# A Circular Argument : Does RoPE need to be Equivariant for Vision?

arXiv: https://arxiv.org/abs/2511.08368 · HTML: https://mlsanity.com/paper/2511.08368/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 89 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 30 of 62)

- [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)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [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)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)

## Built on by (most cited first, 3 of 3)

- [SpheRoPE: Zero-Shot Optimization-Free 360 Panorama Generation with Spherical RoPE](https://mlsanity.com/paper/2606.32033/) (2026)
- [Do Vision Transformers Need All-to-All Attention? Global Communication Through Elastic Learned Cores](https://mlsanity.com/paper/2605.12491/) (2026)
- [SO(3)-RoPE for Spherical Transformers](https://mlsanity.com/paper/2610.06229/) (2026)

## Abstract (arXiv)

Rotary Positional Encodings (RoPE) have emerged as a highly effective technique for one-dimensional sequences in Natural Language Processing spurring recent progress towards generalizing RoPE to higher-dimensional data such as images and videos. The success of RoPE has been thought to be due to its positional equivariance, i.e. its status as a relative positional encoding. In this paper, we mathematically show RoPE to be one of the most general solutions for equivariant positional embedding in one-dimensional data. Moreover, we show Mixed RoPE to be the analogously general solution for M-dimensional data, if we require commutative generators -- a property necessary for RoPE's equivariance. However, we question whether strict equivariance plays a large role in RoPE's performance. We propose Spherical RoPE, a method analogous to Mixed RoPE, but assumes non-commutative generators. Empirically, we find Spherical RoPE to have the equivalent or better learning behavior compared to its equivariant analogues. This suggests that relative positional embeddings are not as important as is commonly believed, at least within computer vision. We expect this discovery to facilitate future work in positional encodings for vision that can be faster and generalize better by removing the preconception that they must be relative.