CATeye: Coupled Attribute-Topology Invariance Learning for Voucher Abuse Detection

arXiv:2609.01425v1 [cs.LG] 1 Sep 2026

CATeye: Coupled Attribute–Topology Invariance Learning for Voucher Abuse Detection Tian Tian

Shuaicheng Niu

Hao Kuang

tian006@e.ntu.edu.sg Nanyang Technological University Singapore

shuaicheng.niu@ntu.edu.sg Nanyang Technological University Singapore

h.kuang@alibaba-inc.com Lazada Inc. Singapore

Yuanhang Hu

Dong Li

Zhiqi Shen

huyuanhang.hyh@alibaba-inc.com Lazada Inc. Beijing, China

shiping@taobao.com Alibaba Group Hangzhou, Zhejiang, China

zqshen@ntu.edu.sg Nanyang Technological University Singapore

Abstract Voucher abuse poses a major challenge in e-commerce, where malicious users exploit promotional vouchers for profit. Unfortunately, fraud patterns evolve rapidly over time and across regions, causing distribution shifts that degrade existing detection models unless retrained frequently. To tackle this, we propose the Coupled Attribute–Topology Invariance Learning framework (CATeye). The key challenge arises from coupled attribute–topology shift, where edges built from attribute proximity cause environmentdriven attribute shift to induce shifted topology, thereby amplifying variant signals through GNN message passing. CATeye sees through such coupled shifts with two learnable selectors. First, an Attribute Invariance Selector (AIS) learns node-adaptive masks to filter out non-invariant attributes. Then, conditioned on retained invariant attributes, an Edge Invariance Selector (EIS) samples an invariant subgraph and isolates non-invariant edges. Using the resulting invariant and non-invariant components, CATeye constructs multiple views and applies view-specific objectives to emphasize domain-invariant representations while suppressing domain-specific variations. Experiments on both a proprietary dataset from Lazada, a major Southeast Asian e-commerce platform, and a public benchmark show that CATeye consistently outperforms nine strong domain generalization and graph anomaly detection baselines, achieving up to an 8.61% improvement in average F1 score over the strongest baseline. Source code is publicly available at https://github.com/Tian0426/CATeye.

CCS Concepts • Computing methodologies → Machine learning algorithms; Learning settings; Neural networks.

Keywords Graph anomaly detection, Domain generalization, Invariance learning, Voucher abuse detection

This work is licensed under a Creative Commons Attribution 4.0 International License. CIKM ’26, Rome, Italy © 2026 Copyright held by the owner/author(s). ACM ISBN 979-8-4007-2539-5/2026/11 https://doi.org/10.1145/3799682.3840105

ACM Reference Format: Tian Tian, Shuaicheng Niu, Hao Kuang, Yuanhang Hu, Dong Li, and Zhiqi Shen. 2026. CATeye: Coupled Attribute–Topology Invariance Learning for Voucher Abuse Detection. In Proceedings of the 35th ACM International Conference on Information and Knowledge Management (CIKM ’26), November 07–11, 2026, Rome, Italy. ACM, New York, NY, USA, 8 pages. https://doi.org/ 10.1145/3799682.3840105

1

Introduction

E-commerce platforms widely distribute promotional vouchers to acquire users [5, 14], but this creates significant financial risk. Malicious actors register fake accounts to redeem vouchers, purchase goods for resale, or collude with sellers. Such behaviors cause substantial financial losses and undermine fairness for legitimate users, making accurate and robust voucher abuse detection essential. Voucher abuse often occurs in coordinated groups, where multiple fraudulent accounts share common entities (e.g., devices, emails). Conventional heuristic rules based on shared entities [10] quickly become ineffective as abusers adapted their strategies. To overcome the rigidity of heuristics, subsequent machine learning–based methods operate on tabular data extracted from orders to capture statistical and behavioral patterns [2]. However, they miss the essential inter-order relations. To address this, the graph-based VPGNN [30] models inter-order relations with graph neural networks (GNNs). Despite its promising performance, it relies on frequent fine-tuning with labeled data to handle distribution shifts in new time periods or markets, as discussed below. In practice, voucher abuse is highly dynamic. First, it evolves rapidly over time as abusers continuously adapt to deployed detection models. Emerging methods to bypass detection based on common devices or addresses include using randomized virtual devices and obfuscating delivery addresses. Second, abuse behavior varies substantially across regions. A device type or payment method strongly correlated with abuse in one country may be common among legitimate users in another country. As a result, models trained on a specific time period or country often degrade when applied to new periods or regions unless retrained frequently. In reality, retraining on every new market or campaign cycle is operationally prohibitive given the scale and pace of promotions. These challenges highlight the need for domain generalization (DG), which aims to train models that generalize to unseen target environments without fine-tuning.

CIKM ’26, November 07–11, 2026, Rome, Italy

Observed Variable Desired Invariant Factor Unwanted Variant Factor Generation Dependency

Figure 1: Illustrative model of graph generation under coupled shifts. Environment 𝐸 introduces variation into attributes 𝑋 and structure 𝐴 via 𝑆𝑋 and 𝑆𝐴 , while the invariant factor 𝐶 drives labels 𝑌 . The observed 𝑋 and 𝐴 are generated through {𝐶, 𝑆𝑋 } →𝑋 and {𝑋 , 𝑆𝐴 } → 𝐴. Arrows indicate generation dependencies. Mechanisms causing coupled shifts are highlighted in red.

Voucher abuse graphs exhibit coupled attribute-topology shifts that make generalization especially challenging. In voucher graphs, shifts arise in both attributes and structure. For example, certain device types or payment methods correlate with abuse only in specific regions, and coincidental connections emerge from overlapping purchasing behaviors during large-scale promotional campaigns, resulting in variant attributes and connections that harm generalization. Moreover, variant attributes can further induce environmentdependent structural shifts, since edges are constructed from attribute proximity. Under such coupled shifts, GNN message passing propagates variant signals through shift-induced edges, amplifying domain-specific patterns that do not generalize. This unique coupled shift challenges existing domain generalization methods. To address distribution shift, recent advances in graph DG aim to learn representations that remain invariant across source domains [35]. EERM [32] and CaNet [31] enforce invariance in the embedding space via risk extrapolation on virtual environments or environment estimation. Data-centric approaches such as TRACI [36] enhance cross-domain alignment through topologyaware adversarial perturbations and prototypical mixup. However, these approaches assume that node attributes and graph structure vary independently, or that invariance can be fully enforced in the embedding space. Both assumptions fail under coupled shifts, where non-invariant attributes induce shifted edges that GNN message passing then amplifies. This makes existing methods insufficient for robust generalization in voucher abuse detection. Motivated by this, we explicitly isolate non-invariant attributes and shift-induced edges to learn representations that remain reliable under coupled shifts across time periods and regions. To this end, we propose Coupled Attribute–Topology Invariance Learning (CATeye) for generalizable voucher abuse detection. It tackles coupled attribute-topology shifts by explicitly isolating invariant context in both node attributes and graph structure. To achieve this, CATeye introduces an Attribute Invariance Selector to predict node-adaptive binary masks to retain invariant attributes, and an Edge Invariance Selector to extract an invariant subgraph conditioned on the selected attributes. It then constructs multiple views with different degrees of invariance and performs multi-view learning to emphasize stable predictive signals of voucher abuse while discouraging reliance on non-invariant views. Together, CATeye sees through coupled shifts and achieves zero-shot generalization to unseen domains without fine-tuning. Our contributions are summarized as follows:

Tian Tian et al.

• We identify coupled attribute-topology shifts in voucher abuse detection over time and across regions, and formulate the task under such domain shifts as a graph domain generalization problem. This formulation is realistic and well-aligned with practical deployment requirements, enabling zero-shot inference without retraining as new markets and time periods emerge. • We propose a novel Coupled Attribute–Topology invariance learning framework (CATeye) that mitigates the unique coupled shifts in voucher abuse graphs. It jointly separates invariant and non-invariant components in both node attributes and graph structure, and learns invariant representations via multi-view objectives. • We conduct extensive experiments on a real-world voucher abuse detection dataset from Lazada (covering a long time span and two countries in the Southeast Asian e-commerce market), as well as on the public Elliptic dataset. Empirical results demonstrate that CATeye consistently outperforms nine state-of-the-art baselines and yields up to an 8.61% improvement in average F1 score over the strongest baseline.

2

Related Work

Graph anomaly detection for voucher abuse detection. Voucher abuse detection has been studied using graph-based models that capture inter-order relations [30]. More broadly, graph anomaly detection (GAD) is widely applied in fraud detection [15], intrusion detection [7], and spam detection [34]. Most GAD methods implicitly assume training and test data follow the same distribution, which is often violated in practice when anomalous patterns evolve over time or vary across regions, causing severe distribution shifts [20]. To improve robustness, recent works explore augmentation [23, 39], leverage target-domain data during training [8, 28], or perform test-time adaptation [27, 37]. In this work, we make the minimal assumption that target-domain data are unavailable during training and focus on the more challenging domain generalization problem. Several studies [9, 11] have shown that GNNs can overfit to variant correlations in the training data and thus degrade under distribution shift, requiring frequent retraining. To address this limitation, we aim to learn models that generalize effectively to future periods and unseen markets in a zero-shot manner. Graph domain generalization (DG). DG aims to train models on multiple source domains that generalize well to unseen target domains without fine-tuning [38]. Although many DG methods have been developed to handle distribution shifts in Euclidean data [1, 3, 16], applying them directly to graph-structured data remains challenging due to the non-Euclidean nature of graphs [35]. Graph-level DG methods mainly extract invariant subgraphs [22, 24, 33] and learn invariant representations via disentanglement objectives [17, 18]. However, they tend to degrade significantly on node-level tasks. Recent attempts extend graph DG to node-level tasks by leveraging risk-extrapolation on virtual environments [32], pseudo-environment estimation [31], data-centric operations [36], and meta-learning [25]. Going beyond these efforts, we focus on voucher abuse graphs with coupled attribute-topology shifts, where attribute shifts induce shifted edges. Existing methods either treat attribute and structure as independent sources of variation, or assume invariance in the embedding space. Thus, they struggle with

CATeye: Coupled Attribute–Topology Invariance Learning for Voucher Abuse Detection Training

Loss Functions

Testing

CIKM ’26, November 07–11, 2026, Rome, Italy

denote its 𝑘-hop ego-graph, where V𝑔𝑖 = {𝑣 |𝑑 (𝑣𝑔𝑖 , 𝑣) ≤ 𝑘, and 𝑣 ∈ V𝑠 },

Linear Classifier

E𝑔𝑖 = {(𝑖, 𝑗)|(𝑖, 𝑗) ∈ E𝑠 , and 𝑣𝑖 , 𝑣 𝑗 ∈ V𝑔𝑖 }, GNN Encoder

Automatic Coupled Invariance Selection AIS

Automatic Coupled Invariance Selection EIS

...

Invariant Attribute Non-invariant Attribute Invariant Edge Non-invariant Edge

-hop Ego-graph Sampling ... Source Domains

Target Domain

Figure 2: An overview of CATeye. Left: Training and testing pipeline. During training, we sample 𝑘-hop ego-graphs 𝑔 from multiple source graphs { G1 , . . . , G𝑡 }. During inference, an unseen target graph G𝑡𝑒 is evaluated without fine-tuning using only the invariant view 𝑔ˆ𝐼 . Lower right: Attribute Invariance Selector (AIS) and Edge Invariance Selector (EIS) are employed to automatically disentangle node attributes X𝑔 and structure A𝑔 into invariant and noninvariant parts. The resulting components form four views: invariant 𝑔ˆ𝐼 = ( X̂𝐼 , Â𝐼 ), partially invariant 𝑔ˆ𝑃𝐼 = ( X̂𝐼 , Â𝑁 ), and non-invariant 𝑔ˆ𝑁 1 = ( X̂𝑁 , Â𝑁 ) and 𝑔ˆ𝑁 2 = ( X̂𝑁 , Â𝐼 ). Upper right: The framework is optimized with multi-view objectives: LCL and LCE on 𝑔ˆ𝐼 , LPI to suppress non-invariant structure in 𝑔ˆ𝑃𝐼 , and entropy maximization LN to discourage reliance on non-invariant views. Subscripts in the notations after the Automatic Coupled Invariance Selection layer are omitted for simplicity.

coupled shifts. To address this, we explicitly disentangle invariant and variant components in both node attributes and graph structure.

3 Methodology 3.1 Problem Statement For each domain 𝑠, we construct an order graph G𝑠 = (V𝑠 , E𝑠 ) with node attributes X𝑠 = [x1, . . . , x | V𝑠 | ] ⊤ ∈ R | V𝑠 | ×𝑑 , where V𝑠 = {𝑣 1, 𝑣 2, . . . , 𝑣 | V𝑠 | } represents the node set associated with X𝑠 , E𝑠 is the edge set containing all the edges between orders, |V𝑠 | is the number of orders in domain 𝑠, and 𝑑 is the number of attributes collected from buyer profiles and behavioral data. Labels are partially observed as Y𝑠 = [𝑦1, . . . , 𝑦 | V𝑠 | ] ⊤ ∈ {0, 1, −1} | V𝑠 | , where 𝑦𝑖 = 1 denotes an abusive order, 𝑦𝑖 = 0 denotes a normal order, and 𝑦𝑖 = −1 indicates an unlabeled order. We are given a set of historical source graphs G𝑡𝑟 , where G𝑡𝑟 = {G1, G2, . . . , G𝑡 } and each graph represents a distinct domain. Given an unseen target graph G𝑡𝑒 = (V𝑡𝑒 , E𝑡𝑒 ) with node attributes X𝑡𝑒 , our goal is to learn a model on G𝑡𝑟 that accurately predicts abuse on G𝑡𝑒 without any further fine-tuning or adaptation. Note that the node sets and structures of G𝑡𝑟 and G𝑡𝑒 are disjoint, i.e., G𝑡𝑟 ∩ G𝑡𝑒 = ∅, and there exists a distribution shift between source and target graphs. Ego-Graph as instance. We sample 𝑘-hop ego-graphs from each source graph independently to build localized training instances. For the 𝑖-th labeled node in a source graph G𝑠 , let 𝑔𝑖 = (V𝑔𝑖 , E𝑔𝑖 )

(1)

𝑑 (·, ·) is the shortest path distance between two nodes, 𝑣𝑔𝑖 is the central node of 𝑔𝑖 and 𝑘 controls the neighborhood radius. This sampling procedure defines localized instances for scalable training and inference. Each instance is represented as {𝑔𝑖 = (X𝑔𝑖 , A𝑔𝑖 ), 𝑦𝑔𝑖 }, where X𝑔𝑖 ∈ R | V𝑔𝑖 | ×𝑑 is the node attributes of V𝑔𝑖 , A𝑔𝑖 is the adjacency matrix corresponding to E𝑔𝑖 , and 𝑦𝑔𝑖 is the label of the central node. Extracted ego-graphs are denoted as 𝐺𝑠 = [𝑔1, 𝑔2, . . . , 𝑔𝑛𝑠 ], where 𝑛𝑠 is the number of labeled nodes in G𝑠 .

3.2

Coupled Shifts in Graph Generation

Prior graph DG works typically assume non-coupled shifts, where attribute and structure shifts are independent, or assume invariance can be fully enforced in the embedding space, making them less effective at mitigating shifts inherent in voucher abuse graphs. To understand the distribution shift in voucher abuse graphs, we introduce an illustrative model of the graph generation process in Figure 1. This model clarifies how the effects of environment propagate and cause coupled attribute-topology shifts. The illustration includes an invariant factor 𝐶, an environment variable 𝐸, variant factors 𝑆𝑋 and 𝑆𝐴 , node attributes 𝑋 , graph structure 𝐴, and labels 𝑌 . Labels follow a stable mechanism 𝐶 →𝑌 , while environment-dependent variations enter through two variant factors with 𝐸 → 𝑆𝑋 and 𝐸 → 𝑆𝐴 . Observed node attributes and graph structure are generated by {𝐶, 𝑆𝑋 } → 𝑋 and {𝑋, 𝑆𝐴 } → 𝐴. The illustrative model shows how environment-driven variations in both attributes and structure lead to coupled attribute-topology shifts. In particular, attribute shifts induce structural shifts because edges are constructed based on order attributes, causing coupled shifts across both attributes and structure. The mechanisms that characterize coupled shifts are highlighted by red arrows. Motivated by this, we aim to train models that rely on invariant components in both attributes and structure while remaining insensitive to environment-specific variations, enabling robust generalization across time periods and regions.

3.3

Overview of CATeye

Our approach addresses the multi-source graph domain generalization problem in voucher abuse detection using a shift-aware invariance perspective. We seek to mitigate coupled attribute-topology shifts by learning invariant order representations whose predictive relationship to abuse remains stable across different environments. The proposed Coupled Attribute–Topology invariance learning framework (CATeye) consists of two stages: (i) Automatic Coupled Invariance Selection, where the Attribute Invariance Selector (AIS) and Edge Invariance Selector (EIS) automatically disentangle node attributes and graph structure into invariant and non-invariant components, and (ii) Multi-View Invariant Representation Learning, where the decomposed components are combined into multiple views with different levels of invariance and optimized via view-specific objectives to emphasize invariance and suppress environment-specific variation. We present Automatic

CIKM ’26, November 07–11, 2026, Rome, Italy

Tian Tian et al.

Coupled Invariance Selection in Section 3.4 and Multi-View Invariant Representation Learning in Section 3.5. These two stages jointly enable zero-shot generalization to unseen time periods and markets. Figure 2 provides an overview of CATeye.

3.4

Automatic Coupled Invariance Selection

To address coupled shifts, CATeye explicitly disentangles invariant and non-invariant information in both attributes and structure. For each sampled ego-graph, two specialized invariance selection modules, the Attribute Invariance Selector (AIS) and the Edge Invariance Selector (EIS), automatically and adaptively extract its invariant attributes and structure. We describe each module in detail below. Attribute Invariance Selector (AIS). CATeye mitigates domaindependent redundancy in node attributes via a learnable Attribute Invariance Selector. Given a node feature x ∈ R𝑑 , the selector ℎ𝜃𝑥 outputs node-adaptive scores p𝑎 = [𝑝𝑎1 , 𝑝𝑎2 , . . . , 𝑝𝑎𝑑 ] ⊤ = ℎ𝜃𝑥 (x) ∈ R𝑑 . This vector is then transformed into a binary mask m𝑎 ∈ {0, 1}𝑑 using Gumbel-Softmax reparameterization [19], i.e., 𝑚𝑖𝑎 = Gumbel-Softmax(𝑝𝑎𝑖 ), where 𝑖 ∈ {1, 2, ..., 𝑑 }. Each element determines whether the corresponding attribute is retained (𝑚𝑖𝑎 = 1) or discarded (𝑚𝑖𝑎 = 0). The Gumbel-Softmax is defined as follows: 𝜎 (𝑝 )

© log 𝜖 − log(1 − 𝜖) + log 1−𝜎 (𝑝 ) ª Gumbel-Softmax(𝑝) = 𝜎 ­ ®, 𝜏𝑤 « ¬

(2) where 𝜎 (·) is the sigmoid function, 𝜖 ∼ Uniform(0, 1), and 𝜏𝑤 is the temperature controlling the discretization. As 𝜏𝑤 → 0, it approximates the Bernoulli distribution parameterized by 𝑝. The reparameterization ensures differentiable binary discretization. For an ego|V | graph 𝑔, stacking node masks yields M𝑎 = [m𝑎1 , m𝑎2 , ..., m𝑎 𝑔 ]𝑇 ∈ | V | ×𝑑 {0, 1} 𝑔 . The invariant attributes X̂𝐼 and non-invariant attributes X̂𝑁 are derived as: X̂𝐼 = M𝑎 ⊙ X𝑔 ,

X̂𝑁 = (1 | V𝑔 | ×𝑑 − M𝑎 ) ⊙ X𝑔 .

(3)

3.5

Multi-View Invariant Representation Learning

View construction. For each ego-graph 𝑔, we generate four views by combining invariant and non-invariant components: (1) Invariant View 𝑔ˆ𝐼 = ( X̂𝐼 , Â𝐼 ), which provides fully invariant context; (2) Partially Invariant View 𝑔ˆ𝑃𝐼 = ( X̂𝐼 , Â𝑁 ), in which the invariant attributes carry information transferable to unseen domains, although the structure is unreliable for generalization; and (3) Non-Invariant Views: 𝑔ˆ𝑁 1 = ( X̂𝑁 , Â𝑁 ) and 𝑔ˆ𝑁 2 = ( X̂𝑁 , Â𝐼 ), which include noninvariant attributes. With invariant structure but non-invariant attributes, 𝑔ˆ𝑁 2 is still considered non-invariant because structure contributes to invariance only when it connects invariant attributes. 3.5.1 Optimization Objectives. For each source graph G𝑠 ∈ G𝑡𝑟 , we sample labeled ego-graphs 𝐺𝑠 = [𝑔1, 𝑔2, . . . , 𝑔𝑛𝑠 ] with labels y𝑠 = [𝑦𝑔1 , 𝑦𝑔2 , ..., 𝑦𝑔𝑛𝑠 ]. Each ego-graph 𝑔𝑖 is decomposed into four views 𝑔ˆ𝑖,𝑣 , where 𝑣 ∈ {𝐼, 𝑃𝐼, 𝑁 1, 𝑁 2}. A shared GNN encoder 𝑔𝜙 produces representations 𝑧𝑖,𝑣 = 𝑔𝜙 (𝑔ˆ𝑖,𝑣 ) ∈ R𝑑ℎ , where 𝑑ℎ denotes the hidden size, followed by a linear classifier ℎ𝜃 producing prediction 𝑦ˆ𝑖,𝑣 = ℎ𝜃 (𝑧𝑖,𝑣 ) ∈ R2 . We optimize the framework with view-specific objectives designed to encourage invariance and suppress variant shortcuts. Invariant View. It should produce a decisive prediction for the label, and remain domain-invariant, i.e., maxΘ I(𝑔ˆ𝑖,𝐼 ; 𝑦𝑔𝑖 ), s.t. 𝑔ˆ𝑖,𝐼 ⊥ ⊥ 𝐸, where Θ = {𝜃 𝑥 , 𝜙𝑒 , 𝜃 𝑒 , 𝜙, 𝜃 } denotes all learnable parameters, I(·; ·) measures the mutual information between two random variables, and 𝐸 denotes the domain label. We implement this with: LI = LCE (𝑦ˆ𝑖,𝐼 , 𝑦𝑔𝑖 ) +𝜔 CL LCL (𝑔ˆ𝑖,𝐼 ) , | {z } | {z } maximize I(𝑔ˆ𝑖,𝐼 ;𝑦𝑔𝑖 )

(5)

enforce 𝑔ˆ𝑖,𝐼 ⊥⊥𝐸

where LCE is the cross-entropy loss, and LCL is an invarianceinducing contrastive loss. LCL is defined as: h i exp(𝑧𝑖,𝐼 ⊤𝑧𝑚,𝐼 /𝜏) LCL (𝑔ˆ𝑖,𝐼 ) = E − log , (6) ⊤ E [exp(𝑧𝑖,𝐼 𝑧𝑘,𝐼 /𝜏)] 𝑚∈ P (𝑖 ) 𝑘 ∈ P (𝑖 )∪N (𝑖 )

Here, X̂𝐼 contains invariant attributes that are stable across domains, while X̂𝑁 captures non-invariant features that fail to generalize. Edge Invariance Selector (EIS). Because the graph structure is induced by attribute proximity, non-invariant attributes and coincidental overlaps inevitably lead to non-invariant edges. Including these connections in message passing amplifies domain-specific information and degrades generalization. To mitigate this negative effect, CATeye employs the Edge Invariance Selector (EIS) to sample an invariant subgraph. EIS consists of a GNN 𝑔𝜙𝑒 and an MLP ℎ𝜃𝑒 . It first computes node embeddings H = [h1, h2, ..., h | V𝑔 | ]𝑇 = 𝑔𝜙𝑒 ( X̂𝐼 , A𝑔 ), then scores each edge 𝑒𝑖,𝑗 by 𝑝𝑒𝑖 𝑗 = ℎ𝜃𝑒 ([h𝑖 ; h 𝑗 ]), where h𝑖 , h 𝑗 ∈ H, and [·; ·] is the concatenation operation. A binary edge mask is then derived as M𝑖𝑒𝑗 = Gumbel-Softmax(𝑝𝑒𝑖 𝑗 ). An edge from node 𝑣𝑖 to node 𝑣 𝑗 remains in the invariant subgraph if M𝑖𝑒𝑗 = 1 and is dropped otherwise. The resulting invariant structure Â𝐼 and non-invariant structure Â𝑁 are: Â𝐼 = M𝑒 ⊙ A𝑔 ,

Â𝑁 = (1 | V𝑔 | × | V𝑔 | − M𝑒 ) ⊙ A𝑔 .

(4)

Computing edge importance from X̂𝐼 rather than from the original X𝑔 keeps the invariant structure from being disturbed by noninvariant attributes.

where P (𝑖) = {𝑚 : 𝑦𝑔𝑚 = 𝑦𝑔𝑖 , 𝑑𝑔𝑚 ≠ 𝑑𝑔𝑖 } is the set of positives (same class, different domain) and N (𝑖) = {𝑛 : 𝑦𝑔𝑛 ≠ 𝑦𝑔𝑖 } is the set of negatives. 𝜏 is a temperature hyperparameter. LCL encourages invariant embeddings by pulling samples from the same class but different domains to be close. Aggregating same-class pairs across all source domains greatly increases the effective supervision signal, making LCL effective even under severe label scarcity in voucher abuse detection. Partially Invariant View. It should be decisive about the label but less informative compared to the Invariant View, because of its noninvariant structure. We therefore optimize it only when it underperforms the Invariant View, i.e., maxΘ I(𝑔ˆ𝑖,𝑃𝐼 ; 𝑦𝑔𝑖 ), s.t. I(𝑔ˆ𝑖,𝐼 ; 𝑦𝑔𝑖 ) > I(𝑔ˆ𝑖,𝑃𝐼 ; 𝑦𝑔𝑖 ). The practical implementation is as follows:   LPI = LCE (𝑦ˆ𝑖,𝑃𝐼 , 𝑦𝑔𝑖 ) · 1 LCE (𝑦ˆ𝑖,𝑃𝐼 , 𝑦𝑔𝑖 ) ≥ LCE (𝑦ˆ𝑖,𝐼 , 𝑦𝑔𝑖 ) . (7) It prevents the model from relying on non-invariant structure. Non-invariant Views. To discourage reliance on 𝑔ˆ𝑖,𝑁 1 and 𝑔ˆ𝑖,𝑁 2 , i.e., minΘ I(𝑔ˆ𝑖,𝑁 1 ; 𝑦𝑔𝑖 ) + I(𝑔ˆ𝑖,𝑁 2 ; 𝑦𝑔𝑖 ), we maximize prediction entropy as follows: 1 LN = − [H(𝑦ˆ𝑖,𝑁 1 ) + H(𝑦ˆ𝑖,𝑁 2 )], (8) 2

CATeye: Coupled Attribute–Topology Invariance Learning for Voucher Abuse Detection

where H(·) is Shannon entropy. This forces the classifier to remain uncertain on Non-invariant Views. Compared to minimizing the negative cross-entropy, entropy maximization avoids overfitting to the limited available labels, which is particularly beneficial in label-scarce scenarios of the voucher abuse detection task. Overall training objective. The final optimization objective combines all view-specific losses: min LI + 𝜔 PI · LPI + 𝜔 N · LN, Θ

(9)

where 𝜔 PI and 𝜔 N balance the partially invariant and non-invariant view objectives. Collectively, the overall objective guides the AIS and EIS to automatically disentangle invariant and non-invariant information from both attributes and structure. It encourages the encoder to learn invariant representations and suppress environmentdependent correlations.

4 Experiments 4.1 Datasets We evaluate our method on datasets that exhibit natural domain shifts and severe class imbalance, which are challenging for graph domain generalization. Voucher Abuse Detection Dataset. We build a proprietary dataset from an e-commerce platform, Lazada, to study voucher abuse detection under distribution shift. The source domains consist of ID0501–ID0505, i.e., order graphs from the Indonesia market collected on 1–5 May 2025. More details regarding graph construction are presented in Section 4.2. The target domains include 16 order graphs from both Indonesia and Vietnam, covering both promotional campaign days and regular days. The most recent target graph is collected on 25 August 2025, which introduces a nearly four-month temporal gap relative to the source data. This dataset captures domain shifts from both time (evolving abusive patterns) and region (cross-country behavioral differences). Abusive orders account for only a tiny fraction of all orders, making this a highly imbalanced task. Elliptic Dataset. The Elliptic dataset1 [29] is a public benchmark of temporal Bitcoin transaction graphs collected evenly with an interval of about two weeks. Nodes represent transactions, and edges represent Bitcoin flows. The task is to detect illicit transactions under temporal distribution shift and class imbalance.

4.2

Graph Construction for the Voucher Abuse Detection Dataset

We construct one order graph for each day in each region. In each graph, nodes represent individual orders, with 𝑑 = 801 attributes from (i) user profiles (e.g., region, account age), (ii) transaction records (e.g., payment method, purchase amount, timestamp), and (iii) click-path embeddings that encode sequences of user actions using an unsupervised skip-gram model FastText [4]. Graph structure is constructed to capture connections between orders that indicate potential abuse. Two nodes are connected if they satisfy both of the following conditions: (1) profile proximity (shared identifiers such as shipping address) and (2) behavior proximity (overlapping transactional patterns such as near-synchronous checkout and similar 1 https://www.kaggle.com/datasets/ellipticco/elliptic-data-set

CIKM ’26, November 07–11, 2026, Rome, Italy

sellers or product categories), consistent with prior findings [6] that abuse often involves loosely synchronized actions across shared entities. Order labels (abusive or legitimate) are generated using rules curated by domain experts. Because only a small fraction of orders can be annotated with high confidence, labeled training data remains limited.

4.3

Baselines

Besides Empirical Risk Minimization (ERM) [26], we compare CATeye against three classes of state-of-the-art baselines. • Graph anomaly detection method with enhanced generalization: AugAN [39] enriches the training data through data augmentation and uses episodic training to learn from the augmented samples. • General-purpose domain generalization baselines: IRM [3], IBIRM [1], V-REx [16], and DANN [12]. These methods aim to learn domain-invariant predictors across multiple domains. • Graph domain generalization baselines: TRACI [36], EERM [32], and CaNet [31]. TRACI improves generalization via data-centric operations, whereas EERM and CaNet enforce invariance in the embedding space.

4.4

Implementation Details

All models are implemented in PyTorch [21] and trained on a single NVIDIA A100 GPU with 80 GB memory. For CATeye, we use a 2-layer GraphSAGE encoder [13] as 𝑔𝜙 with hidden dimension 𝑑ℎ = 128 and ReLU activation function, followed by a linear classifier ℎ𝜃 . The AIS ℎ𝜃𝑥 is implemented as a two-layer MLP with a hidden size 128, and the EIS consists of a two-layer GNN 𝑔𝜙𝑒 followed by a two-layer MLP ℎ𝜃𝑒 with the same hidden size. To avoid mask collapse, after generating M𝑎 and M𝑒 , we retained only the top 𝜌𝑎 fraction of attributes and the top 𝜌𝑒 fraction of edges by score, with 𝜌𝑎 = 𝜌𝑒 = 0.5. An ablation study is conducted in Section 4.6 to analyze the impact of these two parameters on model performance. For baselines, we follow their official implementations with recommended hyperparameters. For DANN, which is originally designed for domain adaptation, we apply its domain-adversarial objective only on the source domains to align with the DG setting. For the voucher abuse detection dataset, we split the labeled data from ID0501–ID0505 into training and validation sets with equal sizes. The evaluation is conducted on 16 target-domain graphs. To reflect the label scarcity of real-world voucher abuse detection, we use only 50 anomalous nodes and 300 normal nodes per source domain for training, following the actual anomaly rate. For the Elliptic dataset, we use snapshots 6–10 for training and validation, split with a ratio of 60% : 40%, and snapshots 11–43 for testing. To account for the temporal shift, we group the 32 test snapshots into 8 chronological folds, named T1–T8, each containing 4 consecutive snapshots. We perform grid search on the hyperparameters as follows: 𝜔 CL, 𝜔 PI, 𝜔 N ∈ {0.03, 0.1, 0.3, 1.0, 3.0}. The temperature parameters, 𝜏𝑤 for discretization and 𝜏 for the domain-invariant contrastive loss, are set to 0.2 and 0.1, respectively. During inference, we make predictions using only the invariant views of the test ego-graphs, making the model compatible with streaming production pipelines without requiring multi-graph

CIKM ’26, November 07–11, 2026, Rome, Italy

Tian Tian et al.

Table 1: The F1 scores (%) on the voucher abuse detection dataset. The best performance is highlighted in bold, and the second-best performance is underlined. Results from campaign days and regular days are distinguished by different background colors. Target Domain

AugAN

ERM

IRM

IB-IRM

V-REx

DANN

TRACI

EERM

CaNet

CATeye (Ours)

ID0605 ID0606 ID0707 ID0808 ID0625 ID0725 ID0825

66.14±6.27 66.61±5.82 60.64±5.89 55.08±3.82 60.71±4.03 60.88±4.29 61.86±4.44

86.11±0.40 81.68±1.42 78.15±0.85 76.42±2.12 76.97±0.94 76.96±1.77 79.96±1.44

86.58±0.92 82.47±1.55 77.72±1.30 75.68±2.17 75.98±1.02 75.57±2.00 79.10±1.95

86.66±0.64 83.48±1.92 76.83±1.12 76.31±1.75 74.07±0.50 74.50±1.54 78.74±1.51

86.67±0.90 82.86±0.80 78.07±1.16 75.91±2.45 76.75±1.28 77.09±1.41 79.69±1.81

77.14±2.17 68.63±2.61 66.13±5.79 61.12±4.67 63.46±8.22 61.25±9.32 64.44±6.19

81.16±0.34 73.10±0.28 76.41±1.73 70.11±1.88 76.70±1.84 77.19±2.52 75.90±1.49

87.06±1.22 83.48±1.30 80.76±2.25 79.09±2.28 79.47±2.11 78.99±2.00 82.17±1.62

85.67±1.04 81.28±1.61 77.52±1.62 75.23±3.22 77.41±2.54 79.46±2.94 79.88±1.54

88.05±1.05 84.42±2.14 83.24±1.41 82.38±1.94 81.20±1.37 81.33±2.18 84.57±1.34

VN0605 VN0606 VN0607 VN0608 VN0707 VN0808 VN0625 VN0725 VN0825

58.14±5.67 56.92±4.13 66.65±4.99 68.30±5.89 70.67±2.96 64.67±4.68 67.93±4.59 70.09±4.62 67.30±8.73

74.56±2.92 73.58±3.74 76.83±1.92 71.51±3.43 83.71±1.06 82.39±1.00 71.05±4.34 81.93±1.90 81.43±1.53

73.15±3.51 71.09±4.05 75.77±2.29 69.67±4.36 82.88±1.50 81.31±0.90 69.66±4.63 80.78±2.06 80.63±1.96

71.73±3.67 69.10±4.58 74.79±2.85 67.33±4.91 81.75±1.54 80.06±0.87 67.24±4.93 79.22±0.97 79.46±2.16

73.91±3.39 73.07±3.58 76.68±2.45 70.96±3.20 83.26±1.27 82.11±1.09 70.90±4.73 81.72±1.77 81.28±1.69

67.32±6.60 64.22±3.28 68.47±3.90 64.47±4.22 72.09±2.53 68.81±2.63 65.13±4.61 72.56±3.73 72.94±3.08

73.43±1.42 72.10±1.56 76.32±1.74 72.83±2.46 80.60±1.52 76.98±1.36 72.39±2.26 80.34±2.58 81.05±1.61

74.40±3.81 70.65±4.84 76.51±2.92 68.83±4.14 83.41±2.12 82.09±2.12 68.88±4.53 79.82±2.69 81.36±2.30

70.59±6.22 70.21±6.63 76.96±4.38 72.01±8.49 84.10±1.38 81.54±1.24 72.59±5.95 82.68±4.13 82.15±3.96

77.56±2.85 76.01±2.71 79.36±1.95 73.02±3.34 86.09±1.60 85.06±1.33 73.15±3.03 83.45±1.53 82.95±1.48

Avg.

63.91

78.33

77.38

76.33

78.18

67.39

76.04

78.56

78.08

81.37

Table 2: The F1 scores (%) on the Elliptic dataset. The best performance is highlighted in bold, and the second-best performance is underlined. Target Domain

AugAN

ERM

IRM

IB-IRM

V-REx

DANN

TRACI

EERM

CaNet

CATeye (Ours)

T1 T2 T3 T4 T5 T6 T7 T8

65.47±1.52 57.42±1.05 42.55±1.98 28.04±7.04 33.01±1.17 41.44±1.83 42.35±3.95 29.36±4.06

92.73±0.48 78.37±3.01 62.34±5.01 54.41±4.56 58.76±2.70 60.88±6.41 67.13±1.56 52.77±2.28

92.04±0.26 79.17±1.81 64.58±4.00 57.76±3.74 60.18±2.12 64.95±5.58 70.64±4.30 56.49±4.47

93.55±0.40 68.46±8.33 44.64±14.95 40.33±15.19 48.34±10.90 49.40±16.31 64.72±6.71 44.22±8.08

92.61±0.36 79.80±1.74 63.71±4.89 56.04±4.43 59.89±2.36 64.46±4.24 67.73±6.77 55.15±4.19

83.95±1.08 73.86±3.85 56.53±8.24 45.77±6.63 48.15±4.23 45.33±4.95 30.75±3.40 26.94±3.58

92.07±0.46 71.99±6.87 52.03±9.41 37.20±11.90 41.16±11.41 41.03±12.00 56.09±13.77 28.77±13.85

89.51±0.63 84.43±0.53 70.30±0.86 60.00±1.19 59.72±0.41 63.76±1.02 54.48±2.44 50.04±1.87

95.13±0.83 83.73±6.21 67.22±11.83 43.03±18.41 49.03±12.80 51.15±18.27 56.64±15.65 36.48±20.85

94.20±1.31 89.74±0.85 76.47±4.95 68.98±2.04 74.04±2.89 71.24±4.87 79.17±4.70 60.84±11.27

Avg.

42.46

65.92

68.23

56.71

67.42

51.41

52.54

66.53

60.30

76.84

context or retraining as new daily graphs arrive. CATeye supports zero-shot deployment to new markets and campaign periods as they emerge. We report the mean and standard deviation of F1 scores over 5 random seeds.

4.5

Main Results

The overall results on the voucher abuse detection dataset are presented in Table 1. CATeye consistently achieves the highest performance across all target domains, with an overall average F1 score of 81.37%, outperforming the strongest baseline by 2.81%. Since all methods share identical constructed graphs, these gains stem entirely from model design. Compared with general-purpose DG methods, i.e., IRM, IB-IRM, V-REx, and DANN, CATeye yields larger and more consistent improvements. The performance gain comes from jointly extracting invariant information from both attributes and structure, rather than learning invariance only in the hidden space. Notably, the improvements are most evident on campaign days, where coincidental overlaps in purchases introduce more unstable edges and variant correlations. By effectively filtering

out such information, CATeye reduces the influence of environmentdependent signals and maintains robust performance in detecting abusive behavior. Among graph DG baselines, TRACI underperforms several strong baselines, suggesting its data-centric transformations fail to address coupled shifts. EERM and CaNet, which enforce embeddinglevel invariance, occasionally achieve second-best on individual domains but lack consistency. They still fall 2.81% and 3.29% short of CATeye, respectively, providing direct empirical evidence that invariance in the embedding space alone cannot resolve coupled attribute–topology shifts. ERM performs competitively when shifts are mild or variant correlations remain predictive, but degrades unpredictably under stronger shifts due to the reliance on unstable signals. Graph anomaly detection methods such as AugAN provide limited improvements, indicating that data augmentation alone is insufficient for generalization under domain shifts. Evaluation on the Elliptic dataset, recorded in Table 2, further highlights the enhanced generalization ability of our approach. CATeye achieves the best average F1 of 76.84%, exceeding the secondbest method by 8.61% and delivering consistent improvements on later test folds, i.e., T4–T7, where temporal shift is larger.

CATeye: Coupled Attribute–Topology Invariance Learning for Voucher Abuse Detection

CIKM ’26, November 07–11, 2026, Rome, Italy

Avg. 80.85 (-0.52) 75.91 (-5.46) 80.30 (-1.07)

stochastic attribute selection with random M𝑎 stochastic edge selection with random M𝑒 EIS conditioned on original X (not X̂𝐼 ) both selections are random

74.87 (-6.50) 80.35 (-1.02) 80.91 (-0.46) 73.62 (-7.75)

CATeye (Ours)

81.37

In summary, the results on both datasets demonstrate that CATeye not only generalizes effectively across time and regions in voucher abuse detection but also performs strongly on a public benchmark with temporal domain shifts. CATeye provides an effective and broadly applicable solution for graph anomaly detection under distribution shift.

4.6

Ablation Study

Effect of each component. We conduct ablation studies to evaluate the effect of the learning objectives for each view and the two invariance selectors. Results are presented in Table 3. Disabling any view-specific objective degrades performance, confirming that each loss term plays a distinct role in supporting generalization. In particular, LPI yields the largest enhancement of 5.46%, indicating that constraining the partially invariant view is crucial to prevent non-invariant structure from contaminating generalization. LCL and LN complement the objectives, showing benefits from strengthening invariant representations and discouraging reliance on non-invariant views. We further replace the learned masks in AIS and EIS with random binary masks. The results demonstrate that both selectors are critical. Randomizing AIS drastically reduces the performance by 6.50%, highlighting the importance of identifying invariant attributes as a complement to invariant structure. Randomizing EIS causes a smaller but still notable degradation of 1.02%, showing that refining the graph structure is useful, though the model is less sensitive to structural shortcuts than to attribute shortcuts. Replacing AIS-filtered X̂𝐼 with original X as EIS input drops F1 by 0.46%, demonstrating that AIS captures genuinely invariant attributes and X̂𝐼 provides more reliable input for EIS. Randomizing both produces the largest performance decline by 7.75%. These results highlight that identifying invariant attributes is especially important, and jointly selecting invariant attributes and edges yields the best generalization against coupled shifts. Sensitivities to hyperparameters. The upper plot in Figure 3 reports the average F1 scores of CATeye across eight test folds of the Elliptic dataset under varying values of hyperparameters 𝜔 CL , 𝜔 PI , and 𝜔 N , respectively. The grey dashed line shows the performance of the second-best baseline for reference. Overall, CATeye consistently outperforms the second-best baseline by a large margin and exhibits stable performance across different values of parameters. This indicates that our method remains robust to

F1 Score (%)

Variants w/o LCL on the invariant view w/o LPI on the partially invariant view w/o LN on non-invariant views

F1 Score (%)

Table 3: Effects of the learning objectives for the views, and the two invariance selectors AIS and EIS. Results are average F1 scores (%) over 16 target domains of the voucher abuse detection dataset. The number in the bracket illustrates the performance gap with CATeye.

78 76 74 72 70 68 78 76 74 72 70 68

Average Performance over Varying CL Average Performance over Varying PI Average Performance over Varying N Second-best Baseline 0.03 0.1 0.3 1.0

3.0

Average Performance over Varying a Average Performance over Varying e Second-best Baseline 0.4 0.5 0.6 0.7

0.8

Figure 3: The plots show the average F1 scores (%) of CATeye across eight test folds of the Elliptic dataset under varying hyperparameters. Top: Effects of 𝜔 CL , 𝜔 PI , and 𝜔 N , which control the loss weights for different views. Bottom: Effects of 𝜌𝑎 and 𝜌𝑒 , which determine the proportion of unmasked invariant attributes and edges retained by the AIS and EIS. The grey dashed line indicates the performance of the second-best baseline for comparison.

the configuration of hyperparameters. The lower plot examines the sensitivity to 𝜌𝑎 and 𝜌𝑒 , which control the proportion of unmasked invariant attributes and edges, respectively. The results show that CATeye remains stable across a broad range of unmask ratios, with performance consistently above the second-best baseline. This indicates that the model effectively leverages both attribute-level and structure-level manipulations without requiring exhaustive tuning of the masking ratios.

5

Conclusion

In this paper, we present the Coupled Attribute–Topology invariance learning (CATeye) for voucher abuse detection under domain shift. To see through coupled shifts in voucher abuse graphs, CATeye automatically extracts invariant information from both node attributes and graph structure, and applies multi-view objectives to emphasize invariant representations and mitigate reliance on environment-specific variations. Extensive experiments on a realworld voucher abuse dataset and the public Elliptic benchmark show that CATeye consistently outperforms nine strong baselines and achieves robust zero-shot generalization to unseen domains.

Acknowledgments This research is partly supported by Alibaba Group and AlibabaNTU Singapore Joint Research Institute (JRI), Nanyang Technological University, Singapore. It is also supported by the RIE2025 Industry Alignment Fund – Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL).

CIKM ’26, November 07–11, 2026, Rome, Italy

6

GenAI Usage Disclosure

We used large language models only to polish the writing and improve the clarity of the manuscript. All research ideas, methods, experiments, analyses, and conclusions were developed and verified by the authors.

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