and Yuan Qi. A semi-supervised graph attentive network for financial fraud detection. In Proceedings of the IEEE International Conference Data Mining, pp. 598-607. IEEE, 2019.
Haibo Wang. Chuan Zhou, Jia Wu, Weizhen Dang, Xingquan Zhu, and Jilong Wang. Deep structure learning for fraud detection. In Proceedings of the IEEE International Conference on Data Mining, pp. 567-576. IEEE, 2018
Lukasz Wawrowski, Andrzej Biatas, Adrian Kajzer, Artur Kozlowski, Rafal Kurianowicz, Marek Sikora, Agnieszka Baymanska-Kwiees Kwiecien, Mariusz Uchroński, Milosz Biatczak, Maciej Olejnik, et al. Anomaly detection module for network traffic monitoring in public institutions. Sensors, 23 (6):2974, 2023.
Max Welling and Thomas N Kipf. Semi-supervised classification with graph convolutional networks. In Proceedings of the International Conference on Learning Representations, 2016.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In Proceedings of the International Conference on Learning Representations, 2019.
Yiming Xu, Zhen Peng. Bin Shi, Xu Hua, Bo Dong, Song Wang, and Chen Chen. Revisiting graph contrastive learning on anomaly detection: structural imbalance perspective. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 12972-12980. 2025.
Yunpei Xu, Shaokai Wang, Qilong Feng, Jiazhi Xia, Yaohang Li, Hong-Dong Li, and Jianxin Wang. sccad: Cluster decomposition -based anomaly detection for rare cell identification in single-cell expression data. Nature Communications, 15(1):7561, 2024.
Zhiming Xu, Xiao Huang. Yue Zhao, Yushum Dong, and Jundong Li. Contrastive attributed network anomaly detection with data augmentation. In Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp. 457. Springer, 2022.
13

---

Published as a conference paper at ICLR 2026
Yunhe Zhang, Yan Sun, Jinyu Cai, and Jicong Fan. Deep orthogonal hypersphere compression for anomaly detection. Proceedings of the International Conference on Learning Representations, 2024.
Zheng Zhang and Liang Zhao. Unsupervised deep subgraph anomaly detection. In Proceedings of the IEEE International Conference on Data Mining, pp. 753-762. IEEE, 2022.
Yunfeng Zhao, Yixin Liu, Shiyuan Li, Qingfeng Chen, Yu Zheng, and Shirui Pan. Freegad: A training-free yet effective approach for graph anomaly detection. In Proceedings of the ACM International Conference Information and Knowledge Management, pp. 4379-4389, 2025.
Yu Zheng, Ming Jin, Yixin Liu, Lianhua Chi, Khoa T Phan, and Yi-Ping Phoebe Chen. Generative and contrastive supfrvuue learning for graph anomaly detection. IEEE Transactions on Knowledge and Data Engineering, 35(12): 22200-12233, 2021.
Yingjie Zhou, Guangmin Hu, and Weisong He. Using graph to detect network traffic anomaly. In Proceedings of the International Conference on Communications, Circuits and Systems, pp. IEEE, 2009.
Zhecheng Zhou, Jinhang Wei, Mingzhe Liu, Linlin Zhuo Xiangzheng Fu, and Quan Zou. Anomalgrn: deciphering single-cell gene regulation network with graph anomaly detection. BMC Biology, 23 (1):73, 2025.
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A PROOF OF PROPOSITION 1
Proof. Assume that the shortest path between node i and j is r, the gradient of activation function in the 1-th layer follows |oo a, the gradient of aggregating function at layer / satisfies VAggr, - and 2; = X,, then the Jacobian at layer / is bounded by:
dzz (1)
S (a'))
(15)
0x;
Next step, let M() be the neighbor set of node j. we have the Jacobian at layer / + 1 via the chain rule for diffcrentiation:
doi (Aggri ((z/)) (E)
θz 0z 1++
dAggr, (2N())
Ozk
(
(16)
0x
aAggr
Ozk
(1)
0x:
Thus, will obtain:
Oz (2((11)
0z (!)
S a
(17)
Ox;
Ox;
kEN())
and the bound would become:
Oz (22(+11)
S aB Σ (aB) kEN()
(18)
8x:
Herein, A' represents the adjacency matrix raised to the layer 1, the sum EkeNg) (A)) essentially counts the number of paths of length / from node i to node j. This can be further expressed as:
Oz (+1)
-
141 1)))
(19)
Ox,
where (A En (A")))) )a and A₁k 1 due to k E W(). As is the shortest distance between node and j. then the inequality becomes:
Oz ;
(r+1)
S (a.3)+1(Art))
(20)
Ox;
Then finished the proof.
B DETAILED ALGORITHM PROCEDURES
Here, we present the detailed procedures for CER-GOD in Algorithms !
C COMPLEXITY ANALYSIS
Assume that there is a graph of N nodes, each with feature dimension d, E edges, and latent dimension k; the complexity of the overall framework is computed follows:
The whole encoder adopts an L-layer GCN backbone, where each layer involves two key operations: neighbor aggregation (O(E) and linear transformation (each layer has complexity of O(N O(N-d --k))..
The decoder typically involves a linear transformation to reconstruct the input feature matrix, where complexity ONN d k)). The complexity of computing topology Á O(V2 kk).
The clustering layer computes the similarity between each node's embedding and the cluster centroids and further calculates the KL Divergence loss. Hence, the complexity is O(N c), where is the class number.
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Algorithm I Clustering-guiders Edge Reweighting for Graph Outlier Detection (CER-GOD)
Input:
The input graph set G, dimensions of GCN hidden layers k, trade-off parameters of clustering loss a and distribution repulsion loss $3, and diversity loss learning rate
Output:
The outlier detection scores s. 1: Initialize the parameters M and Φ of celf-disrriminative masking spoiler and Glustering-basee
outlier detector network parameters fo;
2: Reallocate topology through Eq. ( and normalized it with À + IN;
3: Initialize the cluster centroids via performing K-Means latent representation Z
/ /X, A);
4: while not convergence
5: Obtain the latent and ( by Z = Fenc X, A) and Eq. (
6:
Calculate the reconstruction loss via Eq.
7:
Compute the current cluster assignment distribution Q by Eq.
8:
Compute the target cluster assignment distribution P by Eq. 10
9:
Calculate the diversity loss via Eq. (12):
Compute the cluster label for sample
vi arg max, (gig), 1,,,
11:
Calculate the distribution repulsion loss based on Eq.
Calculate total loss via Eq. (14):
13:
Back propagate masking spoiler and outlier detector networks and update M, Φ, and respectively;
14:
end while
15:
Calculate the outlier detection scores s through Eq.
13
16:
return The outlier detection scores s.
The diversity loss is computed by calculating the proportion of samples assigned to each cluster, then applying penalty term. The complexity of this operation is O(N .c.
For lar. assume that positive set Dps contains m nodes, intra-calculation consumes O(m² k)) and O(N - m)² k). Inter-calculation consumes Om (N (0mm)) m) k). the worst case, it would be O(N2, k))
Thus, the total computational complexity is O(L O(L-(E+) N k- N N2.
We also provide the running time comparison in Table for reference. Across all four datasets, CER- GOD demonstrates highly competitive efficiency, consistently ranking among the fastest methods. On Email, Cora, and Disney, CER-GOD achieves second-tier performance, running notably faster than most baselines. These results confirm that CER-GOD provides an effective balance between accuracy and efficiency, making it a practical choice for large-scale anomaly detection.
Table Running time (in seconds) comparison on four datasets, the results are recorded at the time of running 200 epochs for fairness.
Methods/Datasets
Email
Cora
Disney
CiteSeer
DOMINANT (Ding et al.
2019
5.6278
17.7207
1.4391
49.0877
AnomalyDAE
4,0151
6.1372
0.9438
24.4646
CONAD Xu et o. 2022
9,0529
33.0815
2.9236
73.6654
AS-GAB
2022
24.7159
2.81466
27.9659
ADA GAD Uie el 2024
52,4239
321.3380
7.2619
1258. 2931
21.2274
5.9707
AD-GCL
X ét al. 20755
1991.0725
5510.4095
116.0679
3223.6459
CER-GOL
42.4534
82.8717
6.7685
101,0798
D EXPERIMENT ON LARGE-SCALE GRAPH BENCHMARK
We evaluated CER-GOD on the GGB-Proteins dataset, which contains 132,534 nodes and 79,164,28
edges, where CER-GOD is compared with 5 state-of- the art baselines: DOMINANT (Ding al.
2019), ComGA (Luo et al., 2022). SL-GAD (Zheng et al. 2021). CoLA (Liu et al. 20216) and TAM As shown in the Table (note that we reported the performance of all baseline
(Qao & Pang 2023
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methods directly from QQiao & Pang 2023)), CER-GOD scales successfully and outperforms several state-of-the-ane baselines in comparison.
Table 4: AUCs (%) different graph anomaly detection algorithms on large-scale dataset OGB-
Proteins. The best result is bolded.
Metsods/Datasets DOMINANT
ComGA
CoLA
SL-GAD
TAM
CER-GOD
CGB-Proteins
72.67
71.34
71.42
73.71
74.49
74.81
E DISCUSSION OF CLUSTER NUMBER SELECTION
In this paper, we focus on the unsupervised outlier detection task. In a fully unsupervised setting, we lack labels to map multiple learned clusters the binary ground truth. For example, we set 5, determining which specific subsets of clusters represent "normal" and which represent "anomalous" requires additional heuristics (e.g., "the smallest clusters are anomalies"), which introduces significant instability and potential bias. Therefore,
followed the standard one-class
classification setting and set the number of clusters as = 2. as many previous works (Ding et al.) 2019 Fan et al. 20200; Xu et al. [2022] He al.) 2024 Xu al. (025) did: The "anomalous candidate cluster" does not assume all anomalies are homogeneous, but instead treats anomalous patterns (e.g., point/structurall/ttrbbbuu anomalies) different manifestations of deviating from the manifold with respect to the normal pattern.
Regarding computational cost, analyzed in Appendix C the reconstruction process indeed a major time-consuming component in our method. Compared to the reconstruction component, the clustering overhead is linear to N and proportional to the small e (here c 2). Thus, adding clustering does not change the overall asymptotic time complexity and adds only a modest overhead in practice.
SUPPLEMENTARY VISUALIZATION RESULTS
Homophily Trap Visualizations. Here, we supplement four additional histograms of maximum mean discrepancy distances on two synthetic datasets (Attribute Anomaly and Structure Anomaly), and two real-world datasets (Cora and Flickr) in Fig. g The distance computed between the standard Gaussian distribution (0, La) and three types of node embeddings (normal node multi- hop away from anomalies, normal node 1-hop away from anomalies, and anomalous nodes). modes).Thy The embeddings obtained through a single-layer graph convolution operation without any additional linear projection layer, isolating the pure effects of graph convolution. The synthetic datasets, derived from (Zhang & Zhao 2022), demonstrate the homophily trap phenomenon in data containing either attribute anomalies or structure anomalies alone. Real-wond world data further exhibits both anomaly types simultaneously. This confirms the presence of the 'homophily trap' in real-world applications: graph convolution significantly influences the embeddings of neighboring normal nodes, causing them to become nearly indistinguishable from I-hop anomalous nodes.
22201
Desetty
11:00
1230
487
550
32
22
12
75 20
359
(3) Antibate Anemaly
(b) Stracturr Anomaly
(c) Cor
(d) Flickr
Figure 8: The histograms of maximum mean discrepancy distances synthetic datasets and two real-world datasets.
Embedding Visualizations. Figure 9 presents 3D scatter plots comparing the performance of
various anomaly detection methods the Cora dataset. The blue points represent normal data, and
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the pink points represent anomalies. Overall, the proposed method CER-GOD achieves the best separation between normal and anomalous points, demonstrating superior performance compared to other methods such LISUB, DOMINANT, and CONAD, which show less distinct separation. While methods like AS-GAE and ADA-GAD improve anomaly detection, the proposed approach clearly outperforms all, providing the most effective distinction between normal and anomalous data.
LiSU
(9 DOMENANT
(O CONAD
(0 AomrayDDA
(0ASGAE
IDADUGAD
Ca
BRADEGE
CO
Figure 9: The comparison of t-SNE visualizations on the Cora dataset for all baseline methods and the proposed model. Normal nodes are depicted in blue, while anomalous nodes are shown red.
Impact of GNN Backbone. We also conduct parameter analysis of the adopted different GNN backbones in Figure I0, which includes GCN (Welling & Kipf 2016), GIN (Xu al., 2019). and GAT (Velicković et al. 2018). This
figure compares the AUC performance of the above-mentioned backbones three datasets: Cora, Email, and CiteSeer. GCN outperforms the others across Cora and Email, with the largest gap on Cora. GAT follows closely, espe- cially CiteSeer and Email, while GIN shows the weakest performance, particularly on Email. While GCN and GIN show similar performance with no significant gap, GAT tends to perform weaker. This is likely because GAT already in- corporates masking in its mechanism, which adds an additional optimization burden to the eelf-discrininative module. is worth noting that all three backbones outperform the other baselines.
GDN
GAT
Ohrdwer
Dataeet
Figure 10: The performance comparison of differ- adopted backbones the Cora, Email, and CiteSeer datasets.
Ancratios Dara
Freaveng Devaty
Frequenyy
12
1.0
10
1.097
1008
w/o SD
with SD-MS
CiteSeer
Figure 11: Distribution histograms of embedding distances with or w/o SD-MS on Email and CiteSeer datasets. The distance is computed between leamed embeddings and vectors sampled from standard Gaussian distribution (0 I through T.znorm.
Ablation Visualizations of SD-MS. Similar conclusions can be observed in Figure I1 The area of the overlapping region obviously decreases after the masking procedure. Also, the distance distributions of normal and anomalous nodes are more discriminative intuitively.
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36
sistas cinra26620
(a) Original Topology
(b) Learned Mask
(c) Masked Topology
Visualization of the learned mask in the proposed model on the Flickr dataset. The color bar represents the masking strength of edge connections. Connections between different-class node pairs are highlighted with black frames.
Figure 12:
Mask Visualizations. The learned mask and its impact are illustrated in Figure [2] A subgraph consisting of 30 randomly selected nodes is shown, with elements corresponding to different-class node pairs highlighted in black frame. It is clearly evident that the relationships framed in the figure are significantly weakened, most of them are close white or even in blue, indicating high masking strength. For example, the relationships between Node 12 and Node 2, well between Node 25 and Node 11, exhibit such weakened connections.
G DATASETS
The detailed statistical descriptions are shown in Table We also report the number of edges with "Homophily Trap" (HT) for the reference. Specifically, we adopt the Email and Cora in (Zhang & Zhao 2022), CiteSeer, Flickr in (Pan et al. 2023), Amazon, DGB--roteiin in QQao Pang 2023).
and Disney, Enron, Reddit in PyG
Table 5: Detailed information of the graph benchmark datasets.
Nodes
Edges
Average
Edges
Average [E]]
Anomaly
Types
Email
LO05
28,275
28. 1300
22,190
22.0796
6.01%
Communication Network
Flickr
7,575
482,585
63.7036
428,301
56.5413
6.24%
Social Network
Cora
2,708
15,045
5,5557
5,3112
4.07%
Citaton Network
CiteSeer
3,327
10,275
3.0883
9,563
2,8744
4, 4,72%
Citaion Network
Disncy
124
335
2,7016
518
2,5645
4 4.80%
Organic
13,533
176,794
Organic
Reddit
10,984
168,016
15.2964
159,688
14,5382
3,30%
Organic
Amazon
10,244
351,216
34,3521
283,594
27.7381
6, 6,66%
Co-review
132,534
79.164,284
597.3130
Biology Network
H DETAILED EXPERIMENTAL SETTINGS
Trade-off Parameters: For the proposed method, there are three critical papee--arameters, a, 3 and y, in their loss functions, which control the contributions of the clustering loss and distribution repulsion loss, and diversity loss, respectively. Section 4.3 includes the evaluation the impact of variations in the values of all sypee-parammters main experiments, the complete hyperparameter configurations are summarized in Table
the anomaly detection performance. For our
Baseline Settings: All baselines are reproduced via publicly available code with their default parameter settings. Particularly, we employ the same architecture of the backbone network as the proposed method ensure fair comparison.
Training Details: We utilize Adam (Kingma & Ba 2014 for training. Besides, set the learning rate 7) to 5e-5 with the total training epochs to 300. For the proposed model, a 3-layer GCN backbone is adopted for the outlier detector, and the hidden dimension 16.
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Published as a conference paper at ICLR 2026
Implementation: All experiments executed on the NVIDIA Tesla H100 GPU (80 GB) with Intel Xeon Platinum 8480CL CPU.
Table 6: Detailed hyper-parameter settings all datasets.
paramerrrs
Email
Cora
Disney
Flickr
CiteSecr
Enron
Reddit
Amazon
a
0.001
0.1
0.001
0.1
0.001
0.001
10
B
0.001
10
0.01
0.001
0.001
0.1
7
1
1
1
1
1
1
I RELATED WORK
1.1 GRAPH NEURAL NETWORK
Graph neural networks (GNNs) have emerged as dominant framework for modeling graph graph-structured data, owing to their ability to aggregate information from node's neighbors based the underlying topology. Over the past decade, wide range of architectural innovations have been introduced to improve their expressivity, efficiency, and generalization, spanning foundational models such GCN, GraphSAGE, and GIN to more recent advances like InfoGraph and kernel-based graph learning
(Welling& & Kipt 2016 Hammilon al. 2017 Xu et al. 2019 Sun al. 2019 2023 Cai et al.) 2024 2026). GNNs are applicable to both node-level and graph-level tasks, with the latter often relying on readout operations map graph into vector space. Recent research has further expanded the
landscape (Scholkemper et al. 2025 Pahng & Hormoz 2025 Sun et al. 2024). For example, Luo et al.
(2025) introduced GNN+ showing that classical GNNs augmented with edge features, normalization, dropout, residual connections, feed-forward layers, and positional encodings can match or outperform graph Transformers on graph-level tasks while being more efficient; Papillon et al. (2025) also presented TonoTTuee extending GNNs to topological deep learning via Generalized Combinatorial Complex Neural Networks that capture higher-order interactions with reduced complexity.
1.2 GRAPH OUTLIER DETECTION
Node-level outlier detection on graphs (Qiao al. 2025 Zhao et al. 2025 Pan al. 2025 has developed through several methodological paradigms, each emphasizing different aspects of structural and attribute information. Reconstruction- based methods (Ding al. 2019 Fan al. 2020 Cai iet al. 2225a b) aim to rebuild node attributes or graph structures using autoencoders, flagging nodes with high reconstruction errors anomalies. Prediction- -baed methods (e.g.. [i et al. (2017) infer node features or links based on neighbors or learned patterns, where deviations from predictions indicate abnormality. Contrastive learning- learning-based methods (Liu et al.) [2021b] DDillon et al. 2024]
Xu et al. [2025] Sun & Fan] 2024) distinguish normal and abnormal behaviors by learning robust node representations through contrasting positive and negative samples, thereby enlarging margins between inliers and outliers. Distance deviation-based methods (Chen et al. 2020 Breunig et al., 2000 Zhang et al.) (024)) measure statistical divergence in local neighborhoods, leveraging density clustering cues to spot anomalies. Beyond these categories, hybrid and advanced designs have emerged: adversarial approaches like AS-GAE (Zhang & Zhao, (202)) enhance discrimination via perturbation; boundary-awan representations such BOURNE (Liu et al.) 2024) and adaptive augmentation in ADA-GAD (He et al. 2024) refine normality decision boundaries; and interpretable designs like CONAD (Xu al. (022)) integrate atlention for anomaly explanation. Recent efforts also target robustness under homophily and heterophily by incorporating denoising strategies, geometric embeddings (e.g., hyperbolic spaces), and transformer-style encoders to mitigate smoothing and over-squashing. Collectively, these approaches represent progression from early subspace and residual scoring to more sophisticated adversarial, contrastive, and one-class objectives, reflecting the field's ongoing pursuit of greater accuracy, interpretability in node-level anomaly detection.
1.3 GRAPH REWRITING FOR GRAPH MINING
For the homophily trap issue, graph rewriting is a direct solution that aims at breaking the connection between inter-class nodes while keeping intra-class connections. Dou al. (0000) raised label-
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Published as a conference paper at ICLR 2026
aware similarity measure identify informative neighbors, reinforcement learning determine the optimal number to select, and aggregate the chosen neighbors across different relations. [Luu et al. (2021a) proposed that for the fraud target node, the redundant links could be filtered by choosing neighbors that are far from the target, measured by the distance, and removing them from the neighbor set. And the necessary links, which are beneficial for fraud prediction, would be created by choosing similar nodes of the fraud class and regarding them as neighbors, Qiao & Pang (2023) calculated the Euclidean distance and removed the relatively farther neighbor nodes for one node, finally adopting the similarity of nodes to detect anomalies. [aasteiger et al. (2019) designed the Graph Diffusion Convolution aggregate information from a larger neighborhood by constructing through a new graph, generated by sparsifying generalized form of graph diffusion. [Topping et al. (2022) introduced new combinatorial edge-based curvature, the Balanced Forman curvature, which provides sharp lower bound to the standard Ollivier curvature on graphs, and demonstrated that negatively curved edges contribute to this phenomenon. The limitations of current works have been discussed in Section
J REPRODUCIBILITY STATEMENT
To ensure full reproducibility, source code is provided in the supplementary material. We also plan to release the curated training dataset and final model weights. The experimental framework is described throughout the paper for transparency, and details on hardware details, model configurations, and hyper-parameters settings can be found in Appendix H Dataset resources are summarized in Appendix G and all evaluation benchmarks, which are publicly available, are listed in Section 4.
K
THE USE OF LARGE LANGUAGE MODELS (LLMS)
The conceptual framework and core ideas outlined in this paper represent the authors' original contributions. Al-driven language models were employed solely as auxiliary tools to support specific well-defined tasks. These tasks encompassed implementing basic utility functions, and assisting with manuscript translation and linguistic polishing. The authors take full responsibility for the content of the manuscript, including any text generated or polished by the LLM. We have ensured that the LLM-generater text adheres to ethical guidelines and does not contribute to plagiarism or scientific misconduct.
21


Reviews:
[{"review_id": "bJNrp968W0", "reviewer": "Reviewer_A5bT", "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. Extensive experiments on multiple benchmark datasets demonstrate that CER-GOD significantly outperforms a wide range of state-of-the-art baselines.", "questions": "1. Please also include a parameter sensitivity analysis examining how the distribution repulsion loss performs when applied to different graph convolutional layers.\n2. 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.\n3. 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?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "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.\n\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.\n\n3. A comparison with existing graph rewriting baselines is missing, which would help validate the method's effectiveness.", "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": "VlB2X1c5oB", "reviewer": "Reviewer_ErB5", "summary": "This paper proposes a learnable clustering-guided edge reweighting framework that jointly optimizes a self-discriminative masking module and an adaptive clustering-based outlier detector. The clustering process generates pseudo labels in an unsupervised manner, which are then utilized to guide the training process.", "questions": "See above **Weaknesses**", "limitations": "", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "(1) The method is straightforward to understand, but the paper’s writing quality needs improvement.  am particularly confused about the role of the pseudo labels. \n\n(2) The proposed method achieves the best performance across six small-scale graph anomaly detection  datasets.", "weaknesses": "(1) The authors should provide a clear technical definition or explanation for the newly introduced concepts “multi-hop away from anomalies” and “1-hop away from anomalies.” For instance, a 1-hop-away node should refer to a normal node that is directly connected to at least one anomalous node.\nAdditionally, the description of “data distribution” in the framework is misleading — it should be clarified as the anomaly score distribution or MMD score distribution if you use the histogram. Moreover, the current explanation of the framework implies that only two clusters are considered in the diversity loss. The role of the pseudo-labeling process is also not clearly reflected in the framework diagram, and the legend is missing. The type of latent embedding *z* is not consistent with the main paper. The authors should revise the figure and explanation to make these components explicit.\n\n(2)Most of the benchmark datasets used are relatively small, making the experimental results less reliable—especially on Enron, which contains only five anomalies. I suggest that the authors include larger-scale datasets, covering both more injected or real-world data with real anomalies, to better demonstrate the robustness and effectiveness of the proposed method.\n\n(3) The approach appears to focus primarily on the reconstruction process and the learning of discriminating representations.  The unsupervised clustering module is learnable, and the inference relies on the distance to the centroids. In this case, it is unclear why a reconstruction component is still necessary. Why not directly apply clustering to the graph representations learned by the GCN encoder? Moreover, the ablation study is not sufficiently comprehensive—additional variants, like directly applying the learnable clustering, should be included for a more thorough evaluation\n\n(4)Determining the appropriate number of clusters for each dataset is challenging. How do the authors decide on the cluster count in practice? Additionally, the reconstruction process is computationally complex, and the inclusion of clustering further increases the overall computational cost. Besides, the performance with varying the number of clusters should be provided.\n\n(5) As you mention in lines 244-247, ”Then we first designate the cluster containing a relatively larger number of samples as the normal cluster, and temporarily treat all nodes within it as normal candidates. Conversely, the remaining clusters are considered the anomalous candidate cluster“.  How many large clusters are treated as normal nodes? In real GAD datasets, the data distribution often consists of multiple normal clusters with relatively large sample sizes, along with multiple anomalous clusters and some isolated outlier points.", "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": "GSaApiH7TO", "reviewer": "Reviewer_Q1xe", "summary": "This paper introduces CER-GOD, a graph outlier detection framework designed to mitigate the \"Homophily Trap\" in graph convolutional networks (GCNs), where aggregating features from anomalous neighbors contaminates normal node representations. The method combines a self-discriminative masking spoiler that adaptively re-weights edges to reduce heterogeneous influences, guided by a learnable clustering layer that generates pseudo-labels without predefined thresholds. A diversity loss prevents class collapse during clustering. The overall objective balances reconstruction, clustering, distribution repulsion, and diversity terms. Experiments on six datasets show superior AUC performance over baselines. Contributions include: (1) analysis of the homophily issue with a masking mechanism, (2) threshold-free pseudo-labeling via clustering, and (3) a regularization to stabilize optimization.", "questions": "1.\tCan the authors clearly explain how the proposed masking differs mathematically from the attention coefficients in GAT or the relation-strength function in ADA-GAD?\n2.\tHow sensitive is the model to the initial K-Means clustering used for pseudo-label initialization?\n3.\tDoes the method scale to larger graphs (e.g., >100k nodes)? Have the authors considered mini-batch or approximate MMD computation?\n4.\tCan the authors provide quantitative evidence (e.g., correlation coefficients) showing that the learned edge weights actually correlate with homophily or anomaly boundaries?", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The paper creatively combines edge re-weighting with unsupervised clustering for outlier detection, extending the \"Homophily Trap\" concept (He et al., 2024) into a joint optimization framework. The diversity loss is a novel tweak to address a specific failure mode in clustering under homophily constraints, potentially applicable beyond outliers.", "weaknesses": "1. The paper's core innovation—adaptive edge masking guided by binary clustering—feels incremental rather than transformative, building too closely on existing ideas without sufficient novelty. For instance, the masking spoiler resembles attention mechanisms in GAT or adaptive topology learning, but lacks a rigorous comparison showing why global MMD guidance (Eq. (8)) outperforms local feature-based weighting. \n2. The \"self-discriminative\" claim is undersold: it primarily enforces intra-cluster aggregation via pseudo-labels, which is akin to DEC (Guo et al., 2017) but without justifying why two clusters suffice for diverse anomaly types (e.g., point vs. structural outliers). \n3. Proposition 1, while neat, is a straightforward extension of over-squashing bounds (Topping et al., 2022) and does not uniquely motivate the framework—empirical validation in Fig. 1 is limited to one dataset (Email) and single-layer GCN, ignoring multi-layer or heterophilic graphs.", "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": "m9Vb5gqzGp", "reviewer": "Reviewer_6mWp", "summary": "The authors propose a Clustering-guided Edge Reweighting framework for Graph Outlier Detection (CER-GOD), which jointly optimizes a self-discriminative masking spoiler with an adaptive clustering-based outlier detector. Experiments show their improvement to some extent.", "questions": "Please refer to the weaknesses.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The authors propose a cluster-based edge reweighting framework for unsupervised graph outlier detection. \n2. Experiments show their improvement to some extent.", "weaknesses": "1. Although the authors provide a time complexity, the N-squared complexity might be a hindrance for real deployment. It will be better if the authors can provide an experimental comparison. \n2. The included datasets are relatively small compared to the newest anomaly (outlier) detection datasets, such as those in [1]. The authors should include the real-world datasets in their comparison. \n3. The included baselines are not comprehensive, which questions the effectiveness of the framework. The authors should include SOTA works such as [2], [3], and [4].\n4. Figure 3 shows that the method can be very sensitive to the variation of hyperparameters. As stated in Appendix G, they adopt grid search for finding the hyperparameters. It can be a question of how to utilize grid search for unsupervised learning without any ground truth labels. Furthermore, it can be difficult for the method to choose proper hyperparameters to operate on new datasets. \n5. The authors should show the finetuned hyperparameters and how many times they conduct the experiments to search for the hyperparameters. \n\n[1] Jianheng Tang, Fengrui Hua, Ziqi Gao, Peilin Zhao, Jia Li. GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection. NeurIPS 2023. \n\n[2] Hezhe Qiao, Guansong Pang. Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection. NeurIPS 2023. \n\n[3] Jingyan Chen, Guanghui Zhu, Chunfeng Yuan, Yihua Huang. Boosting Graph Anomaly Detection with Adaptive Message Passing. ICLR 2024. \n\n[4] Xiangyu Dong, Xingyi Zhang, Yanni Sun, Lei Chen, Mingxuan Yuan, Sibo Wang. SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection. WWW 2025.", "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)