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.

Wide & Deep Learning for Node Classification

Wide & Deep, a simple yet effective learning architecture for recommendation systems developed by Google, has had a significant impact in both academia and industry due to its combination of the memorization ability of generalized linear models and the generalization ability of deep models. Graph convolutional networks (GCNs) remain dominant in node classification tasks; however, recent studies have highlighted issues such as heterophily and expressiveness, which focus on graph structure while seemingly neglecting the potential role of node features. In this paper, we propose a flexible framework GCNIII, which leverages the Wide & Deep architecture and incorporates three techniques: Intersect memory, Initial residual and Identity mapping. We provide comprehensive empirical evidence showing that GCNIII can more effectively balance the trade-off between over-fitting and over-generalization on various semi- and full- supervised tasks. Additionally, we explore the use of large language models (LLMs) for node feature engineering to enhance the performance of GCNIII in cross-domain node classification tasks. Our implementation is available at https://github.com/CYCUCAS/GCNIII.