# MrRoPE: Mixed-radix Rotary Position Embedding

arXiv: https://arxiv.org/abs/2601.22181 · HTML: https://mlsanity.com/paper/2601.22181/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [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)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (2024)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Effective Long-Context Scaling of Foundation Models](https://mlsanity.com/paper/2309.16039/) (2023)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [Advancing Transformer Architecture in Long-Context Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2311.12351/) (2023)
- [Base of RoPE Bounds Context Length](https://mlsanity.com/paper/2405.14591/) (2024)
- [Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization](https://mlsanity.com/paper/2412.17739/) (2024)
- [Resonance RoPE: Improving Context Length Generalization of Large Language Models](https://mlsanity.com/paper/2403.00071/) (2024)
- [LongRoPE2: Near-Lossless LLM Context Window Scaling](https://mlsanity.com/paper/2502.20082/) (2025)

## Built on by (most cited first, 4 of 4)

- [RoVE: Rotary Value Embeddings Attention for Relative Position-dependent Value Pathways](https://mlsanity.com/paper/2606.11275/) (2026)
- [T-RoPE: Time-Aware Rotary Position Embedding for Sequential Recommendation](https://mlsanity.com/paper/2609.30576/) (2026)
- [Anti-Periodic Positional Encoding: M"obius Boundary Conditions Make In-Context Retrieval Reliable](https://mlsanity.com/paper/2607.21405/) (2026)
- [WavePrune: One period is often enough for RoPE](https://mlsanity.com/paper/2610.06963/) (2026)

## Abstract (arXiv)

Rotary Position Embedding (RoPE)-extension refers to modifying or generalizing the Rotary Position Embedding scheme to handle longer sequences than those encountered during pre-training. However, current extension strategies are highly diverse and lack a unified theoretical foundation. In this paper, we propose MrRoPE (Mixed-radix RoPE), a generalized encoding formulation based on a radix system conversion perspective, which elegantly unifies various RoPE-extension approaches as distinct radix conversion strategies. Based on this theory, we introduce two training-free extensions, MrRoPE-Uni and MrRoPE-Pro, which leverage uniform and progressive radix conversion strategies, respectively, to achieve 'train short, test long' generalization. Without fine-tuning, MrRoPE-Pro sustains over 85% recall in the 128K-context Needle-in-a-Haystack test and achieves more than double YaRN's accuracy on Infinite-Bench retrieval and dialogue subsets. Theoretical analysis confirms that MrRoPE-Pro effectively raises the upper bound of RoPE's attainable encoding length, which further validates the reliability and utility of our theory and methodology.