Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction

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.

Mitigating Message Imbalance in Fraud Detection with Dual-View Graph Representation Learning

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.

Controllable Logical Hypothesis Generation for Abductive Reasoning in Knowledge Graphs

Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis oversensitivity. To address these challenges, we propose CtrlHGen, a Controllable logcial Hypothesis Generation framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning. To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines.

An Out-Of-Distribution Membership Inference Attack Approach for Cross-Domain Graph Attacks

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.

Galaxy Walker: Geometry-aware VLMs For Galaxy-scale Understanding

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 pre-training 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 ($R^2$ scores 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.

Robust Graph Learning Against Adversarial Evasion Attacks via Prior-Free Diffusion-Based Structure Purification

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.

Discrete Curvature Graph Information Bottleneck

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.

Graph Size-imbalanced Learning with Energy-guided Structural Smoothing

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 \textbf{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 \textit{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.

Bi-Directional Multi-Scale Graph Dataset Condensation via Information Bottleneck

Dataset condensation has significantly improved model training efficiency, but its application on devices with different computing power brings new requirements for different data sizes. 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, for non-Euclidean structures of sparse graph data, 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.

Prompt-based Unifying Inference Attack on Graph Neural Networks

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.