Preserving Geometric Integrity in Graph Prompting via Measure-Constrained Optimal Transport
cs.LG
Submitted: 2026-09-20
Updated: 2026-09-20
Comments: 28 pages, 4 figures
Code: https://github.com/Ga1axy0051/MINT
License: http://creativecommons.org/licenses/by/4.0/
The gist: Graph prompt learning enables parameter-efficient adaptation of frozen Graph Neural Networks to downstream tasks through lightweight prompt parameters.
Terminology
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.
Sources
- The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning
- Dynamic Graph Prompting via Topology-Routed Mixed-Curvature Experts
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