Do traveling waves make good positional encodings?

Chase van de Geijn, Ayush Paliwal, Timo Lüddecke, Alexander S. Ecker

Keywords: Traveling Waves, RoPE, Relative Positional Encodings, Equivariance, Topographic DL

TL;DR: We propose a simple traveling wave positional encoding and show that it has similar performance and is directly related to RoPE. These encodings have many ties to neuroscience.

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 \emph{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.

Submission Number: 141