# Mesa-Extrapolation: A Weave Position Encoding Method for Enhanced Extrapolation in LLMs

arXiv: https://arxiv.org/abs/2410.15859 · HTML: https://mlsanity.com/paper/2410.15859/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 49 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Efficient Attentions for Long Document Summarization](https://mlsanity.com/paper/2104.02112/) (2021)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Landmark Attention: Random-Access Infinite Context Length for Transformers](https://mlsanity.com/paper/2305.16300/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning](https://mlsanity.com/paper/2401.01325/) (2024)
- [Focused Transformer: Contrastive Training for Context Scaling](https://mlsanity.com/paper/2307.03170/) (2023)
- [Unlimiformer: Long-Range Transformers with Unlimited Length Input](https://mlsanity.com/paper/2305.01625/) (2023)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [Tracr: Compiled Transformers as a Laboratory for Interpretability](https://mlsanity.com/paper/2301.05062/) (2023)

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

- [Positional Encoding via Token-Aware Phase Attention](https://mlsanity.com/paper/2509.12635/) (2025)
- [Length Generalization Needs Proper Regularization](https://mlsanity.com/paper/2610.04518/) (2026)

## Abstract (arXiv)

Large language models (LLMs), although having revolutionized many fields, still suffer from the challenging extrapolation problem, where the inference ability of LLMs sharply declines beyond their max training lengths. In this work, we conduct a theoretical analysis to better understand why No Position Encoding (NoPE) fails outside its effective range, as well as examining the power of Position Encoding (PE) in this context. Our findings reveal that with meticulous weave position, PE can indeed be extended beyond effective range. Our theorems establish that LLMs equipped with weave PE can achieve improved extrapolation performance without additional cost. Furthermore, we introduce a novel weave PE method, Mesa-Extrapolation, which utilizes a chunk-based triangular attention matrix and applies Stair PE to manage the final chunk. This method not only retains competitive performance but also offers substantial benefits such as significantly reduced memory demand and faster inference speed. Extensive experiments validate the effectiveness of Mesa-Extrapolation, demonstrating its potential as a scalable solution to enhancing LLMs applicative reach. Our code is available at urlhttps://github.com/soacker/Mesa-Extrapolation.