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.

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.

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.

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.

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.

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.