Knowledge Tracing (KT) diagnoses students’ concept mas- tery through continuous learning state monitoring in education. Existing methods primarily focus on studying behavioral sequences based on ID or textual information. While existing methods rely on ID-based sequences or shallow textual features, they often fail to capture (1) the hierarchical evolution of cognitive states and (2) individualized prob- lem difficulty perception due to limited semantic modeling. Therefore, this paper proposes a Large Language Model Hyperbolic Aligned Knowledge Tracing(L-HAKT). First, the teacher agent deeply parses question semantics and explicitly constructs hierarchical dependencies of knowledge points; the student agent simulates learning behaviors to generate synthetic data. Then, contrastive learning is performed between synthetic and real data in hyperbolic space to reduce distribution differences in key features such as question difficulty and forgetting patterns. Finally, by optimizing hyperbolic curvature, we explicitly model the tree-like hierarchical structure of knowledge points, precisely characterizing differences in learning curve morphology for knowledge points at different levels. Extensive experiments on four real-world educational datasets validate the effectiveness of our Large Language Model Hyperbolic Aligned Knowledge Tracing (L-HAKT) framework.

The Information Bottleneck (IB) principle facilitates effective representation learning by preserving label-relevant information while compressing irrelevant information. However, its strong reliance on accurate labels makes it inherently vulnerable to label noise, prevalent in real-world scenarios, resulting in significant performance degradation and overfitting. To address this issue, we propose LaT-IB, a novel Label-Noise ResistanT Information Bottleneck method which introduces a "Minimal-Sufficient-Clean" (MSC) criterion. Instantiated as a mutual information regularizer to retain task-relevant information while discarding noise, MSC addresses standard IB’s vulnerability to noisy label supervision. To achieve this, LaT-IB employs a noise-aware latent disentanglement that decomposes the latent representation into components aligned with to the clean label space and the noise space. Theoretically, we first derive mutual information bounds for each component of our objective including prediction, compression, and disentanglement, and moreover prove that optimizing it encourages representations invariant to input noise and separates clean and noisy label information. Furthermore, we design a three-phase training framework: Warmup, Knowledge Injection and Robust Training, to progressively guide the model toward noise-resistant representations. Extensive experiments demonstrate that LaT-IB achieves superior robustness and efficiency under label noise, significantly enhancing robustness and applicability in real-world scenarios with label noise.

Graph Foundation Models (GFMs) are pre-trained on diverse source domains and adapted to unseen targets, enabling broad generalization for graph machine learning. Despite that GFMs have attracted considerable attention recently, their vulnerability to backdoor attacks remains largely underexplored. A compromised GFM can introduce backdoor behaviors into downstream applications, posing serious security risks. However, launching backdoor attacks against GFMs is non-trivial due to three key challenges. (1) Effectiveness: Attackers lack knowledge of the downstream task during pre-training, complicating the assurance that triggers reliably induce misclassifications into desired classes. (2) Stealthiness: The variability in node features across domains complicates trigger insertion that remains stealthy. (3) Persistence: Downstream fine-tuning may erase backdoor behaviors by updating model parameters. To address these challenges, we propose GFM-BA, a novel Backdoor Attack model against Graph Foundation Models. Specifically, we first design a label-free trigger association module that links the trigger to a set of prototype embeddings, eliminating the need for knowledge about downstream tasks to perform backdoor injection. Then, we introduce a node-adaptive trigger generator, dynamically producing node-specific triggers, reducing the risk of trigger detection while reliably activating the backdoor. Lastly, we develop a persistent backdoor anchoring module that firmly anchors the backdoor to fine-tuning-insensitive parameters, enhancing the persistence of the backdoor under downstream adaptation. Extensive experiments demonstrate the effectiveness, stealthiness, and persistence of GFM-BA.

Multi-domain graph pre-training has emerged as a pivotal technique in developing graph foundation models. While it greatly improves the generalization of graph neural networks, its privacy risks under membership inference attacks (MIAs), which aim to identify whether a specific instance was used in training (member), remain largely unexplored. However, effectively conducting MIAs against multi-domain graph pre-trained models is a significant challenge due to: (i) Enhanced Generalization Capability: Multi-domain pre-training reduces the overfitting characteristics commonly exploited by MIAs. (ii) Unrepresentative Shadow Datasets: Diverse training graphs hinder the obtaining of reliable shadow graphs. (iii) Weakened Membership Signals: Embedding-based outputs offer less informative cues than logits for MIAs. To tackle these challenges, we propose MGP-MIA, a novel framework for Membership Inference Attacks against Multi-domain Graph Pre-trained models. Specifically, we first propose a membership signal amplification mechanism that amplifies the overfitting characteristics of target models via machine unlearning. We then design an incremental shadow model construction mechanism that builds a reliable shadow model with limited shadow graphs via incremental learning. Finally, we introduce a similarity-based inference mechanism that identifies members based on their similarity to positive and negative samples. Extensive experiments demonstrate the effectiveness of our proposed MGP-MIA and reveal the privacy risks of multi-domain graph pre-training.

While Graph Foundation Models (GFMs) have achieved notable progress across diverse tasks recently, their robustness under domain noise, structural perturbations, and adversarial attacks remains largely underexplored. A core limitation lies in inadequate modeling of hierarchical structural semantics, which are intrinsic priors and critical for generalization. In this work, we propose SA^2GFM, a robust GFM framework that enhances domain adaptable representations through Structure Aware Semantic Augmentation. First, to embed hierarchical structural priors, we transform entropy based encoding trees into structure aware textual prompts for feature augmentation. The enriched inputs are processed by a novel self supervised Information Bottleneck mechanism that distills robust and transferable representations through structure guided compression. To mitigate negative transfer in cross domain adaptation, we develop an expert adaptive routing mechanism that integrates a mixture of experts architecture with a null expert design. To enable efficient downstream adaptation, we propose a fine tuning module that optimizes hierarchical structures through joint intra and inter community structure learning. Extensive experiments validate the superiority of SA^2GFM in effectiveness and robustness against random noise and adversarial perturbations on node and graph classification, compared with nine state of the art baselines.

Graph condensation reduces large graphs into smaller synthetic ones for efficient training and potential privacy protection. While existing studies demonstrate graph condensation's resilience against membership inference attacks (MIAs), key questions remain unanswered: Can the common MIAs' accuracy truly represent the privacy-preserving capabilities of graph condensation? Does it remain robust against more powerful adversaries? And what are the underlying reasons for its performance? This paper investigates the privacy risks of gradient-matching-based condensation via tailored MIAs. We reveal that existing methods often face a trade-off between performance and generalization, where increasing node diversity can unintentionally amplify privacy leakage. Moreover, existing methods either homogenize nodes of the same class to maximize task-specific performance at the cost of generalization or enhance node diversity by efficiently incorporating additional information to improve model generalization, but such diversity inevitably expands the attack reasoning due to increased data disparity. To better balance performance and privacy, we propose a novel graph condensation framework (HDGC) that investigates privacy issues in graph condensation from a hyperbolic geometric perspective. Specifically, we first leverage hyperbolic geometric properties to constrain gradient-matching directions ( HGGM ), thereby obtaining latent hierarchical semantic guidance when learning the synthetic graph's topology. This mechanism measures node importance in hyperbolic space to enhance model generalization. Subsequently, we introduce hyperbolic adaptive differentially private noise during gradient matching ( HADP ). This perturbation intelligently adjusts noise influence based on local gradient importance and global geometric radius, ensuring diversity among same-class nodes while preserving differential privacy. Finally, relying on the post-processing principle of differential privacy, we incorporate distributionally robust optimization to mitigate excessive utility degradation caused by noise injection without compromising privacy guarantees. Experiments and analyses demonstrate that HDGC effectively captures geometric space characteristics, achieves superior performance, and provides a great foundation for defending inference attacks.

The diffusion model with multiple conditions has received widespread attention in the field of drug design due to its high-quality generation ability. However, the paradigm of directly generating new molecules from conditions used in existing work has not accurately fitted the joint distribution of multiple conditions during the generation process. To address this issue, we propose Graph Diffusion Evolution Model(GDEM) for multi conditional molecule generation. GDEM decomposes the process of molecular generation into a chain-like Markov evolution process, continuously adjusting the molecular structure and gradually approaching the true multi-conditional joint distribution. Meanwhile, in order to effectively train this chain evolution generative model, we also propose a two-stage training approximation method to complete the training of intermediate steps. We validated the effectiveness of GDEM on multiple polymer datasets and small molecule datasets, and the results showed that GDEM has advantages in molecular properties and condition control compared to traditional methods.

Deductive and abductive reasoning are two critical paradigms for analyzing knowledge graphs, enabling applications from financial query answering to scientific discovery. Deductive reasoning on knowledge graphs usually involves retrieving entities that satisfy a complex logical query, while abductive reasoning generates plausible logical hypotheses from observations. Despite their clear synergistic potential, where deduction can validate hypotheses and abduction can uncover deeper logical patterns, existing methods address them in isolation. To bridge this gap, we propose DARK, a unified framework for Deductive and Abductive Reasoning in Knowledge graphs. As a masked diffusion model capable of capturing the bidirectional relationship between queries and conclusions, DARK has two key innovations. First, to better leverage deduction for hypothesis refinement during abductive reasoning, we introduce a self-reflective denoising process that iteratively generates and validates candidate hypotheses against the observed conclusion. Second, to discover richer logical associations, we propose a logic-exploration reinforcement learning approach that simultaneously masks queries and conclusions, enabling the model to explore novel reasoning compositions. Extensive experiments on multiple benchmark knowledge graphs show that DARK achieves competitive performance on both deductive and abductive reasoning tasks, demonstrating the significant benefits of our unified approach.

Graph neural networks have shown remarkable success in exploiting the spatial and temporal patterns on dynamic graphs. However, existing GNNs exhibit poor generalization ability under distribution shifts, which is inevitable in dynamic scenarios. As dynamic graph generation progresses amid evolving latent non-stationary environments, it is imperative to explore their effects on out-of-distribution (OOD) generalization. This paper proposes a novel Evolving Graph Learning framework for OOD generalization (EvoGOOD) by environment-aware invariant pattern recognition. Specifically, we first design an environment sequential variational auto-encoder to model environment evolution and infer underlying environment distribution. Then, we introduce a mechanism for environment-aware invariant pattern recognition, tailored to address environmental diversification through inferred distributions. Finally, we conduct fine-grained causal interventions on individual nodes using a mixture of instantiated environment samples. This approach helps to distinguish spatio-temporal invariant patterns for OOD prediction, especially in non-stationary environments. Experimental results demonstrate the superiority of EvoGOOD on both real-world and synthetic dynamic datasets under distribution shifts. To the best of our knowledge, it is the first attempt to study the dynamic graph OOD generalization problem from the environment evolution perspective.

Dataset condensation has significantly improved model training efficiency, but its application on devices with different computing power brings new requirements for different data sizes. For sparse graph data with non-Euclidean structures, repeated condensation of each scale may lead to significant computational costs. Thus, condensing multiple scale graphs simultaneously is the core of achieving efficient training in different on-device scenarios. Existing efficient works for multi-scale graph dataset condensation mainly perform efficient approximate computation in scale order (large-to-small or small-to-large scales). However, these two commonly used paradigms for multi-scale graph dataset condensation have serious ''scaling down degradation'' and ''scaling up collapse" problems of a graph. The main bottleneck of the above paradigms is whether the effective information of the original graph is fully preserved when consenting to the primary sub-scale (the first of multiple scales), which determines the condensation effect and consistency of all scales. In this paper, we proposed a novel GNN-centric Bi-directional Multi-Scale Graph Dataset Condensation (BiMSGC) framework, to explore unifying paradigms by operating on both large-to-small and small-to-large for multi-scale graph condensation. Based on the mutual information theory, we estimate an optimal ''meso-scale'' to obtain the minimum necessary dense graph preserving the maximum utility information of the original graph, and then we achieve stable and consistent ''bi-directional'' condensation learning by optimizing graph eigenbasis matching with information bottleneck on other scales. Encouraging empirical results on several datasets demonstrates the significant superiority of the proposed framework in graph condensation at different scales.

Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency with a geometric perspective, and has been raised in recent years to explore the efficient message-passing structure of GNNs. However, most empirical studies are based on directly observed graph structures or heuristic topological assumptions, and lack in-depth exploration of underlying optimal information transport structures for downstream tasks. We suggest that graph curvature optimization is more in-depth and essential than directly rewiring or learning for graph structure with richer message-passing characterization and better information transport interpretability. From both graph geometry and information theory perspectives, we propose the novel Discrete Curvature Graph Information Bottleneck (CurvGIB) framework to optimize the information transport structure and learn better node representations simultaneously. CurvGIB advances the Variational Information Bottleneck (VIB) principle for Ricci curvature optimization to learn the optimal information transport pattern for specific downstream tasks. The learned Ricci curvature is used to refine the optimal transport structure of the graph, and the node representation is fully and efficiently learned. Moreover, for the computational complexity of Ricci curvature differentiation, we combine Ricci flow and VIB to deduce a curvature optimization approximation to form a tractable IB objective function. Extensive experiments on various datasets demonstrate the superior effectiveness and interpretability of CurvGIB.

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex geometric shapes, resulting in low-quality embeddings with high distortion. This also constitutes a critical challenge for graph foundation models, which are expected to uniformly handle a wide variety of diverse graph data. Recent studies have indicated that product manifold gains the possibility to address topological heterogeneity. However, the product manifold is still homogeneous, which is inadequate and inflexible for representing the mixed heterogeneous topology. In this paper, we propose a novel Graph Mixture of Riemannian Experts (GraphMoRE) framework to effectively tackle topological heterogeneity by personalized fine-grained topology geometry pattern preservation. Specifically, to minimize the embedding distortion, we propose a topology-aware gating mechanism to select the optimal embedding space for each node. By fusing the outputs of diverse Riemannian experts with learned gating weights, we construct personalized mixed curvature spaces for nodes, effectively embedding the graph into a heterogeneous manifold with varying curvatures at different points. Furthermore, to fairly measure pairwise distances between different embedding spaces, we present a concise and effective alignment strategy. Extensive experiments on real-world and synthetic datasets demonstrate that our method achieves superior performance with lower distortion, highlighting its potential for modeling complex graphs with topological heterogeneity, and providing a novel architectural perspective for graph foundation models.

Graph neural networks (GNNs) provide important prospective insights in applications such as social behavior analysis and financial risk analysis based on their powerful learning capabilities on graph data. Nevertheless, GNNs' predictive performance relies on the quality of task-specific node labels, so it is common practice to improve the model's generalization ability in the downstream execution of decision-making tasks through pre-training. Graph prompting is a prudent choice but risky without taking measures to prevent data leakage. In other words, in high-risk decision scenarios, prompt learning can infer private information by accessing model parameters trained on private data (publishing model parameters in pre-training, i.e., without directly leaking the raw data, is a tacitly accepted trend). However, myriad graph inference attacks necessitate tailored module design and processing to enhance inference capabilities due to variations in supervision signals. In this paper, we propose a novel Prompt-based unifying Inference Attack framework on GNNs, named ProIA. Specifically, ProIA retains the crucial topological information of the graph during pre-training, enhancing the background knowledge of the inference attack model. It then utilizes a unified prompt and introduces additional disentanglement factors in downstream attacks to adapt to task-relevant knowledge. Finally, extensive experiments show that ProIA enhances attack capabilities and demonstrates remarkable adaptability to various inference attacks.

Dynamic graphs exhibit intertwined spatio-temporal evolutionary patterns, widely existing in the real world. Nevertheless, the structure incompleteness, noise, and redundancy result in poor robustness for Dynamic Graph Neural Networks (DGNNs). Dynamic Graph Structure Learning (DGSL) offers a promising way to optimize graph structures. However, aside from encountering unacceptable quadratic complexity, it overly relies on heuristic priors, making it hard to discover underlying predictive patterns. How to efficiently refine the dynamic structures, capture intrinsic dependencies, and learn robust representations, remains under-explored. In this work, we propose the novel DG-Mamba, a robust and efficient Dynamic Graph structure learning framework with the Selective State Space Models (Mamba). To accelerate the spatio-temporal structure learning, we propose a kernelized dynamic message-passing operator that reduces the quadratic time complexity to linear. To capture global intrinsic dynamics, we establish the dynamic graph as a self-contained system with State Space Model. By discretizing the system states with the cross-snapshot graph adjacency, we enable the long-distance dependencies capturing with the selective snapshot scan. To endow learned dynamic structures more expressive with informativeness, we propose the self-supervised Principle of Relevant Information for DGSL to regularize the most relevant yet least redundant information, enhancing global robustness. Extensive experiments demonstrate the superiority of the robustness and efficiency of our DG-Mamba compared with the state-of-the-art baselines against adversarial attacks.

The ''Frontiers in Graph Machine Learning for the Large Model Era (GMLLM'25)'' workshop focuses on advancing graph machine learning (GML) techniques in the context of increasingly large and powerful models. Graphs offer a principled way to represent structured and relational data, making them essential for capturing complex dependencies in knowledge, systems, and behaviors. As the scale and influence of foundation models grow, graph learning stands at a unique vantage point to enhance model robustness, improve interpretability, and integrate domain-specific relational priors. This workshop explores how graph learning can support emerging needs in knowledge reasoning, temporal and multi-hop inference, and AI systems. It also investigates how advances in representation learning, structure-aware generalization, and efficient graph processing can contribute to trustworthy and scalable AI systems. By convening experts in graph learning, knowledge management, and LLMs, the workshop aims to identify core challenges and opportunities of GML in the large model era.

Modern vision-language models (VLMs) develop patch embedding and convolution backbone within vector space, especially Euclidean ones, at the very founding. When expanding VLMs to a galaxy scale for understanding astronomical phenomena, the integration of spherical space for planetary orbits and hyperbolic spaces for black holes raises two formidable challenges. a) The current pretraining model is confined to Euclidean space rather than a comprehensive geometric embedding. b) The predominant architecture lacks suitable backbones for anisotropic physical geometries. In this paper, we introduced Galaxy-Walker, a geometry-aware VLM, for the universe-level vision understanding tasks. We proposed the geometry prompt that generates geometry tokens by random walks across diverse spaces on a multi-scale physical graph, along with a geometry adapter that compresses and reshapes the space anisotropy in a mixture-of-experts manner. Extensive experiments demonstrate the effectiveness of our approach, with Galaxy-Walker achieving state-of-the-art performance in both galaxy property estimation (R2scores up to 0.91 ) and morphology classification tasks (up to +0.17 F1 improvement in challenging features), significantly outperforming both domain-specific models and general-purpose VLMs.

Graph classification is crucial for diverse real-world applications, such as drug discovery and social network analysis. Reinforcement learning (RL) has been introduced to graph tasks for its advantage in sequential decision-making and exploration. However, existing RL-based methods face challenges: improper state/action definitions can trap policies in local optima, while contrastive learning approaches often rely on random sampling, struggling to guarantee effective negative samples. To address these issues, this paper proposes a graph classification framework with stepwise optimization embedded with multi-agent collaboration. Specifically, we first optimize the pooling ratio adjustment agent, adopt more advanced reinforcement learning algorithms, and design richer and more informative action spaces and reward functions to support the agent in conducting more sufficient environmental exploration, thereby approximating the global optimal policy. Additionally, we introduce a sampling agent that adaptively optimizes its sampling strategy during the contrastive learning process, aiming to generate more distinguishable hard negative samples. Extensive experiments on six classic benchmark datasets demonstrate that the proposed method achieves superior performance in graph classification tasks, significantly outperforming existing baseline methods and exhibiting strong competitiveness.

Deep graph learning has gained grand popularity over the past years due to its versatility and success in representing graph data across a wide range of domains. However, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose a significant barrier to comprehending advancements in this field. To bridge this gap, we introduce **IGL-Bench**, a foundational comprehensive benchmark for imbalanced graph learning, embarking on **17** diverse graph datasets and **24** distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, IGL-Bench systematically investigates state-of-the-art IGL algorithms in terms of **effectiveness**, **robustness**, and **efficiency** on node-level and graph-level tasks, with the scope of class-imbalance and topology-imbalance. Extensive experiments demonstrate the potential benefits of IGL algorithms on various imbalanced conditions, offering insights and opportunities in the IGL field. Further, we have developed an open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, available at: https://github.com/RingBDStack/IGL-Bench.

The increasing scale of graph datasets significantly enhances deep learning models but also presents substantial training challenges. Graph dataset condensation has emerged to condense large datasets into smaller yet informative ones that maintain similar test performance. However, these methods require downstream usage to match the original dataset and task, which is impractical in real-world scenarios. Our empirical studies show that existing methods fail in "cross-task" and "cross-dataset" scenarios, often performing worse than training from scratch. To address these challenges, we propose a novel method: Self-supervised and Transferable Graph dataset Condensation (ST-GCond). For cross-task transferability, we propose a task-disentangled meta optimization strategy to adaptively update the condensed graph according to the task relevance, encouraging information preservation for various tasks. For cross-dataset transferability, we propose a multi-teacher self-supervised optimization strategy to incorporate auxiliary self-supervised tasks to inject universal knowledge into the condensed graph. Additionally, we incorporate mutual information guided joint condensation mitigating the potential conflicts and ensure the condensing stability. Experiments on both node-level and graph-level datasets show that ST-GCond outperforms existing methods by 2.5% to 18.7% in all cross-task and cross-dataset scenarios, and also achieves state-of-the-art performance on 5 out of 6 datasets in the single dataset and task scenario.

Graph Foundation Models hold significant potential for advancing multi-domain graph learning, yet their full capabilities remain largely untapped. Existing works show promising task performance with the “pretrain-then-prompt” paradigm, which lacks theoretical foundations to understand why it works and how much knowledge can be transferred from source domains to the target. In this paper, we introduce BRIDGE, a bounded graph foundation model pre-trained on multi-domains with Generalization guarantees. To learn discriminative source knowledge, we align multi-domain graph features with domain-invariant aligners during pre-training. Then, a lightweight Mixture of Experts (MoE) network is proposed to facilitate downstream prompting through self-supervised selective knowledge assembly and transfer. Further, to determine the maximum amount of transferable knowledge, we derive an optimizable generalization error upper bound from a graph spectral perspective given the Lipschitz continuity. Extensive experiments demonstrate the superiority of BRIDGE on both node and graph classification compared with 15 state-of-the-art baselines.

Graph contrastive learning (GCL) enhances the self-supervised learning capacity for graph representation learning. Nevertheless, the previous research has neglected to consider one fundamental nature of GCL -- graph contrastive learning operates as a one-shot learner, guided by the widely utilized noise contrastive estimation (e.g., the InfoNCE loss). Theoretically, to initially investigate the factors that contribute to the one-shot learner essence, we analyze the InfoNCE-based objective and derive its equivalent form of the softmax-based cross-entropy function. It is concluded that the InfoNCE-based GCL is determined to be a (2n-1)-way 1-shot classifier (n is the number of nodes). In this particular context, each sample is indicative of a unique ideational class, and each class has only one sample. Consequently, the one-shot learning nature of GCL leads to the issue of the limited self-supervised signal. To further address the above issue, we propose a One-Shot Learner in Graph Contrastive Learning (OS-GCL). Firstly, we estimate the potential probability distributions of the deterministic node features and discrete graph topology. Secondly, we develop a probabilistic message-passing mechanism to propagate probability (of feature) on probability (of topology). Thirdly, we propose the ProbNCE loss functions to contrast distributions. Extensive experimental results demonstrate the superiority of OS-GCL. To the best of our knowledge, this is the first study to examine the one-shot learning essence and the limited self-supervised signal issue of GCL.

Graph representation learning has become a mainstream method for fraud detection due to its strong expressive power, which focuses on enhancing node representations through improved neighborhood knowledge capture. However, the focus on local interactions leads to imbalanced transmission of global topological information and increased risk of node-specific information being overwhelmed during aggregation due to the imbalance between fraud and benign nodes. In this paper, we first summarize the impact of topology and class imbalance on downstream tasks in GNN-based fraud detection, as the problem of imbalanced supervisory messages is caused by fraudsters' topological behavior obfuscation and identity feature concealment. Based on statistical validation, we propose a novel dual-view graph representation learning method to mitigate Message imbalance in Fraud Detection (MimbFD). Specifically, we design a topological message reachability module for high-quality node representation learning to penetrate fraudsters' camouflage and alleviate insufficient propagation. Then, we introduce a local confounding debiasing module to adjust node representations, enhancing the stable association between node representations and labels to balance the influence of different classes. Finally, we conducted experiments on three public fraud datasets, and the results demonstrate that MimbFD exhibits outstanding performance in fraud detection.

Graph Neural Networks (GNNs) excel in node classification tasks but often assume homophily, where connected nodes share similar labels. This assumption does not hold in many real-world heterophilic graphs. Existing models for heterophilic graphs primarily rely on pairwise relationships, overlooking multi-scale information from higher-order structures. This leads to suboptimal performance, particularly under noise from conflicting class information across nodes. To address these challenges, we propose HPGNN, a novel model integrating Higher-order Personalized PageRank with Graph Neural Networks. HPGNN introduces an efficient high-order approximation of Personalized PageRank (PPR) to capture long-range and multiscale node interactions. This approach reduces computational complexity and mitigates noise from surrounding information. By embedding higher-order structural information into convolutional networks, HPGNN effectively models key interactions across diverse graph dimensions. Extensive experiments on benchmark datasets demonstrate HPGNN’s effectiveness. The model achieves better performance than five out of seven state-of-the-art methods on heterophilic graphs in downstream tasks while maintaining competitive performance on homophilic graphs. HPGNN’s ability to balance multi-scale information and robustness to noise makes it a versatile solution for real-world graph learning challenges. Codes are available at https://github.com/streetcorner/HPGNN.

Graph Neural Network-based methods face privacy leakage risks due to the introduction of topological structures about the targets, which allows attackers to bypass the target's prior knowledge of the sensitive attributes and realize membership inference attacks (MIA) by observing and analyzing the topology distribution. As privacy concerns grow, the assumption of MIA, which presumes that attackers can obtain an auxiliary dataset with the same distribution, is increasingly deviating from reality. In this paper, we categorize the distribution diversity issue in real-world MIA scenarios as an Out-Of-Distribution (OOD) problem, and propose a novel Graph OOD Membership Inference Attack (GOOD-MIA) to achieve cross-domain graph attacks. Specifically, we construct shadow subgraphs with distributions from different domains to model the diversity of real-world data. We then explore the stable node representations that remain unchanged under external influences and consider eliminating redundant information from confounding environments and extracting task-relevant key information to more clearly distinguish between the characteristics of training data and unseen data. This OOD-based design makes cross-domain graph attacks possible. Finally, we perform risk extrapolation to optimize the attack's domain adaptability during attack inference to generalize the attack to other domains. Experimental results demonstrate that GOOD-MIA achieves superior attack performance in datasets designed for multiple domains.

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.

Graph incremental learning (GIL), which continuously updates graph models by sequential knowledge acquisition, has garnered significant interest recently. However, existing GIL approaches focus on task-incremental and class-incremental scenarios within a single domain. Graph domain-incremental learning (Domain-IL), aiming at updating models across multiple graph domains, has become critical with the development of graph foundation models (GFMs), but remains unexplored in the literature. In this paper, we propose **Graph** Domain-Incremental Learning via **K**nowledge Dis**e**ntangl**e**ment and **P**res**er**vation (**GraphKeeper**), to address catastrophic forgetting in Domain-IL scenario from the perspectives of embedding shifts and decision boundary deviations. Specifically, to prevent embedding shifts and confusion across incremental graph domains, we first propose the domain-specific parameter-efficient fine-tuning together with intra- and inter-domain disentanglement objectives. Consequently, to maintain a stable decision boundary, we introduce deviation-free knowledge preservation to continuously fit incremental domains. Additionally, for graphs with unobservable domains, we perform domain-aware distribution discrimination to obtain precise embeddings. Extensive experiments demonstrate the proposed GraphKeeper achieves state-of-the-art results with 6.5%\~16.6% improvement over the runner-up with negligible forgetting. Moreover, we show GraphKeeper can be seamlessly integrated with various representative GFMs, highlighting its broad applicative potential.

Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such cases, we observe that the performance of GC deteriorates significantly, while existing robust graph learning technologies offer only limited effectiveness. Through both empirical investigation and theoretical analysis, we reveal that GC is inherently an intrinsic-dimension-reducing process, synthesizing a condensed graph with lower classification complexity. Although this property is critical for effective GC performance, it remains highly vulnerable to adversarial perturbations. To tackle this vulnerability and improve GC robustness, we adopt the geometry perspective of graph data manifold and propose a novel **M**anifold-constrained **R**obust **G**raph **C**ondensation framework named **MRGC**. Specifically, we introduce three graph data manifold learning modules that guide the condensed graph to lie within a smooth, low-dimensional manifold with minimal class ambiguity, thereby preserving the classification complexity reduction capability of GC and ensuring robust performance under universal adversarial attacks. Extensive experiments demonstrate the robustness of MRGC across diverse attack scenarios.

Inspired by the remarkable success of foundation models in language and vision, Graph Foundation Models (GFMs) hold significant promise for broad applicability across diverse graph tasks and domains. However, existing GFMs struggle with unstable few-shot fine-tuning, where both performance and adaptation efficiency exhibit significant fluctuations caused by the randomness in the support sample selection and structural discrepancies between the pre-trained and target graphs. How to fine-tune GFMs robustly and efficiently to enable trustworthy knowledge transfer across domains and tasks is the major challenge. In this paper, we propose **GRAVER**, a novel **G**enerative g**RA**ph **V**ocabulari**E**s for **R**obust GFM fine-tuning framework that tackles the aforementioned instability via generative augmentations. Specifically, to identify transferable units, we analyze and extract key class-specific subgraph patterns by ego-graph disentanglement and validate their transferability both theoretically and empirically. To enable effective pre-training across diverse domains, we leverage a universal task template based on ego-graph similarity and construct graph vocabularies via graphon-based generative experts. To facilitate robust and efficient prompt fine-tuning, we grave the support samples with in-context vocabularies, where the lightweight MoE-CoE network attentively routes knowledge from source domains. Extensive experiments demonstrate the superiority of GRAVER over **effectiveness**, **robustness**, and **efficiency** on downstream few-shot node and graph classification tasks compared with **15** state-of-the-art baselines.

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.

Adversarial evasion attacks pose significant threats to graph learning, with lines of studies that have improved the robustness of Graph Neural Networks (GNNs).However, existing works rely on priors about clean graphs or attacking strategies, which are often heuristic and inconsistent.To achieve robust graph learning over different types of evasion attacks and diverse datasets, we investigate this problem from a prior-free structure purification perspective.Specifically, we propose a novel Diffusion-based Structure Purification framework named DiffSP, which creatively incorporates the graph diffusion model to learn intrinsic distributions of clean graphs and purify the perturbed structures by removing adversaries under the direction of the captured predictive patterns without relying on priors.DiffSP is divided into the forward diffusion process and the reverse denoising process, during which structure purification is achieved.To avoid valuable information loss during the forward process, we propose an LID-driven nonisotropic diffusion mechanism to selectively inject noise anisotropically.To promote semantic alignment between the clean graph and the purified graph generated during the reverse process, we reduce the generation uncertainty by the proposed graph transfer entropy guided denoising mechanism.Extensive experiments demonstrate the superior robustness of DiffSP against evasion attacks.

Graph contrastive learning (GCL) has demonstrated remarkable efficacy in graph representation learning. However, previous studies have overlooked the inherent conflict that arises when employing graph neural networks (GNNs) as encoders for node-level contrastive learning. This conflict pertains to the partial incongruity between the feature aggregation mechanism of graph neural networks and the embedding distinction characteristic of contrastive learning. Theoretically, to investigate the location and extent of the conflict, we analyze the participation of message-passing from the gradient perspective of InfoNCE loss. Different from contrastive learning in other domains, the conflict in GCL arises due to the presence of certain samples that contribute to both the gradients of positive and negative simultaneously under the manner of message passing, which are opposite optimization directions. To further address the conflict issue, we propose a practical framework called ReGCL, which utilizes theoretical findings of GCL gradients to effectively improve graph contrastive learning. Specifically, two gradient-based strategies are devised in terms of both message passing and loss function to mitigate the conflict. Firstly, a gradient-guided structure learning method is proposed in order to acquire a structure that is adapted to contrastive learning principles. Secondly, a gradient-weighted InfoNCE loss function is designed to reduce the impact of false negative samples with high probabilities, specifically from the standpoint of the graph encoder. Extensive experiments demonstrate the superiority of the proposed method in comparison to state-of-the-art baselines across various node classification benchmarks.

Hierarchy is an important and commonly observed topological property in real-world graphs that indicate the relationships between supervisors and subordinates or the organizational behavior of human groups. As hierarchy is introduced as a new inductive bias into the Graph Neural Networks (GNNs) in various tasks, it implies latent topological relations for attackers to improve their inference attack performance, leading to serious privacy leakage issues. In addition, existing privacy-preserving frameworks suffer from reduced protection ability in hierarchical propagation due to the deficiency of adaptive upper-bound estimation of the hierarchical perturbation boundary. It is of great urgency to effectively leverage the hierarchical property of data while satisfying privacy guarantees. To solve the problem, we propose the Poincar\'e Differential Privacy framework, named PoinDP, to protect the hierarchy-aware graph embedding based on hyperbolic geometry. Specifically, PoinDP first learns the hierarchy weights for each entity based on the Poincar\'e model in hyperbolic space. Then, the Personalized Hierarchy-aware Sensitivity is designed to measure the sensitivity of the hierarchical structure and adaptively allocate the privacy protection strength. Besides, Hyperbolic Gaussian Mechanism (HGM) is proposed to extend the Gaussian mechanism in Euclidean space to hyperbolic space to realize random perturbations that satisfy differential privacy under the hyperbolic space metric. Extensive experiment results on five real-world datasets demonstrate the proposed PoinDP’s advantages of effective privacy protection while maintaining good performance on the node classification task.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of it to graph generation. The existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Graph condensation (GC) has recently garnered considerable attention due to its ability to reduce large-scale graph datasets while preserving their essential properties. The core concept of GC is to create a smaller, more manageable graph that retains the characteristics of the original graph. Despite the proliferation of graph condensation methods developed in recent years, there is no comprehensive evaluation and in-depth analysis, which creates a great obstacle to understanding the progress in this field. To fill this gap, we develop a comprehensive Graph Condensation Benchmark (GC-Bench) to analyze the performance of graph condensation in different scenarios systematically. Specifically, GC-Bench systematically investigates the characteristics of graph condensation in terms of the following dimensions: effectiveness, transferability, and complexity. We comprehensively evaluate 12 state-of-the-art graph condensation algorithms in node-level and graph-level tasks and analyze their performance in 12 diverse graph datasets. Further, we have developed an easy-to-use library for training and evaluating different GC methods to facilitate reproducible research.The GC-Bench library is available at https://github.com/RingBDStack/GC-Bench.

Dynamic Graphs widely exist in the real world, which carry complicated spatial and temporal feature patterns, challenging their representation learning. Dynamic Graph Neural Networks (DGNNs) have shown impressive predictive abilities by exploiting the intrinsic dynamics. However, DGNNs exhibit limited robustness, prone to adversarial attacks. This paper presents the novelDynamic Graph Information Bottleneck (DGIB) framework to learn robust and discriminative representations. Leveraged by the Information Bottleneck (IB) principle, we first propose the expected optimal representations should satisfy theMinimal-Sufficient-Consensual (MSC) Condition. To compress redundant as well as conserve meritorious information into latent representation, DGIB iteratively directs and refines the structural and feature information flow passing through graph snapshots. To meet theMSC Condition, we decompose the overall IB objectives into DGIBMS and DGIBC, in which the DGIB_MS channel aims to learn the minimal and sufficient representations, with the DGIBC channel guarantees the predictive consensus. Extensive experiments on real-world and synthetic dynamic graph datasets demonstrate the superior robustness of DGIB against adversarial attacks compared with state-of-the-art baselines in the link prediction task. To the best of our knowledge, DGIB is the first work to learn robust representations of dynamic graphs grounded in the information-theoretic IB principle.

Most Graph Neural Networks follow the message-passing paradigm, assuming the observed structure depicts the ground-truth node relationships. However, this fundamental assumption cannot always be satisfied, as real-world graphs are always incomplete, noisy, or redundant. How to reveal the inherent graph structure in a unified way remains under-explored. We proposed PRI-GSL, a Graph Structure Learning framework guided by the Principle of Relevant Information, providing a simple and unified framework for identifying the self-organization and revealing the hidden structure. PRI-GSL learns a structure that contains the most relevant yet least redundant information quantified by von Neumann entropy and Quantum Jensen Shannon divergence. PRI-GSL incorporates the evolution of quantum continuous walk with graph wavelets to encode node structural roles, showing in which way the nodes interplay and self-organize with the graph structure. Extensive experiments demonstrate the superior effectiveness and robustness of PRI-GSL.

Reasoning complex logical queries on incomplete and massive knowledge graphs (KGs) remains a significant challenge. The prevailing method for this problem is query embedding, which embeds KG units (i.e., entities and relations) and complex queries into low-dimensional space. Recent developments in the field show that embedding queries as geometric shapes is a viable means for modeling entity set and logical relationships between them. Despite being promising, current geometric-based methods face challenges in capturing hierarchical structures of complex queries, which leaves considerable room for improvement. This paper presents POINE2, a geometric-based query embedding framework based on hyperbolic geometry to handle complex queries on knowledge graphs. POINE2 maps entities and queries as geometric shapes on a Cartesian product space of Poincaré ball spaces. To capture the hierarchical structures of complex queries, we use the Poincaré radius to represent the different levels of the hierarchy, and we use the aperture of the shape to indicate semantic differences at the same level of the hierarchy. Additionally, POINE2 offers a flexible and expressive definition of logical operations. Experimental results show that POINE2 outperforms existing salient geometric-based embedding methods and significantly improves these methods on evaluation datasets.

Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have attracted increasing concerns. Existing graph condensation methods primarily focus on optimizing the feature matrices of condensed graphs while overlooking the impact of the structure information from the original graphs. To investigate the impact of the structure information, we conduct analysis from the spectral domain and empirically identify substantial Laplacian Energy Distribution (LED) shifts in previous works. Such shifts lead to poor performance in cross-architecture generalization and specific tasks, including anomaly detection and link prediction. In this paper, we propose a novel Structure-broadcasting Graph Dataset Distillation (\textbf{SGDD}) scheme for broadcasting the original structure information to the generation of the synthetic one, which explicitly prevents overlooking the original structure information. Theoretically, the synthetic graphs by SGDD are expected to have smaller LED shifts than previous works, leading to superior performance in both cross-architecture settings and specific tasks. We validate the proposed SGDD~across 9 datasets and achieve state-of-the-art results on all of them: for example, on YelpChi dataset, our approach maintains 98.6\% test accuracy of training on the original graph dataset with 1,000 times saving on the scale of the graph. Moreover, we empirically evaluate there exist 17.6\% $\sim$ 31.4\% reductions in LED shift crossing 9 datasets. Extensive experiments and analysis verify the effectiveness and necessity of the proposed designs. The code will be made public.

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As the generation of dynamic graphs is heavily influenced by latent environments, investigating their impacts on the out-of-distribution (OOD) generalization is critical. However, it remains unexplored with the following two major challenges: **(1)** How to properly model and infer the complex environments on dynamic graphs with distribution shifts? **(2)** How to discover invariant patterns given inferred spatio-temporal environments? To solve these challenges, we propose a novel **E**nvironment-**A**ware dynamic **G**raph **LE**arning (**EAGLE**) framework for OOD generalization by modeling complex coupled environments and exploiting spatio-temporal invariant patterns. Specifically, we first design the environment-aware EA-DGNN to model environments by multi-channel environments disentangling. Then, we propose an environment instantiation mechanism for environment diversification with inferred distributions. Finally, we discriminate spatio-temporal invariant patterns for out-of-distribution prediction by the invariant pattern recognition mechanism and perform fine-grained causal interventions node-wisely with a mixture of instantiated environment samples. Experiments on real-world and synthetic dynamic graph datasets demonstrate the superiority of our method against state-of-the-art baselines under distribution shifts. To the best of our knowledge, we are the first to study OOD generalization on dynamic graphs from the environment learning perspective.

Contrastive Learning (CL) has been proved to be a powerful self-supervised approach for a wide range of domains, including computer vision and graph representation learning. However, the incremental learning issue of CL has rarely been studied, which brings the limitation in applying it to real-world applications. Contrastive learning identifies the samples with the negative ones from the noise distribution that changes in the incremental scenarios. Therefore, only fitting the change of data without noise distribution causes bias, and directly retraining results in low efficiency. To bridge this research gap, we propose a self-supervised Incremental Contrastive Learning (ICL) framework consisting of (i) a novel Incremental InfoNCE (NCE-II) loss function by estimating the change of noise distribution for old data to guarantee no bias with respect to the retraining, (ii) a meta-optimization with deep reinforced Learning Rate Learning (LRL) mechanism which can adaptively learn the learning rate according to the status of the training processes and achieve fast convergence which is critical for incremental learning. Theoretically, the proposed ICL is equivalent to retraining, which is based on solid mathematical derivation. In practice, extensive experiments in different domains demonstrate that, without retraining a new model, ICL achieves up to 16.7x training speedup and 16.8x faster convergence with competitive results.

Learning unbiased node representations for imbalanced samples in the graph has become a more remarkable and important topic. For the graph, a significant challenge is that the topological properties of the nodes (e.g., locations, roles) are unbalanced (topology-imbalance), other than the number of training labeled nodes (quantity-imbalance). Existing studies on topology-imbalance focus on the location or the local neighborhood structure of nodes, ignoring the global underlying hierarchical properties of the graph, i.e., hierarchy. In the real-world scenario, the hierarchical structure of graph data reveals important topological properties of graphs and is relevant to a wide range of applications. We find that training labeled nodes with different hierarchical properties have a significant impact on the node classification tasks and confirm it in our experiments. It is well known that hyperbolic geometry has a unique advantage in representing the hierarchical structure of graphs. Therefore, we attempt to explore the hierarchy-imbalance issue for node classification of graph neural networks with a novelty perspective of hyperbolic geometry, including its characteristics and causes. Then, we propose a novel hyperbolic geometric hierarchy-imbalance learning framework, named HyperIMBA, to alleviate the hierarchy-imbalance issue caused by uneven hierarchy-levels and cross-hierarchy connectivity patterns of labeled nodes. Extensive experimental results demonstrate the superior effectiveness of HyperIMBA for hierarchy-imbalance node classification tasks.

Graph embedding is essential for graph mining tasks. With the prevalence of graph data in real-world applications, many methods have been proposed in recent years to learn high-quality graph embedding for various types of graphs, among which the Generative Adversarial Networks (GAN) based methods attract increasing attention among researchers. However, most GAN-based generator-discriminator frameworks randomly generate the negative samples from the original graph distributions to enhance the training process of the discriminator without considering the noise. In addition, most of these methods only focus on the explicit graph structures and cannot fully capture complex semantics of edges such as various relationships or asymmetry. In order to address these issues, we propose a robust and generalized framework named AGE. It generates fake neighbors as the enhanced negative samples from the implicit distribution, and enables the discriminator and generator to jointly learn robust and generalized node representations. Based on this framework, we propose three models to handle three types of graph data and derive the corresponding optimization algorithms, namely the UG-AGE and DG-AGE for undirected and directed homogeneous graphs, respectively, and the HIN-AGE for heterogeneous information networks. Extensive experiments show that our methods consistently and significantly outperform existing state-of-the-art methods across multiple graph mining tasks.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real-world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL is the first attempt to advance the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of the proposed VIB-GSL.

Topology-imbalance is a graph-specific imbalance problem caused by the uneven topology positions of labeled nodes, which significantly damages the performance of GNNs. What topology-imbalance means and how to measure its impact on graph learning remain under-explored. In this paper, we provide a new understanding of topology-imbalance from a global view of the supervision information distribution in terms of under-reaching and over-squashing, which motivates two quantitative metrics as measurements. In light of our analysis, we propose a novel position-aware graph structure learning framework named PASTEL, which directly optimizes the information propagation path and solves the topology-imbalance issue in essence. Our key insight is to enhance the connectivity of nodes within the same class for more supervision information, thereby relieving the under-reaching and over-squashing phenomena. Specifically, we design an anchor-based position encoding mechanism, which better incorporates relative topology position and enhances the intra-class inductive bias by maximizing the label influence. We further propose a class-wise conflict measure as the edge weights, which benefits the separation of different node classes. Extensive experiments demonstrate the superior potential and adaptability of PASTEL in enhancing GNNs' power in different data annotation scenarios

Social networks are considered to be heterogeneous graph neural networks (HGNNs) with deep learning technological advances. HGNNs, compared to homogeneous data, absorb various aspects of information about individuals in the training stage. That means more information has been covered in the learning result, especially sensitive information. However, the privacy-preserving methods on homogeneous graphs only preserve the same type of node attributes or relationships, which cannot effectively work on heterogeneous graphs due to the complexity. To address this issue, we propose a novel heterogeneous graph neural network privacy-preserving method based on a differential privacy mechanism named HeteDP, which provides a double guarantee on graph features and topology. In particular, we first define a new attack scheme to reveal privacy leakage in the heterogeneous graphs. Specifically, we design a two-stage pipeline framework, which includes the privacy-preserving feature encoder and the heterogeneous link reconstructor with gradients perturbation based on differential privacy to tolerate data diversity and against the attack. To better control the noise and promote model 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 show that the HeteDP method is equipped to resist heterogeneous graph privacy leakage with admirable model generalization.

Generative adversarial network (GAN) is widely used for generalized and robust learning on graph data. However, for non-Euclidean graph data, the existing GAN-based graph representation methods generate negative samples by random walk or traverse in discrete space, leading to the information loss of topological properties (e.g. hierarchy and circularity). Moreover, due to the topological heterogeneity (i.e., different densities across the graph structure) of graph data, they suffer from serious topological distortion problems. In this paper, we proposed a novel Curvature Graph Generative Adversarial Networks method, named CurvGAN, which is the first GAN-based graph representation method in the Riemannian geometric manifold. To better preserve the topological properties, we approximate the discrete structure as a continuous Riemannian geometric manifold and generate negative samples efficiently from the wrapped normal distribution. To deal with the topological heterogeneity, we leverage the Ricci curvature for local structures with different topological properties, obtaining to low-distortion representations. Extensive experiments show that CurvGAN consistently and significantly outperforms the state-of-the-art methods across multiple tasks and shows superior robustness and generalization.

Graph Neural Networks (GNNs) have been widely studied in various graph data mining tasks. Most existing GNNs embed graph data into Euclidean space and thus are less effective to capture the ubiquitous hierarchical structures in real-world networks. Hyperbolic Graph Neural Networks (HGNNs) extend GNNs to hyperbolic space and thus are more effective to capture the hierarchical structures of graphs in node representation learning. In hyperbolic geometry, the graph hierarchical structure can be reflected by the curvatures of the hyperbolic space, and different curvatures can model different hierarchical structures of a graph. However, most existing HGNNs manually set the curvature to a fixed value for simplicity, which achieves a suboptimal performance of graph learning due to the complex and diverse hierarchical structures of the graphs. To resolve this problem, we propose an Adaptive Curvature Exploration Hyperbolic Graph Neural Network named ACE-HGNN to adaptively learn the optimal curvature according to the input graph and downstream tasks. Specifically, ACE-HGNN exploits a multi-agent reinforcement learning framework and contains two agents, ACE-Agent and HGNN-Agent for learning the curvature and node representations, respectively. The two agents are updated by a Nash Q-leaning algorithm collaboratively, seeking the optimal hyperbolic space indexed by the curvature. Extensive experiments on multiple real-world graph datasets demonstrate a significant and consistent performance improvement in model quality with competitive performance and good generalization ability.