# Higher-Dimensional Rotary Position Embedding

arXiv: https://arxiv.org/abs/2608.29715 · HTML: https://mlsanity.com/paper/2608.29715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [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)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (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)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [SlimPajama-DC: Understanding Data Combinations for LLM Training](https://mlsanity.com/paper/2309.10818/) (2023)
- [Rope to Nope and Back Again: A New Hybrid Attention Strategy](https://mlsanity.com/paper/2501.18795/) (2025)
- [Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization](https://mlsanity.com/paper/2412.17739/) (2024)
- [Ada-LEval: Evaluating long-context LLMs with length-adaptable benchmarks](https://mlsanity.com/paper/2404.06480/) (2024)
- [Extending the Context of Pretrained LLMs by Dropping Their Positional Embeddings](https://mlsanity.com/paper/2512.12167/) (2025)
- [Meta-rater: A Multi-dimensional Data Selection Method for Pre-training Language Models](https://mlsanity.com/paper/2504.14194/) (2025)
- [ComRoPE: Scalable and Robust Rotary Position Embedding Parameterized by Trainable Commuting Angle Matrices](https://mlsanity.com/paper/2506.03737/) (2025)
- [3D-RPE: Enhancing Long-Context Modeling Through 3D Rotary Position Encoding](https://mlsanity.com/paper/2406.09897/) (2024)
- [Decoupling the "What" and "Where" With Polar Coordinate Positional Embeddings](https://mlsanity.com/paper/2509.10534/) (2025)
- [The Rotary Position Embedding May Cause Dimension Inefficiency in Attention Heads for Long-Distance Retrieval](https://mlsanity.com/paper/2502.11276/) (2025)

## Abstract (arXiv)

Transformers rely on position embedding mechanisms in long context modeling in most cases. Rotary Position Embedding (RoPE) embeds positional information with independent 2D rotations, forming relative position terms in self-attention. However, its pairwise, block-based, and decoupled structure limits deep mixing and robustness across channels. We propose HD-RoPE, which extends RoPE from independent 2D rotations to higher-dimensional rotations and introduces a Paley-I orthogonal basis to obtain balanced, isotropic, and dense phase mixing within each rotation subspace. This significantly enhances channel coupling and rotational degrees of freedom while maintaining orthogonal stability and the relative position closure property. Furthermore, HD-RoPE is easily optimized for engineering efficiency without introducing additional trainable parameters. We have conducted extensive evaluation results demonstrating that HD-RoPE achieves significant performance improvements over standard RoPE across various popular benchmarks and in both long and short contexts.