Does Graph Prompt Work? A Data Operation Perspective with Theoretical Analysis

In recent years, graph prompting has emerged as a promising research direction, enabling the learning of additional tokens or subgraphs appended to original graphs without requiring retraining of pre-trained graph models across various applications. This novel paradigm, shifting from the traditional "pre-training and fine-tuning" to "pre-training and prompting," has shown significant empirical success in simulating graph data operations, with applications ranging from recommendation systems to biological networks and graph transferring. However, despite its potential, the theoretical underpinnings of graph prompting remain underexplored, raising critical questions about its fundamental effectiveness. The lack of rigorous theoretical proof of why and how much it works is more like a "dark cloud" over the graph prompting area for deeper research. To fill this gap, this paper introduces a theoretical framework that rigorously analyzes graph prompting from a data operation perspective. Our contributions are threefold: First, we provide a formal guarantee theorem, demonstrating graph prompts’ capacity to approximate graph transformation operators, effectively linking upstream and downstream tasks. Second, we derive upper bounds on the error of these data operations for a single graph and extend this discussion to batches of graphs, which are common in graph model training. Third, we analyze the distribution of data operation errors, extending our theoretical findings from linear graph models (e.g., GCN) to non-linear graph models (e.g., GAT). Extensive experiments support our theoretical results and confirm the practical implications of these guarantees.