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

Abstract: 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.