We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined _Wave-Induced Rotary Encodings_ (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.
@article{arxiv.2509.22259,
title = {Rotary Position Encodings for Graphs},
author = {Isaac Reid and Arijit Sehanobish and Cederik Höfs and Bruno Mlodozeniec and Leonhard Vulpius and Federico Barbero and Adrian Weller and Krzysztof Choromanski and Richard E. Turner and Petar Veličković},
journal= {arXiv preprint arXiv:2509.22259},
year = {2026}
}