提出可迁移图结构的新框架，用黎曼几何建模深层表示空间。
Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
- 基于黎曼几何构建神经向量丛，学习图的内在几何结构。
- 在零样本链接预测与图同构任务中表现优于现有方法。
- 适合对图神经网络几何原理感兴趣的研究者。
基础模型通过预训练-微调范式引发革命，近期研究已将这一成功扩展至图结构。不同于其他模态，图包含丰富的结构模式，但其结构可迁移性仍不清楚。以往研究在离散层面分析共现子结构，本文提出根本问题：共现子结构是否可迁移？其底层理论尚待探索。本文转向从功能行为角度学习可迁移结构，理论上将可迁移子结构与表示空间的内在几何关联。然而，刻画这种内在几何鲜有研究。基于黎曼几何，我们提出图内在几何学习框架Neural Vector Bundle，通过局部坐标解析内在几何。在此基础上设计可预训练的GAUGE架构，构建向量丛、平坦化几何相容的局部坐标，并引入新狄利克雷损失以度量迁移成本。实证验证其在零样本链接预测和图同构等挑战任务中的优越表达能力。
原文摘要 · Abstract (English)
Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework called Neural Vector Bundle, which enables parsing intrinsic geometry with local coordinates. Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.
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