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Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation

Published: January 8, 2026 | arXiv ID: 2601.04517v1

By: Zimo Yan , Zheng Xie , Runfan Duan and more

Potential Business Impact:

Helps computers understand molecules better using distances.

Business Areas:
Indoor Positioning Navigation and Mapping

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.

Country of Origin
🇨🇳 China

Page Count
18 pages

Category
Computer Science:
Information Theory