# Base of RoPE Bounds Context Length

arXiv: https://arxiv.org/abs/2405.14591 · HTML: https://mlsanity.com/paper/2405.14591/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 43 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [Landmark Attention: Random-Access Infinite Context Length for Transformers](https://mlsanity.com/paper/2305.16300/) (2023)
- [Rethinking Positional Encoding in Language Pre-training](https://mlsanity.com/paper/2006.15595/) (2020)
- [Focused Transformer: Contrastive Training for Context Scaling](https://mlsanity.com/paper/2307.03170/) (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)
- [Scaling Laws vs Model Architectures: How does Inductive Bias Influence Scaling?](https://mlsanity.com/paper/2207.10551/) (2022)
- [Hierarchically Gated Recurrent Neural Network for Sequence Modeling](https://mlsanity.com/paper/2311.04823/) (2023)
- [Impact of Code Language Models on Automated Program Repair](https://mlsanity.com/paper/2302.05020/) (2023)

## Built on by (most cited first, 30 of 52)

- [mGTE: Generalized Long-Context Text Representation and Reranking Models for Multilingual Text Retrieval](https://mlsanity.com/paper/2407.19669/) (2024)
- [Test-Time Training Done Right](https://mlsanity.com/paper/2505.23884/) (2025)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [VideoRoPE: What Makes for Good Video Rotary Position Embedding?](https://mlsanity.com/paper/2502.05173/) (2025)
- [Why Does the Effective Context Length of LLMs Fall Short?](https://mlsanity.com/paper/2410.18745/) (2024)
- [Rope to Nope and Back Again: A New Hybrid Attention Strategy](https://mlsanity.com/paper/2501.18795/) (2025)
- [Baichuan-M1: Pushing the Medical Capability of Large Language Models](https://mlsanity.com/paper/2502.12671/) (2025)
- [LongLLaDA: Unlocking Long Context Capabilities in Diffusion LLMs](https://mlsanity.com/paper/2506.14429/) (2025)
- [ALR2: A Retrieve-then-Reason Framework for Long-context Question Answering](https://mlsanity.com/paper/2410.03227/) (2024)
- [LongRoPE2: Near-Lossless LLM Context Window Scaling](https://mlsanity.com/paper/2502.20082/) (2025)
- [Mamba Modulation: On the Length Generalization of Mamba](https://mlsanity.com/paper/2509.19633/) (2025)
- [Understanding the RoPE Extensions of Long-Context LLMs: An Attention Perspective](https://mlsanity.com/paper/2406.13282/) (2024)
- [When Precision Meets Position: BFloat16 Breaks Down RoPE in Long-Context Training](https://mlsanity.com/paper/2411.13476/) (2024)
- [On the token distance modeling ability of higher RoPE attention dimension](https://mlsanity.com/paper/2410.08703/) (2024)
- [Biology-Instructions: A Dataset and Benchmark for Multi-Omics Sequence Understanding Capability of Large Language Models](https://mlsanity.com/paper/2412.19191/) (2024)
- [Technical Report of TeleChat2, TeleChat2.5 and T1](https://mlsanity.com/paper/2507.18013/) (2025)
- [Untie the Knots: An Efficient Data Augmentation Strategy for Long-Context Pre-Training in Language Models](https://mlsanity.com/paper/2409.04774/) (2024)
- [KV Shifting Attention Enhances Language Modeling](https://mlsanity.com/paper/2411.19574/) (2024)
- [RoPE Distinguishes Neither Positions Nor Tokens in Long Contexts, Provably](https://mlsanity.com/paper/2605.15514/) (2026)
- [Rotary Positional Embeddings as Phase Modulation: Theoretical Bounds on the RoPE Base for Long-Context Transformers](https://mlsanity.com/paper/2602.10959/) (2026)
- [SkyLadder: Better and Faster Pretraining via Context Window Scheduling](https://mlsanity.com/paper/2503.15450/) (2025)
- [Decoupling Positional and Symbolic Attention Behavior in Transformers](https://mlsanity.com/paper/2511.11579/) (2025)
- [Beyond In-Distribution Success: Scaling Curves of CoT Granularity for Language Model Generalization](https://mlsanity.com/paper/2502.18273/) (2025)
- [EgoMem: Lifelong Memory Agent for Full-duplex Omnimodal Models](https://mlsanity.com/paper/2509.11914/) (2025)
- [Mi:dm 2.0 Korea-centric Bilingual Language Models](https://mlsanity.com/paper/2601.09066/) (2026)
- [Scaling Instruction-Tuned LLMs to Million-Token Contexts via Hierarchical Synthetic Data Generation](https://mlsanity.com/paper/2504.12637/) (2025)
- [HoPE: Hybrid of Position Embedding for Long Context Vision-Language Models](https://mlsanity.com/paper/2505.20444/) (2025)
- [Rotary Masked Autoencoders are Versatile Learners](https://mlsanity.com/paper/2505.20535/) (2025)
- [MrRoPE: Mixed-radix Rotary Position Embedding](https://mlsanity.com/paper/2601.22181/) (2026)
- [Fractional Rotation, Full Potential? Investigating Performance and Convergence of Partial RoPE](https://mlsanity.com/paper/2603.11611/) (2026)

## Abstract (arXiv)

Position embedding is a core component of current Large Language Models (LLMs). Rotary position embedding (RoPE), a technique that encodes the position information with a rotation matrix, has been the de facto choice for position embedding in many LLMs, such as the Llama series. RoPE has been further utilized to extend long context capability, which is roughly based on adjusting the textitbase parameter of RoPE to mitigate out-of-distribution (OOD) problems in position embedding. However, in this paper, we find that LLMs may obtain a superficial long-context ability based on the OOD theory. We revisit the role of RoPE in LLMs and propose a novel property of long-term decay, we derive that the textitbase of RoPE bounds context length: there is an absolute lower bound for the base value to obtain certain context length capability. Our work reveals the relationship between context length and RoPE base both theoretically and empirically, which may shed light on future long context training.