Parabolic Position Encoding: Vision-Centric, Principled, Extrapolatable, General

Christoffer Koo Øhrstrøm; Rafael I. Cabral Muchacho; Yifei Dong; Filippos Moumtzidellis; Ronja Güldenring; Florian T. Pokorny; Lazaros Nalpantidis

arXiv · 2602.01418

Parabolic Position Encoding: Vision-Centric, Principled, Extrapolatable, General

Christoffer Koo Øhrstrøm·Rafael I. Cabral Muchacho·Yifei Dong·Filippos Moumtzidellis·Ronja Güldenring·Florian T. Pokorny·Lazaros Nalpantidis

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Abstract

We propose Parabolic Position Encoding (PaPE), a parabola-based position encoding for vision modalities in attention-based architectures. Given a set of vision tokens-such as from videos, event camera streams, images, or point clouds-our objective is to encode their positions while accounting for the characteristics of vision modalities. Prior works have largely extended position encodings from 1D-sequences in language to nD-structures in vision, but only with partial account of vision characteristics. We address this gap by designing PaPE from principles distilled from prior work: translation invariance, rotation invariance (PaPE-RI), distance decay, directionality, and context awareness. Extrapolation experiments on ImageNet-1K show how PaPE extrapolates remarkably well, improving in absolute terms by up to 10.5\% over the next-best encoding. Generality experiments on 8 datasets across 4 modalities show that PaPE is a general vision position encoding, as PaPE matches the best baseline on 5 datasets and exceeds all on 2 datasets. Code is available at https://github.com/DTU-PAS/parabolic-position-encoding.

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Christoffer Koo Øhrstrøm, Rafael I. Cabral Muchacho, Yifei Dong, Filippos Moumtzidellis, Ronja Güldenring, Florian T. Pokorny, Lazaros Nalpantidis. 2026-02-01. Parabolic Position Encoding: Vision-Centric, Principled, Extrapolatable, General. https://arxiv.org/abs/2602.01418

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