# Rethinking RoPE Scaling in Quantized LLM: Theory, Outlier, and Channel-Band Analysis with Weight Rescaling

arXiv: https://arxiv.org/abs/2510.00028 · HTML: https://mlsanity.com/paper/2510.00028/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 30 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [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)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [Efficient Attentions for Long Document Summarization](https://mlsanity.com/paper/2104.02112/) (2021)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [LongLoRA: Efficient Fine-tuning of Long-Context Large Language Models](https://mlsanity.com/paper/2309.12307/) (2023)
- [How to Train Long-Context Language Models (Effectively)](https://mlsanity.com/paper/2410.02660/) (2024)
- [LongAlign: A Recipe for Long Context Alignment of Large Language Models](https://mlsanity.com/paper/2401.18058/) (2024)

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

- [Rotation-Aligned Key Channel Pruning for Efficient Vision-Language Model Inference](https://mlsanity.com/paper/2605.19218/) (2026)
- [When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation](https://mlsanity.com/paper/2608.13365/) (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)

Extending the context window support of large language models (LLMs) is crucial for tasks with long-distance dependencies. RoPE-based interpolation and extrapolation methods, such as linear scaling and frequency-aware schemes, enable longer input length support without retraining, while post-training quantization (PTQ) makes deployment practical. However, we show that combining RoPE position interpolation (PI) with PTQ degrades accuracy due to coupled effects including long-context aliasing, dynamic-range dilation, anisotropy from axis-aligned quantizers vs. rotated RoPE pairs, and outlier shifting that produces position-dependent logit noise. We provide, to the best of our knowledge, the first systematic analysis of the PI+PTQ approach and introduce two practical diagnostics: interpolation pressure (per-band sensitivity to phase scaling) and tail-inflation ratios (outlier shift from short to long contexts). Following the analysis results, we propose Q-ROAR (Quantization, RoPE-interpolation, and Outlier Aware Rescaling), a weight-only, interpolation-aware stabilization of PI for quantized LLMs. Q-ROAR groups RoPE dimensions into a small number of frequency bands and performs a lightweight search over per-band scales for Key and Query weights (with an optional symmetric variant to preserve logit scale). The search is guided by our diagnostics and uses a tiny long-context development dataset, requiring no fine-tuning to the model, no architecture or kernel changes, and no additional deployment overhead. Empirically, Q-ROAR reduces the model's perplexity on long-context workloads by more than 14%, while preserving short-context performance, inference throughput, and compatibility with existing LLM system stacks.