Prompt tuning has become a key mechanism for adapting pre-trained Graph Neural Networks (GNNs) to new downstream tasks. However, existing approaches are predominantly supervised, relying on labeled data to optimize the prompting parameters and typically fine-tuning a task-specific prediction head -- practices that undermine the promise of parameter-efficient adaptation. We propose Unsupervised Graph Prompting Problem (UGPP), a challenging new setting where the pre-trained GNN is kept entirely frozen, labels on the target domain are unavailable, the source data is inaccessible, and the target distribution exhibits covariate shift. To address this, we propose UGPrompt, the first fully unsupervised GNN prompting framework. UGPrompt leverages consistency regularization and pseudo-labeling to train a prompting function, complemented with diversity and domain regularization to mitigate class imbalance and distribution mismatch. Our extensive experiments demonstrate that UGPrompt consistently outperforms state-of-the-art supervised prompting methods with access to labeled data, demonstrating the viability of unsupervised prompting as a practical adaptation paradigm for GNNs.
Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.
Graph Foundation Models (GFMs), built upon the Pre-training and Adaptation paradigm, have emerged as a research hotspot in graph learning. For GNN-based GFMs, graph prompt tuning has become the prevailing adaptation method for downstream tasks. Although recent methods explain why graph prompt tuning works, how to rigorously measure its adaptation capacity remains an open problem. Addressing this problem is critical for understanding the capability limits of graph prompt tuning and for developing more powerful adaptation methods. In this paper, we propose Prismatic Space Theory (PS-Theory), a novel mathematical framework to quantify the capacity of adaptation methods, while focusing on establishing the upper bound for the adaptation capacity of graph prompt tuning. Building upon the proposed PS-Theory, we further introduce Message Tuning for GFMs (MTG), a lightweight approach that injects a small set of learnable message prototypes into each layer of the GNN backbone to adaptively guide message fusion without updating pre-trained weights. Through our PS-Theory, we prove that the adaptation capacity of MTG can exceed the theoretical upper bound of graph prompt tuning. Extensive experiments demonstrate that MTG consistently outperforms graph prompt baselines across diverse benchmark datasets, providing strong empirical support for our theoretical findings.
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.