Preserving Geometric Integrity in Graph Prompting via Measure-Constrained Optimal Transport

2026-09-20

AI Summary

本文通过提出MINT方法，利用最优传输框架解决图提示学习中节点自适应导致的几何完整性问题，实现全局耦合分配。

Abstract

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.

Problem

• Graph Prompt Learning
• Node-Adaptive Routing
• Geometric Integrity

Innovation

• Optimal Transport
• Graph Prompt Learning
• Geometric Integrity
• Entropy Regularization
• Variance Decomposition