# CoPE: Clipped RoPE as A Scalable Free Lunch for Long Context LLMs

arXiv: https://arxiv.org/abs/2602.05258 · HTML: https://mlsanity.com/paper/2602.05258/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 5 Feb 2026.

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

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [Mem0: Building Production-Ready AI Agents with Scalable Long-Term Memory](https://mlsanity.com/paper/2504.19413/) (2025)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [∞Bench: Extending Long Context Evaluation Beyond 100K Tokens](https://mlsanity.com/paper/2402.13718/) (2024)
- [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)
- [MemAgent: Reshaping Long-Context LLM with Multi-Conv RL-based Memory Agent](https://mlsanity.com/paper/2507.02259/) (2025)
- [MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents](https://mlsanity.com/paper/2506.15841/) (2025)
- [How to Train Long-Context Language Models (Effectively)](https://mlsanity.com/paper/2410.02660/) (2024)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [HELMET: How to Evaluate Long-Context Language Models Effectively and Thoroughly](https://mlsanity.com/paper/2410.02694/) (2024)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [WebResearcher: Unleashing unbounded reasoning capability in Long-Horizon Agents](https://mlsanity.com/paper/2509.13309/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [Base of RoPE Bounds Context Length](https://mlsanity.com/paper/2405.14591/) (2024)
- [Massive Values in Self-Attention Modules are the Key to Contextual Knowledge Understanding](https://mlsanity.com/paper/2502.01563/) (2025)
- [LongRoPE2: Near-Lossless LLM Context Window Scaling](https://mlsanity.com/paper/2502.20082/) (2025)

## Built on by (most cited first, 2 of 2)

- [RoPE at the End of Its Rope? Theory, Diagnosis, and Mitigation of Long-Context Failures](https://mlsanity.com/paper/2609.39929/) (2026)
- [WavePrune: One period is often enough for RoPE](https://mlsanity.com/paper/2610.06963/) (2026)

## Abstract (arXiv)

Rotary Positional Embedding (RoPE) is a key component of context scaling in Large Language Models (LLMs). While various methods have been proposed to adapt RoPE to longer contexts, their guiding principles generally fall into two categories: (1) out-of-distribution (OOD) mitigation, which scales RoPE frequencies to accommodate unseen positions, and (2) Semantic Modeling, which posits that the attention scores computed with RoPE should always prioritize semantically similar tokens. In this work, we unify these seemingly distinct objectives through a minimalist intervention, namely CoPE: soft clipping lowfrequency components of RoPE. CoPE not only eliminates OOD outliers and refines semantic signals, but also prevents spectral leakage caused by hard clipping. Extensive experiments demonstrate that simply applying our soft clipping strategy to RoPE yields significant performance gains that scale up to 256k context length, validating our theoretical analysis and establishing CoPE as a new state-of-the-art for length generalization. Our code, data, and models are available at https://github.com/hrlics/CoPE.