# URoPE: Universal Relative Position Embedding across Geometric Spaces

arXiv: https://arxiv.org/abs/2604.18747 · HTML: https://mlsanity.com/paper/2604.18747/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 47 references that are in the map.
- First posted on arXiv 20 Apr 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [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)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Center-based 3D Object Detection and Tracking](https://mlsanity.com/paper/2006.11275/) (2020)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries](https://mlsanity.com/paper/2110.06922/) (2021)
- [PETR: Position Embedding Transformation for Multi-View 3D Object Detection](https://mlsanity.com/paper/2203.05625/) (2022)
- [Conditional DETR for Fast Training Convergence](https://mlsanity.com/paper/2108.06152/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Exploring Object-Centric Temporal Modeling for Efficient Multi-View 3D Object Detection](https://mlsanity.com/paper/2303.11926/) (2023)
- [Unifying Flow, Stereo and Depth Estimation](https://mlsanity.com/paper/2211.05783/) (2022)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [Scene Representation Transformer: Geometry-Free Novel View Synthesis Through Set-Latent Scene Representations](https://mlsanity.com/paper/2111.13152/) (2021)

## Built on by (most cited first, 6 of 6)

- [SCoPE: Sightline-Coordinate Positional Encoding for Video Diffusion Transformers](https://mlsanity.com/paper/2606.27345/) (2026)
- [Teaching Video Generators to Remember: Eliciting Dynamic Memory for Out-of-Sight State Evolution](https://mlsanity.com/paper/2605.25333/) (2026)
- [DPPE: Rethinking Camera-Based Positional Encoding for Scaling Multi-View Transformers](https://mlsanity.com/paper/2606.31585/) (2026)
- [MeRoPE: Metric Rotary Position Embedding for Camera-Controlled Video Generation](https://mlsanity.com/paper/2609.01252/) (2026)
- [G-ray: Ray-Level Relative Geometric Position Encoding in Multi-View Vision Transformers under Camera Heterogeneity](https://mlsanity.com/paper/2609.15018/) (2026)
- [WorldRoPE: Probabilistic World-Centric Rotary Embedding for Multi-View Attention](https://mlsanity.com/paper/2610.16337/) (2026)

## Abstract (arXiv)

Relative position embedding has become a standard mechanism for encoding positional information in Transformers. However, existing formulations are typically limited to a fixed geometric space, namely 1D sequences or regular 2D/3D grids, which restricts their applicability to many computer vision tasks that require geometric reasoning across camera views or between 2D and 3D spaces. To address this limitation, we propose URoPE, a universal extension of Rotary Position Embedding (RoPE) to cross-view or cross-dimensional geometric spaces. For each key/value image patch, URoPE samples 3D points along the corresponding camera ray at predefined depth anchors and projects them into the query image plane. Standard 2D RoPE can then be applied using the projected pixel coordinates. URoPE is a parameter-free and intrinsics-aware relative position embedding that is invariant to the choice of global coordinate systems, while remaining fully compatible with existing RoPE-optimized attention kernels. We evaluate URoPE as a plug-in positional encoding for transformer architectures across a diverse set of tasks, including novel view synthesis, 3D object detection, object tracking, and depth estimation, covering 2D-2D, 2D-3D, and temporal scenarios. Experiments show that URoPE consistently improves the performance of transformer-based models across all tasks, demonstrating its effectiveness and generality for geometric reasoning. Our code is available on our project website: https://urope-pe.github.io/.