@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://aclanthology.org/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.}
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%0 Conference Proceedings
%T Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
%A Zimo, Yan
%A Xie, Zheng
%A Duan, Runfan
%A Liu, Chang
%A Du, Wumei
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F zimo-etal-2026-bridging
%X 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.
%U https://aclanthology.org/2026.acl-long.596/
%P 13066-13085
Markdown (Informal)
[Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation](https://aclanthology.org/2026.acl-long.596/) (Zimo et al., ACL 2026)
ACL