# DCIS: Efficient Length Extrapolation of LLMs via Divide-and-Conquer Scaling Factor Search

arXiv: https://arxiv.org/abs/2412.18811 · HTML: https://mlsanity.com/paper/2412.18811/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 23 of 23)

- [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 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [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)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [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)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [Retrieval Head Mechanistically Explains Long-Context Factuality](https://mlsanity.com/paper/2404.15574/) (2024)
- [Landmark Attention: Random-Access Infinite Context Length for Transformers](https://mlsanity.com/paper/2305.16300/) (2023)
- [LongNet: Scaling Transformers to 1,000,000,000 Tokens](https://mlsanity.com/paper/2307.02486/) (2023)
- [Evaluating Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2310.19736/) (2023)
- [FuxiTranyu: A Multilingual Large Language Model Trained with Balanced Data](https://mlsanity.com/paper/2408.06273/) (2024)

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

- [LongRoPE2: Near-Lossless LLM Context Window Scaling](https://mlsanity.com/paper/2502.20082/) (2025)
- [From Curated Data to Scalable Models: Continual Pre-training of Dense and MoE Large Language Models for Tibetan](https://mlsanity.com/paper/2507.09205/) (2025)
- [SAT: Balancing Reasoning Accuracy and Efficiency with Stepwise Adaptive Thinking](https://mlsanity.com/paper/2604.07922/) (2026)

## Abstract (arXiv)

Large language models (LLMs) based on the Transformer architecture usually have their context length limited due to the high training cost. Recent advancements extend the context window by adjusting the scaling factors of RoPE and fine-tuning. However, suboptimal initialization of these factors results in increased fine-tuning costs and reduced performance at target length. To address these challenges, we propose a novel RoPE-based fine-tuning framework that diverges from conventional scaling factors search. Specifically, we present a Divide-and-Conquer Incremental Search (DCIS) algorithm that strategically determines the better scaling factors. Further fine-tuning with the identified scaling factors effectively extends the context window of LLMs. Empirical results demonstrate that our methodology not only mitigates performance decay at extended target lengths but also allows the model to fine-tune on short contexts and generalize to long contexts, thereby reducing the cost of fine-tuning. The scaling factors obtained through DCIS can even perform effectively without fine-tuning. Further analysis of the search space reveals that DCIS achieves twice the search efficiency compared to other methods. We also examine the impact of the non-strictly increasing scaling factors utilized in DCIS and evaluate the general capabilities of LLMs across various context lengths.