Message Tuning Outshines Graph Prompt Tuning: A Prismatic Space Perspective

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.

Existing methods for adapting graph models lack a rigorous theory to measure how well they can adapt. As a result, we don’t know their upper limit of capability. We propose “Prismatic Space Theory”, a geometric way to explain and compute how much a model can achieve during adaptation, and we identify the ceiling of existing methods. Inspired by this theory, we design “Message Tuning”, which injects a few small learnable “guides” into every layer of the model, allowing its adaptation ability to successfully break through the original ceiling. This helps graph AI models perform more stably and effectively in real-world applications such as drug discovery and fraud detection.