Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space

Graph Neural Networks (GNNs) have shown great success in various graph-based learning tasks. However, it often faces the issue of over-smoothing as the model depth increases, which causes all node representations to converge to a single value and become indistinguishable. This issue stems from the inherent limitations of GNNs, which struggle to distinguish the importance of information from different neighborhoods. In this paper, we introduce MbaGCN, a novel graph convolutional architecture that draws inspiration from the Mamba paradigm-originally designed for sequence modeling. MbaGCN presents a new backbone for GNNs, consisting of three key components: the Message Aggregation Layer, the Selective State Space Transition Layer, and the Node State Prediction Layer. These components work in tandem to adaptively aggregate neighborhood information, providing greater flexibility and scalability for deep GNN models. While MbaGCN may not consistently outperform all existing methods on each dataset, it provides a foundational framework that demonstrates the effective integration of the Mamba paradigm into graph representation learning. Through extensive experiments on benchmark datasets, we demonstrate that MbaGCN paves the way for future advancements in graph neural network research.

Graph Defense Diffusion Model

Graph Neural Networks (GNNs) demonstrate significant potential in various applications but remain highly vulnerable to adversarial attacks, which can greatly degrade their performance. Existing graph purification methods attempt to address this issue by filtering attacked graphs; however, they struggle to effectively defend against multiple types of adversarial attacks simultaneously due to their limited flexibility, and they lack comprehensive modeling of graph data due to their heavy reliance on heuristic prior knowledge. To overcome these challenges, we propose a more versatile approach for defending against adversarial attacks on graphs. In this work, we introduce the Graph Defense Diffusion Model (GDDM), a flexible purification method that leverages the denoising and modeling capabilities of diffusion models. The iterative nature of diffusion models aligns well with the stepwise process of adversarial attacks, making them particularly suitable for defense. By iteratively adding and removing noise, GDDM effectively purifies attacked graphs, restoring their original structure and features. Our GDDM consists of two key components: (1) Graph Structure-Driven Refiner, which preserves the basic fidelity of the graph during the denoising process, and ensures that the generated graph remains consistent with the original scope; and (2) Node Feature-Constrained Regularizer, which removes residual impurities from the denoised graph, further enhances the purification effect. Additionally, we design tailored denoising strategies to handle different types of adversarial attacks, improving the model's adaptability to various attack scenarios. Extensive experiments conducted on three real-world datasets demonstrate that GDDM outperforms state-of-the-art methods in defending against a wide range of adversarial attacks, showcasing its robustness and effectiveness.