Organizations: University of Electronic Science and Technology of China · 2Michigan State University · 3Singapore Management University · 4Tsinghua University · 5Western University
Dynamic graph prompting freezes a pre-trained temporal backbone and adapts it to label-scarce downstream tasks using lightweight prompts. However, existing methods operate within a single, fixed embedding space. In this work, we reveal that temporal shifts in local clustering and degree heterogeneity actively reorganize the edge curvature spectrum---indicating that the optimal representation geometry dynamically evolves with local topology over time. We formalize this unaddressed mismatch as geometry under-adaptation. To overcome this limitation, we propose CurvPrompt, a topology-routed geometry prompting framework for dynamic graphs. Instead of relying on a single space, CurvPrompt maintains a bank of curvature-diverse Riemannian experts, each paired with a learnable prompt. A topology-aware gate dynamically routes each node--time instance to a sparse subset of experts, constructing a personalized mixed-curvature representation. To ensure parameter efficiency and training stability under extreme label scarcity, CurvPrompt employs soft routing during pre-training to build a continuous topology--geometry mapping, and transitions to hard Top-K routing with uniform weights during downstream adaptation. Extensive experiments across four benchmark datasets show that CurvPrompt significantly advances few-shot link prediction while delivering strong, consistent performance on node classification tasks, validating the necessity of geometry-adaptive prompting.
Activities in numerous evolving systems can be represented as dynamic graphs in snapshot form at different time intervals, i.e., discrete-time dynamic graphs (DTDGs). Existing methods show impressive advances in capturing historical temporal evolution patterns in DTDGs, but they focus on addressing an offline learning setting, where models are trained using historical snapshots once and then evaluated to all subsequent graph snapshots without further updating. This fails to capture 1) the nature of evolving complexities across graph snapshots and 2) the distribution shift in the testing graph snapshots. To address these problems, we propose PromptDyG, a novel framework that leverages unsupervised test-time Prompt adaptation for Dynamic Graph learning under a live-update online setting. The key insight is that an expressive dynamic graph prompt can be learned on a frozen backbone via minimization of feature-wise, label-free entropy to efficiently and continuously model the evolving patterns. We show theoretically that this unsupervised prompt adaptation can guarantee a larger similarity margin between positive and negative pairs, facilitating more accurate dynamic predictions. It is further confirmed by our extensive empirical results on six benchmark datasets that show consistent and significant improvements of PromptDyG over state-of-the-art baselines.
Graph prompt learning enables parameter-efficient adaptation of frozen Graph Neural Networks to downstream tasks through lightweight prompt parameters. As routing becomes increasingly node-adaptive, however, independently optimized local decisions can collectively concentrate assignment mass on a small subset of a finite shared prompt bank, even when individual node--prompt matches remain locally meaningful. We propose MINT (Measure-INtegrity Transport), an entropically regularized optimal transport framework that formulates node-to-prompt adaptation as a globally coupled allocation problem. The transport cost favors local geometric compatibility, while a prescribed prompt-side marginal explicitly controls graph-wide prompt utilization. We further derive an exact variance decomposition that separates prompt-side geometric variance into retained prompt-update variation and within-node barycentric dispersion, together with a conditional stability bound for the frozen-encoder forward map. Across standard citation networks and additional heterophilic graphs, MINT remains competitive in few-shot adaptation. Controlled and end-to-end experiments further distinguish the roles of routing and topology: fixed-marginal routing controls graph-wide prompt utilization and has measurable end-to-end effects on citation networks, while topology augmentation provides a complementary, graph-dependent mechanism for addressing structural mismatch. Code is available at https://github.com/Ga1axy0051/MINT.
Dynamic graphs are ubiquitous in real-world systems, and building generalizable dynamic Graph Foundation Models has become a frontier in graph learning. However, dynamic graphs from different domains pose fundamental challenges to unified modeling, as their semantic and temporal patterns are inherently inconsistent, making the multi-domain pre-training difficult. Consequently, the widely used "pretrain-then-finetune" paradigm often suffers from severe negative knowledge transfer. To the best of our knowledge, there exists no multi-domain dynamic GFM. In this work, we propose DyGFM, a Dynamic Graph Foundation Model over multiple domains based on decoupled and divergence-conditioned prompting. To disentangle transferable semantics from the domain-specific dynamics, we introduce a dual-branch pre-training strategy with semantic-temporal decoupling. To alleviate negative transfer during domain adaptation, we further develop a cross-domain routing mechanism with divergence-aware expert selection. To enable efficient downstream fine-tuning, we design a divergence-conditioned prompt generator that injects lightweight, learnable graph prompts tailored to semantic and temporal traits. Extensive experiments on continuous dynamic graph benchmarks demonstrate that DyGFM consistently outperforms 12 state-of-the-art baselines on both node classification and link prediction tasks, achieving superior effectiveness and efficiency.