通过基于锚点的扩散几何近似桥接距离与谱位置编码
Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
AI总结：
本文通过基于锚点的扩散几何近似方法，桥接距离与谱位置编码，提升分子图学习的性能。
摘要：
分子图学习受益于能够捕捉局部邻域和全局拓扑的定位信号。两种广泛使用的家族是源自拉普拉斯或扩散算子的谱编码，以及基于最短路径信息的基于锚点的距离编码，但它们之间的精确关系尚不明确。我们将距离编码解释为扩散几何的低秩替代品，并推导出一个显式的三角测量图，该图从变换后的锚点距离和锚点谱位置中重建截断的扩散坐标，随机正则图上有逐点和Frobenius-gap保证。在使用共享的GNP基于DDI预测骨干的DrugBank分子图上，一种由距离驱动的Nyström方案紧密恢复了扩散几何，且拉普拉斯和距离编码显著优于无编码基线。
英文摘要：
Molecular graph learning benefits from positional signals that capture both local neighborhoods and global topology. Two widely used families are spectral encodings derived from Laplacian or diffusion operators and anchor-based distance encodings built from shortest-path information, yet their precise relationship is poorly understood. We interpret distance encodings as a low-rank surrogate of diffusion geometry and derive an explicit trilateration map that reconstructs truncated diffusion coordinates from transformed anchor distances and anchor spectral positions, with pointwise and Frobenius-gap guarantees on random regular graphs. On DrugBank molecular graphs using a shared GNP-based DDI prediction backbone, a distance-driven Nyström scheme closely recovers diffusion geometry, and both Laplacian and distance encodings substantially outperform a no-encoding baseline.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
