Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908753113120768 |
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| author | Yan, Zimo Xie, Zheng Duan, Runfan Liu, Chang Du, Wumei |
| author_facet | Yan, Zimo Xie, Zheng Duan, Runfan Liu, Chang Du, Wumei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation Yan, Zimo Xie, Zheng Duan, Runfan Liu, Chang Du, Wumei Information Theory Machine Learning 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. |
| title | Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation |
| topic | Information Theory Machine Learning |
| url | https://arxiv.org/abs/2601.04517 |