Do traveling waves make good positional encodings?

• URL: http://arxiv.org/abs/2511.11668v1
• Date: Tue, 11 Nov 2025 14:32:45 GMT
• Title: Do traveling waves make good positional encodings?
• Authors: Chase van de Geijn, Ayush Paliwal, Timo Lüddecke, Alexander S. Ecker,
• Abstract summary: We propose RollPE, a novel positional encoding mechanism based on traveling waves.<n>We show it significantly outperforms traditional absolute positional embeddings.<n>We derive a mathematical equivalence of RollPE to a particular configuration of RoPE.
• Score: 44.55744608160896
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transformers rely on positional encoding to compensate for the inherent permutation invariance of self-attention. Traditional approaches use absolute sinusoidal embeddings or learned positional vectors, while more recent methods emphasize relative encodings to better capture translation equivariances. In this work, we propose RollPE, a novel positional encoding mechanism based on traveling waves, implemented by applying a circular roll operation to the query and key tensors in self-attention. This operation induces a relative shift in phase across positions, allowing the model to compute attention as a function of positional differences rather than absolute indices. We show this simple method significantly outperforms traditional absolute positional embeddings and is comparable to RoPE. We derive a continuous case of RollPE which implicitly imposes a topographic structure on the query and key space. We further derive a mathematical equivalence of RollPE to a particular configuration of RoPE. Viewing RollPE through the lens of traveling waves may allow us to simplify RoPE and relate it to processes of information flow in the brain.

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