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Most social networks can be modeled as heterogeneous graphs. Recently, advanced graph learning methods exploit the rich node properties and topological relationships for downstream tasks. That means that more private information is embedded in the representation. However, the existing privacy-preserving methods only focus on protecting the single type of node attributes or relationships, which neglect the significance of high-order semantic information. To address this issue, we propose a novel Heterogeneous graph neural network with Semantic-aware Differential privacy Guarantees named HeteSDG, which provides a double privacy guarantee and performance trade-off in terms of both graph features and topology. In particular, we first reveal the privacy leakage in heterogeneous graphs and define a membership inference attack with a semantic enhancement (MIS) that will improve the means of member inference attacks by obtaining side background knowledge through semantics. Then we design a two-stage mechanism, which includes the feature attention personalized mechanism and the topology gradient perturbation mechanism, where the privacy-preserving technologies are based on differential privacy. These mechanisms will defend against MIS and provide stronger interpretation, but simultaneously bring in noise for representation learning. To better balance the noise perturbation and learning performance, we utilize a bi-level optimization pattern to allocate a suitable privacy budget for the above two modules. Our experiments on four public benchmarks conduct performance experiments, ablation studies, inference attack verification, etc. The results show the privacy protection capability and generalization of HeteSDG.

Fraudsters engage in diverse patterns and deceptive interactions, allowing them to move effortlessly within online networks. However, current fraud detection methods heavily rely on correlated experiences and often face challenges in adapting to changing fraud patterns. To solve this problem, our paper introduces a fraud detection method called CausalFD . It includes a mechanism that learns the invariant preference behind evolving camouflaged preference as fraud patterns change. Specifically, we first introduce the concept of camouflaged preference in fraud detection to reveal the importance of identifying fraudster behavior variation and invariance for aiding downstream task inference. Next, we design a module called neighborhood heterophily perception (NHP) to measure the level of heterophily between a node and its neighbors. This helps in understanding the node’s surroundings to identify fraud patterns and establish environmental conditions for causal inference. Lastly, we design the preference invariance mining (PIM) module to uncover potential causal relationships among users. This module analyzes user associations using the causal inference mechanism to identify consistent user preferences. The combination of both methods enables the identification of the fraudster’s motives even amidst changing fraud patterns. We conducted extensive experiments on two widely used fraud datasets, and the results demonstrate that our model exhibits excellent capabilities in fraud detection.

Graph Neural networks (GNNs) which are powerful and widely applied models are based on the assumption that graph topologies play key roles in the graph representation learning.However, the existing GNN methods are based on the Euclidean space embedding, which is difficult to represent a variety of graph geometric properties well. Recently, Riemannian geometries have been introduced into GNNs, such as Hyperbolic Graph Neural Networks proposed for the hierarchy-preserving graph representation learning. In Riemannian geometry, the different graph topological structures can be reflected by corresponding curved embedding spaces, such as a hyperbolic space can be understood as a continuous tree-like structure and a spherical space can be understood as a continuous clique. However, most existing non-Euclidean GNNs are based on heuristic, manual statistical, or estimation methods, which is difficult to automatically select the appropriate embedding space for graphs with different topological properties. To deal with this problem, we propose the Adaptive Curvature Exploration Geometric Graph Neural Network to automatically learn high-quality graph representations and explore the embedding space with optimal curvature at the same time. We optimize the multi-objective optimization problem of the graph representation learning and curvature exploration with the multi-agent reinforcement learning and using the Nash Q-learning algorithm to collaboratively train the two agents to reach Nash equilibrium. We construct extensive experiments including synthetic and real-world graph datasets, and the results demonstrate significant and consistent performance improvement and generalization of our method.

Graph is a prevalent data structure employed to represent the relationships between entities, frequently serving as a tool to depict and simulate numerous systems, such as molecules and social networks. However, real-world graphs usually suffer from the size-imbalanced problem in the multi-graph classification, i.e., a long-tailed distribution with respect to the number of nodes. Recent studies find that off-the-shelf Graph Neural Networks (GNNs) would compromise model performance under the long-tailed settings. We investigate this phenomenon and discover that the long-tailed graph distribution greatly exacerbates the discrepancies in structural features. To alleviate this problem, we propose a novel energy-based size-imbalanced learning framework named SIMBA, which smooths the features between head and tail graphs and re-weights them based on the energy propagation. Specifically, we construct a higher-level graph abstraction named Graphs-to-Graph according to the correlations between graphs to link independent graphs and smooths the structural discrepancies. We further devise an energy-based message-passing belief propagation method for re-weighting lower compatible graphs in the training process and further smooth local feature discrepancies. Extensive experimental results over five public size-imbalanced datasets demonstrate the superior effectiveness of the model for size-imbalanced graph classification tasks.

Relational prediction tasks are fundamental in many real-world applications, where data are naturally stored in relational databases (RDBs). Relational Deep Learning (RDL) addresses this problem by modeling RDBs as graphs and applying graph neural networks (GNNs) for end-to-end learning. However, the full-resolution property is commonly adopted as a design principle in graph construction for RDBs to preserve relational semantics, which leads most existing methods to rely on fixed graph structures. In this paper, we propose FROG, a Full-Resolution and Optimizable Graph Structure Learning framework for RDL that formulates relational structure learning as a learnable table role modeling problem, allowing tables to contribute as nodes and edges in message passing. We further design role-driven message passing mechanisms to capture relational semantics, enabling joint optimization of graph structure and GNN representations. To ensure semantic consistency, we introduce functional dependency constraints that regularize representations across table and entity levels. Extensive experiments demonstrate that our method outperforms existing approaches and reveal how table roles impact downstream tasks, offering new insights into graph construction for RDL

We present Graph Foundation Models (GFMs) which have made significant progress in various tasks, but their robustness against domain noise, structural perturbations, and adversarial attacks remains underexplored. A key limitation is the insufficient modeling of hierarchical structural semantics, which are crucial for generalization. In this paper, we propose SA\\(^2\\)GFM, a robust GFM framework that improves domain-adaptive representations through Structure-Aware Semantic Augmentation. First, we encode hierarchical structural priors by transforming entropy-based encoding trees into structure-aware textual prompts for feature augmentation. The enhanced inputs are processed by a self-supervised Information Bottleneck mechanism that distills robust, transferable representations via structure-guided compression. To address negative transfer in cross-domain adaptation, we introduce an expert adaptive routing mechanism, combining a mixture-of-experts architecture with a null expert design. For efficient downstream adaptation, we propose a fine-tuning module that optimizes hierarchical structures through joint intra- and inter-community structure learning. Extensive experiments demonstrate that SA\\(^2\\)GFM outperforms 9 state-of-the-art baselines in terms of effectiveness and robustness against random noise and adversarial perturbations for node and graph classification.

Graph Anomaly Detection (GAD) aims to identify irregular patterns in graph data, and recent works have explored zero-shot generalist GAD to enable generalization to unseen graph datasets. However, existing zero-shot GAD methods largely ignore intrinsic geometric differences across diverse anomaly patterns, substantially limiting their cross-domain generalization. In this work, we reveal that anomaly detectability is highly dependent on the underlying geometric properties and that embedding graphs from different domains into a single static curvature space can distort the structural signatures of anomalies. To address the challenge that a single curvature space cannot capture geometry-dependent graph anomaly patterns, we propose GAD-MoRE, a novel framework for zero-shot Generalizable Graph Anomaly Detection with a Mixture of Riemannian Experts architecture. Specifically, to ensure that each anomaly pattern is modeled in the Riemannian space where it is most detectable, GAD-MoRE employs a set of specialized Riemannian expert networks, each operating in a distinct curvature space. To align raw node features with curvature-specific anomaly characteristics, we introduce an anomaly-aware multi-curvature feature alignment module that projects inputs into parallel Riemannian spaces, enabling the capture of diverse geometric characteristics. Finally, to facilitate better generalization beyond seen patterns, we design a memory-based dynamic router that adaptively assigns each input to the most compatible expert based on historical reconstruction performance on similar anomalies. Extensive experiments in the zero-shot setting demonstrate that GAD-MoRE significantly outperforms state-of-the-art generalist GAD baselines, and even surpasses strong competitors that are few-shot fine-tuned with labeled data from the target domain.

Graph Foundation Models (GFMs) have emerged as a frontier in graph learning, which are expected to deliver transferable representations across diverse tasks. However, GFMs remain constrained by in-memory bottlenecks: they attempt to encode knowledge into model parameters, which limits semantic capacity, introduces heavy lossy compression with conflicts, and entangles graph representation with the knowledge in ways that hinder efficient adaptation, undermining scalability and interpretability. In this work,we propose RAG-GFM, a Retrieval-Augmented Generation aided Graph Foundation Model that offloads knowledge from parameters and complements parameterized learning. To externalize graph knowledge, we build a dual-modal unified retrieval module, where a semantic store from prefix-structured text and a structural store from centrality-based motif. To preserve heterogeneous information, we design a dual-view alignment objective that contrasts both modalities to capture both content and relational patterns. To enable efficient downstream adaptation, we perform in-context augmentation to enrich supporting instances with retrieved texts and motifs as contextual evidence. Extensive experiments on five benchmark graph datasets demonstrate that RAG-GFM consistently outperforms 13 state-of-the-art baselines in both cross-domain node and graph classification, achieving superior effectiveness and efficiency.

We present Graph Foundation Models (GFMs) which have made significant progress in various tasks, but their robustness against domain noise, structural perturbations, and adversarial attacks remains underexplored. A key limitation is the insufficient modeling of hierarchical structural semantics, which are crucial for generalization. In this paper, we propose SA\\(^2\\)GFM, a robust GFM framework that improves domain-adaptive representations through Structure-Aware Semantic Augmentation. First, we encode hierarchical structural priors by transforming entropy-based encoding trees into structure-aware textual prompts for feature augmentation. The enhanced inputs are processed by a self-supervised Information Bottleneck mechanism that distills robust, transferable representations via structure-guided compression. To address negative transfer in cross-domain adaptation, we introduce an expert adaptive routing mechanism, combining a mixture-of-experts architecture with a null expert design. For efficient downstream adaptation, we propose a fine-tuning module that optimizes hierarchical structures through joint intra- and inter-community structure learning. Extensive experiments demonstrate that SA\\(^2\\)GFM outperforms 9 state-of-the-art baselines in terms of effectiveness and robustness against random noise and adversarial perturbations for node and graph classification.

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified latent space, modeling prediction tasks including classification and regression as a form of conditional generation. However, due to the non-Euclidean nature of graph data, features of different curvatures are entangled in the same latent space without releasing their geometric potential. To address this issue, we aim to construt an ideal Riemannian diffusion model to capture distinct manifold signatures of complex graph data and learn their distribution. This goal faces two challenges: numerical instability caused by exponential mapping during the encoding proces and manifold deviation during diffusion generation. To address these challenges, we propose GeoMancer: a novel Riemannian graph diffusion framework for both generation and prediction tasks. To mitigate numerical instability, we replace exponential mapping with an isometric-invariant Riemannian gyrokernel approach and decouple multi-level features onto their respective task-specific manifolds to learn optimal representations. To address manifold deviation, we introduce a manifold-constrained diffusion method and a self-guided strategy for unconditional generation, ensuring that the generated data remains aligned with the manifold signature. Extensive experiments validate the effectiveness of our approach, demonstrating superior performance across a variety of tasks.