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

arXiv: https://arxiv.org/abs/2602.01418 · HTML: https://mlsanity.com/paper/2602.01418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 54 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Exploring Plain Vision Transformer Backbones for Object Detection](https://mlsanity.com/paper/2203.16527/) (2022)
- [Simple Copy-Paste is a Strong Data Augmentation Method for Instance Segmentation](https://mlsanity.com/paper/2012.07177/) (2020)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [YOLOv10: Real-Time End-to-End Object Detection](https://mlsanity.com/paper/2405.14458/) (2024)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [CROMA: Remote Sensing Representations with Contrastive Radar-Optical Masked Autoencoders](https://mlsanity.com/paper/2311.00566/) (2023)
- [Recurrent Vision Transformers for Object Detection with Event Cameras](https://mlsanity.com/paper/2212.05598/) (2022)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [A Large Scale Event-based Detection Dataset for Automotive](https://mlsanity.com/paper/2001.08499/) (2020)

## Abstract (arXiv)

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.