CurvPrompt Enhances Dynamic Graph Learning with Adaptive Geometry Prompting

Dynamic graph prompting aims to adapt pre-trained temporal models to new, label-scarce tasks by using lightweight prompts. However, existing methods often fall short because they operate within a single, fixed embedding space. This limitation, termed "geometry under-adaptation," arises because the optimal geometric representation for graph data dynamically changes with shifts in local topology, such as clustering and degree heterogeneity. To overcome this, researchers propose CurvPrompt, a topology-routed geometry prompting framework. Instead of a single embedding space, CurvPrompt maintains a collection of Riemannian experts, each designed for different curvatures and paired with a learnable prompt. A topology-aware gate intelligently directs each node-time instance to a select subset of these experts, creating a personalized mixed-curvature representation. CurvPrompt employs a two-stage routing strategy for efficiency and stability: soft routing during pre-training to establish a continuous topology-geometry mapping, and hard Top-K routing with uniform weights for downstream adaptation, especially under limited labels. Extensive evaluations across four benchmark datasets confirm that CurvPrompt substantially improves few-shot link prediction and maintains strong performance on node classification, validating the necessity of geometry-adaptive prompting for dynamic graphs.