Over-smoothing remains a fundamental challenge in deep Graph Neural Networks (GNNs), where repeated message passing causes node representations to become indistinguishable. While existing solutions, such as residual connections and skip layers, alleviate this issue to some extent, they fail to explicitly model how node representations evolve in a node-specific and progressive manner across layers. Moreover, these methods do not take global information into account, which is also crucial for mitigating the over-smoothing problem. To address the aforementioned issues, in this work, we propose a Dual Mamba-enhanced Graph Convolutional Network (DMbaGCN), which is a novel framework that integrates Mamba into GNNs to address over-smoothing from both local and global perspectives. DMbaGCN consists of two modules: the Local State-Evolution Mamba (LSEMba) for local neighborhood aggregation and utilizing Mamba’s selective state space modeling to capture node-specific representation dynamics across layers, and the Global Context-Aware Mamba (GCAMba) that leverages Mamba’s global attention capabilities to incorporate global context for each node. By combining these components, DMbaGCN enhances node discriminability in deep GNNs, thereby mitigating over-smoothing. Extensive experiments on multiple benchmarks demonstrate the effectiveness and efficiency of our method.

Graph Neural Networks (GNNs) are 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 defend effectively against multiple types of adversarial attacks (e.g., targeted attacks and non-targeted attacks) simultaneously due to limited flexibility. Additionally, these methods lack comprehensive modeling of graph data, relying heavily on heuristic prior knowledge. To overcome these challenges, 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 noises (edges), GDDM effectively purifies attacked graphs, restoring their original structures 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 enhancing the purification effect. By designing tailored denoising strategies to handle different types of adversarial attacks, we improve the GDDM's adaptability to various attack scenarios. Furthermore, GDDM demonstrates strong scalability, leveraging its structural properties to seamlessly transfer across similar datasets without retraining. Extensive experiments on three real-world datasets demonstrate that GDDM outperforms state-of-the-art methods in defending against various adversarial attacks, showcasing its robustness and effectiveness.

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. Our code is in https://github.com/hexin5515/MbaGCN.

Recently, with the triumph of deep learning, attention mechanism, and graph convolutional networks in their respective fields, using new representation learning techniques or introducing auxiliary information to improve the representation ability of embedding has become the core content of the recommendation algorithm research. Generally, most existing GNN-based recommendation methods recursively propagate embedding information on the graph structure and capture collaborative signals by exploring the high-level connectivity between users and items. Despite the great success, those methods do not consider the influence of temporal context on user preferences embedding information propagation, nor do they distinguish the contribution of different neighbor node information to the target node. In order to address the two problems, we propose a graph collaborative filtering model TAGCF combing time factors and attention based on the existing method. The model uses the time factor to integrate temporal information into the process of embedding information propagation and uses the attention mechanism to distinguish the influence of embedding information from different neighbors. The effectiveness of TAGCF, time information, and attention mechanism are verified through comparative experiments with multiple baseline methods on the two recommendation system datasets, MovieLens and Amazon-books.

Despite the promising representation learning of graph neural networks (GNNs), the supervised training of GNNs notoriously requires large amounts of labeled data from each application. An effective solution is to apply the transfer learning in graph: using easily accessible information to pre-train GNNs, and fine-tuning them to optimize the downstream task with only a few labels. Recently, many efforts have been paid to design the self-supervised pretext tasks, and encode the universal graph knowledge among the various applications. However, they rarely notice the inherent training objective gap between the pretext and downstream tasks. This significant gap often requires costly fine-tuning for adapting the pre-trained model to downstream problem, which prevents the efficient elicitation of pre-trained knowledge and then results in poor results. Even worse, the naive pre-training strategy usually deteriorates the downstream task, and damages the reliability of transfer learning in graph data. To bridge the task gap, we propose a novel transfer learning paradigm to generalize GNNs, namely graph pre-training and prompt tuning (GPPT). Specifically, we first adopt the masked edge prediction, the most simplest and popular pretext task, to pre-train GNNs. Based on the pre-trained model, we propose the graph prompting function to modify the standalone node into a token pair, and reformulate the downstream node classification looking the same as edge prediction. The token pair is consisted of candidate label class and node entity. Therefore, the pre-trained GNNs could be applied without tedious fine-tuning to evaluate the linking probability of token pair, and produce the node classification decision. The extensive experiments on eight benchmark datasets demonstrate the superiority of GPPT, delivering an average improvement of 4.29% in few-shot graph analysis and accelerating the model convergence up to 4.32X. The code is available in: https://github.com/MingChen-Sun/GPPT.