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

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 this https URL.

Machine Learning (cs.LG)

arXiv:2609.23547 [cs.LG]

(or arXiv:2609.23547v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.23547 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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