# Scaling Laws of RoPE-based Extrapolation

arXiv: https://arxiv.org/abs/2310.05209 · HTML: https://mlsanity.com/paper/2310.05209/

## Key facts

- Cited by 125 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [Reducing Activation Recomputation in Large Transformer Models](https://mlsanity.com/paper/2205.05198/) (2022)

## Built on by (most cited first, 30 of 125)

- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [MemAgent: Reshaping Long-Context LLM with Multi-Conv RL-based Memory Agent](https://mlsanity.com/paper/2507.02259/) (2025)
- [SmolVLM: Redefining small and efficient multimodal models](https://mlsanity.com/paper/2504.05299/) (2025)
- [mGTE: Generalized Long-Context Text Representation and Reranking Models for Multilingual Text Retrieval](https://mlsanity.com/paper/2407.19669/) (2024)
- [World Model on Million-Length Video And Language With Blockwise RingAttention](https://mlsanity.com/paper/2402.08268/) (2024)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [Make Your LLM Fully Utilize the Context](https://mlsanity.com/paper/2404.16811/) (2024)
- [Hymba: A Hybrid-head Architecture for Small Language Models](https://mlsanity.com/paper/2411.13676/) (2024)
- [Flooding Spread of Manipulated Knowledge in LLM-Based Multi-Agent Communities](https://mlsanity.com/paper/2407.07791/) (2024)
- [FiT: Flexible Vision Transformer for Diffusion Model](https://mlsanity.com/paper/2402.12376/) (2024)
- [Exchange-of-Thought: Enhancing Large Language Model Capabilities through Cross-Model Communication](https://mlsanity.com/paper/2312.01823/) (2023)
- [Advancing Transformer Architecture in Long-Context Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2311.12351/) (2023)
- [VideoRoPE: What Makes for Good Video Rotary Position Embedding?](https://mlsanity.com/paper/2502.05173/) (2025)
- [Training-Free Long-Context Scaling of Large Language Models](https://mlsanity.com/paper/2402.17463/) (2024)
- [Human-inspired Episodic Memory for Infinite Context LLMs](https://mlsanity.com/paper/2407.09450/) (2024)
- [ChatQA 2: Bridging the Gap to Proprietary LLMs in Long Context and RAG Capabilities](https://mlsanity.com/paper/2407.14482/) (2024)
- [Base of RoPE Bounds Context Length](https://mlsanity.com/paper/2405.14591/) (2024)
- [Rope to Nope and Back Again: A New Hybrid Attention Strategy](https://mlsanity.com/paper/2501.18795/) (2025)
- [Can Perplexity Reflect Large Language Model's Ability in Long Text Understanding?](https://mlsanity.com/paper/2405.06105/) (2024)
- [NACL: A General and Effective KV Cache Eviction Framework for LLMs at Inference Time](https://mlsanity.com/paper/2408.03675/) (2024)
- [D-CPT Law: Domain-specific Continual Pre-Training Scaling Law for Large Language Models](https://mlsanity.com/paper/2406.01375/) (2024)
- [Mind the Time: Temporally-Controlled Multi-Event Video Generation](https://mlsanity.com/paper/2412.05263/) (2024)
- [LongLLaDA: Unlocking Long Context Capabilities in Diffusion LLMs](https://mlsanity.com/paper/2506.14429/) (2025)
- [SampleAttention: Near-Lossless Acceleration of Long Context LLM Inference with Adaptive Structured Sparse Attention](https://mlsanity.com/paper/2406.15486/) (2024)
- [JudgeRank: Leveraging Large Language Models for Reasoning-Intensive Reranking](https://mlsanity.com/paper/2411.00142/) (2024)
- [PaTH Attention: Position Encoding via Accumulating Householder Transformations](https://mlsanity.com/paper/2505.16381/) (2025)
- [Length Extrapolation of Transformers: A Survey from the Perspective of Positional Encoding](https://mlsanity.com/paper/2312.17044/) (2023)
- [Training Sparse Mixture Of Experts Text Embedding Models](https://mlsanity.com/paper/2502.07972/) (2025)
- [DAPE: Data-Adaptive Positional Encoding for Length Extrapolation](https://mlsanity.com/paper/2405.14722/) (2024)
- [Fortify the Shortest Stave in Attention: Enhancing Context Awareness of Large Language Models for Effective Tool Use](https://mlsanity.com/paper/2312.04455/) (2023)

## Abstract (arXiv)

The extrapolation capability of Large Language Models (LLMs) based on Rotary Position Embedding is currently a topic of considerable interest. The mainstream approach to addressing extrapolation with LLMs involves modifying RoPE by replacing 10000, the rotary base of θn=10000-2n/d in the original RoPE, with a larger value and providing longer fine-tuning text. In this work, we first observe that fine-tuning a RoPE-based LLM with either a smaller or larger base in pre-training context length could significantly enhance its extrapolation performance. After that, we propose textbftextitScaling Laws of RoPE-based Extrapolation, a unified framework from the periodic perspective, to describe the relationship between the extrapolation performance and base value as well as tuning context length. In this process, we also explain the origin of the RoPE-based extrapolation issue by textbftextitcritical dimension for extrapolation. Besides these observations and analyses, we achieve extrapolation up to 1 million context length within only 16K training length on LLaMA2 7B and 13B.