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arXiv · 2509.22259

Rotary Position Encodings for Graphs

Isaac Reid·Arijit Sehanobish·Cederik Höfs·Bruno Mlodozeniec·Leonhard Vulpius·Federico Barbero·Adrian Weller·Krzysztof Choromanski·Richard E. Turner·Petar Veličković
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Abstract

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.

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Isaac Reid, Arijit Sehanobish, Cederik Höfs, Bruno Mlodozeniec, Leonhard Vulpius, Federico Barbero, Adrian Weller, Krzysztof Choromanski, Richard E. Turner, Petar Veličković. 2025-09-26. Rotary Position Encodings for Graphs. https://arxiv.org/abs/2509.22259

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