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.

Decomposing and Fusing Intra- and Inter-Sensor Spatio-Temporal Signal for Multi-Sensor Wearable Human Activity Recognition

Wearable Human Activity Recognition (WHAR) is a prominent research area within ubiquitous computing. Multi-sensor synchronous measurement has proven to be more effective for WHAR than using a single sensor. However, existing WHAR methods use shared convolutional kernels for indiscriminate temporal feature extraction across each sensor variable, which fails to effectively capture spatio-temporal relationships of intra-sensor and inter-sensor variables. We propose the DecomposeWHAR model consisting of a decomposition phase and a fusion phase to better model the relationships between modality variables. The decomposition creates high-dimensional representations of each intra-sensor variable through the improved Depth Separable Convolution to capture local temporal features while preserving their unique characteristics. The fusion phase begins by capturing relationships between intra-sensor variables and fusing their features at both the channel and variable levels. Long-range temporal dependencies are modeled using the State Space Model (SSM), and later cross-sensor interactions are dynamically captured through a self-attention mechanism, highlighting inter-sensor spatial correlations. Our model demonstrates superior performance on three widely used WHAR datasets, significantly outperforming state-of-the-art models while maintaining acceptable computational efficiency. Our codes and supplementary materials are available at https://github.com/Anakin2555/DecomposeWHAR.

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.

GraphMoRE: Mitigating Topological Heterogeneity via Mixture of Riemannian Experts

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.

DG-Mamba: Robust and Efficient Dynamic Graph Structure Learning with Selective State Space Models

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.

IGL-Bench: Establishing the Comprehensive Benchmark for Imbalanced Graph Learning

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 16 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, which is available at https://github.com/RingBDStack/IGL-Bench.

Dynamic Graph Information Bottleneck

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 novel Dynamic 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 the Minimal-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 the MSC Condition, we decompose the overall IB objectives into DGIB$_{MS}$ and DGIB$_C$, in which the DGIB$_{MS}$ channel aims to learn the minimal and sufficient representations, with the DGIB$_{MS}$ 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.

Poincaré Differential Privacy for Hierarchy-Aware Graph Embedding

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, the 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.

Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization

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 Environment-Aware dynamic Graph LEarning (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.

Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification

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.