通过测度约束最优传输保持图提示中的几何完整性
Preserving Geometric Integrity in Graph Prompting via Measure-Constrained Optimal Transport
- University of Electronic Science and Technology of China（电子科技大学）
- Tsinghua University（清华大学）
- Western University（韦仕敦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对图提示学习中提示分配失衡问题，提出熵正则化最优传输框架MINT，通过全局耦合分配和边际约束保持几何完整性，在少样本适配中表现竞争力。
AI中文摘要：
图提示学习通过轻量级提示参数，实现了冻结图神经网络对下游任务的参数高效适配。然而，随着路由变得越来越适应节点，即使单个节点-提示匹配在局部仍然有意义，独立优化的局部决策也可能集体地将分配质量集中到有限共享提示库的一小部分子集上。我们提出了MINT（测度完整性传输），一个熵正则化的最优传输框架，将节点到提示的适配形式化为一个全局耦合的分配问题。传输成本有利于局部几何兼容性，而预设的提示侧边际明确控制图范围内的提示利用。我们进一步推导了一个精确的方差分解，将提示侧几何方差分离为保留的提示更新变化和节点内重心离散，以及冻结编码器前向映射的条件稳定性界。在标准引文网络和额外的异嗜图上，MINT在少样本适配中保持竞争力。受控和端到端实验进一步区分了路由和拓扑的作用：固定边际路由控制图范围内的提示利用，并对引文网络产生可测量的端到端效果，而拓扑增强提供了一种互补的、依赖图的机制来解决结构不匹配。代码可在以下网址获取：此https URL。
英文摘要：
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.
