@inproceedings{zimo-etal-2026-bridging,
    title = "Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation",
    author = "Zimo, Yan  and
      Xie, Zheng  and
      Duan, Runfan  and
      Liu, Chang  and
      Du, Wumei",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.596/",
    pages = "13066--13085",
    ISBN = "979-8-89176-390-6",
    abstract = {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 Nystr{\"o}m accurately recovers diffusion geometry, and both DE and LapPE outperform models without positional encodings, with LapPE showing slightly more consistent performance.}
}