# Towards Infinite Length Extrapolation: A Unified Approach

arXiv: https://arxiv.org/abs/2601.06113 · HTML: https://mlsanity.com/paper/2601.06113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 30 references that are in the map.
- First posted on arXiv 3 Jan 2026.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [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)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [LongLoRA: Efficient Fine-tuning of Long-Context Large Language Models](https://mlsanity.com/paper/2309.12307/) (2023)
- [Landmark Attention: Random-Access Infinite Context Length for Transformers](https://mlsanity.com/paper/2305.16300/) (2023)
- [Chain of Agents: Large Language Models Collaborating on Long-Context Tasks](https://mlsanity.com/paper/2406.02818/) (2024)
- [Leave No Context Behind: Efficient Infinite Context Transformers with Infini-attention](https://mlsanity.com/paper/2404.07143/) (2024)
- [ShadowKV: KV Cache in Shadows for High-Throughput Long-Context LLM Inference](https://mlsanity.com/paper/2410.21465/) (2024)
- [Retrieval meets Long Context Large Language Models](https://mlsanity.com/paper/2310.03025/) (2023)
- [SCBench: A KV Cache-Centric Analysis of Long-Context Methods](https://mlsanity.com/paper/2412.10319/) (2024)
- [Sparser is Faster and Less is More: Efficient Sparse Attention for Long-Range Transformers](https://mlsanity.com/paper/2406.16747/) (2024)
- [LLaMA-Reviewer: Advancing Code Review Automation with Large Language Models through Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2308.11148/) (2023)
- [Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization](https://mlsanity.com/paper/2412.17739/) (2024)
- [The What, Why, and How of Context Length Extension Techniques in Large Language Models -- A Detailed Survey](https://mlsanity.com/paper/2401.07872/) (2024)
- [Length Extrapolation of Transformers: A Survey from the Perspective of Positional Encoding](https://mlsanity.com/paper/2312.17044/) (2023)
- [Are Long-LLMs A Necessity For Long-Context Tasks?](https://mlsanity.com/paper/2405.15318/) (2024)
- [HoPE: A Novel Positional Encoding Without Long-Term Decay for Enhanced Context Awareness and Extrapolation](https://mlsanity.com/paper/2410.21216/) (2024)
- [Understanding the RoPE Extensions of Long-Context LLMs: An Attention Perspective](https://mlsanity.com/paper/2406.13282/) (2024)
- [Positional Encoding Helps Recurrent Neural Networks Handle a Large Vocabulary](https://mlsanity.com/paper/2402.00236/) (2024)
- [Training-Free Exponential Context Extension via Cascading KV Cache](https://mlsanity.com/paper/2406.17808/) (2024)
- [What Should Baby Models Read? Exploring Sample-Efficient Data Composition on Model Performance](https://mlsanity.com/paper/2411.06672/) (2024)

## Abstract (arXiv)

Large language models (LLMs) have revolutionized natural language processing, but their ability to process long sequences is fundamentally limited by the context window size during training. Existing length extrapolation methods often suffer from performance degradation or computational inefficiencies. We thereby use a unified framework that reinterprets positional encoding methods as a decomposition of the attention score into a multiplicative transformation and an additive bias. This perspective not only subsumes popular approaches such as relative position embeddings and attention-bias moderated approaches but also exposes their inherent limitations in handling long-range dependencies. To address these shortcomings, motivated by our framework, we introduce Adaptive Positional Encoding (APE), which leverages adaptive frequency modulation and an intricately designed decay bias that incorporates linear, logarithmic, and square-root terms. Our theoretical analysis establishes conditions for infinite-context extrapolation, ensuring that the softmax normalization remains well-defined over unbounded sequences while preserving long-distance correlations, entropy boundedness and gradient positional sensitivity. We substantiate our claims with an experimental case study on TinyStories dataset as well as a new synthetic dataset, Long Tiny Stories featuring stories up to 32,000 words. Relevant code, dataset and model weights are available at https://anonymous.4open.science/r/Check-2DAD/.