← 研踪 PaperTrailACL Anthology · ACL 2026:acl:2026.acl-long.596 · 记录 #1
Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
来源日期（仅到月份） 2026-07
来源记录日期 2026-07
雷达观测 2026-11-01 22:00
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, but the relationship between them is still not well understood. In this paper, we study when anchor-based distance encodings can approximate diffusion geometry. Under a random r-regular graph model, we derive an explicit trilateration map that reconstructs truncated diffusion coordinates from transformed anchor distances and anchor spectral positions, together with pointwise and Frobenius-gap guarantees. On DrugBank with a shared GNP-based DDI backbone, anchor-distance Nyström accurately recovers diffusion geometry, and both DE and LapPE outperform models without positional encodings, with LapPE showing slightly more consistent performance.
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记录 #1 · 2026-07 · 最新观测版本
Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
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, but the relationship between them is still not well understood. In this paper, we study when anchor-based distance encodings can approximate diffusion geometry. Under a random r-regular graph model, we derive an explicit trilateration map that reconstructs truncated diffusion coordinates from transformed anchor distances and anchor spectral positions, together with pointwise and Frobenius-gap guarantees. On DrugBank with a shared GNP-based DDI backbone, anchor-distance Nyström accurately recovers diffusion geometry, and both DE and LapPE outperform models without positional encodings, with LapPE showing slightly more consistent performance.
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