# DoPE: Denoising Rotary Position Embedding

arXiv: https://arxiv.org/abs/2511.09146 · HTML: https://mlsanity.com/paper/2511.09146/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 12 Nov 2025.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [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)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [KEPLER: A Unified Model for Knowledge Embedding and Pre-trained Language Representation](https://mlsanity.com/paper/1911.06136/) (2019)
- [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)
- [When Attention Sink Emerges in Language Models: An Empirical View](https://mlsanity.com/paper/2410.10781/) (2024)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [KERPLE: Kernelized Relative Positional Embedding for Length Extrapolation](https://mlsanity.com/paper/2205.09921/) (2022)
- [On the Emergence of Position Bias in Transformers](https://mlsanity.com/paper/2502.01951/) (2025)
- [Your Transformer May Not be as Powerful as You Expect](https://mlsanity.com/paper/2205.13401/) (2022)
- [On the Role of Attention Masks and LayerNorm in Transformers](https://mlsanity.com/paper/2405.18781/) (2024)
- [Length Generalization of Causal Transformers without Position Encoding](https://mlsanity.com/paper/2404.12224/) (2024)
- [Massive Values in Self-Attention Modules are the Key to Contextual Knowledge Understanding](https://mlsanity.com/paper/2502.01563/) (2025)
- [Towards Economical Inference: Enabling DeepSeek's Multi-Head Latent Attention in Any Transformer-based LLMs](https://mlsanity.com/paper/2502.14837/) (2025)
- [Functional Interpolation for Relative Positions Improves Long Context Transformers](https://mlsanity.com/paper/2310.04418/) (2023)
- [Position Information Emerges in Causal Transformers Without Positional Encodings via Similarity of Nearby Embeddings](https://mlsanity.com/paper/2501.00073/) (2024)

## Built on by (most cited first, 5 of 5)

- [Attention Sink in Transformers: A Survey on Utilization, Interpretation, and Mitigation](https://mlsanity.com/paper/2604.10098/) (2026)
- [OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond](https://mlsanity.com/paper/2605.19660/) (2026)
- [SnapMLA: Efficient Long-Context MLA Decoding via Hardware-Aware FP8 Quantized Pipelining](https://mlsanity.com/paper/2602.10718/) (2026)
- [Phase Space Attention:A Hairer Lift Circumvents the Single-Layer Induction Obstruction](https://mlsanity.com/paper/2609.32319/) (2026)
- [RoPE at the End of Its Rope? Theory, Diagnosis, and Mitigation of Long-Context Failures](https://mlsanity.com/paper/2609.39929/) (2026)

## Abstract (arXiv)

Positional encoding is essential for large language models (LLMs) to represent sequence order, yet recent studies show that Rotary Position Embedding (RoPE) can induce massive activation. We investigate the source of these instabilities via a spectral analysis of RoPE, and show that its low-frequency components concentrate structured energy, producing low-rank, over-aligned attention patterns. We theoretically reveal that this low-frequency alignment manifests as activation noise, degrading stability during long-context extrapolation. To mitigate this effect, we introduce Denoising Rotary Position Embedding (DoPE), a training-free method that identifies and suppresses noisy attention heads using truncated matrix entropy, then reparameterizes their attention maps with an isotropic Gaussian distribution. Across a range of settings, DoPE improves length extrapolation performance without fine-tuning, increases robustness to perturbations, and boosts both needle-in-a-haystack and many-shot in-context learning tasks. These results suggest that selective positional encoding is key to robust extrapolation. Our project page is Project: https://The-physical-picture-of-LLMs.github.io