# Two Stones Hit One Bird: Bilevel Positional Encoding for Better Length Extrapolation

arXiv: https://arxiv.org/abs/2401.16421 · HTML: https://mlsanity.com/paper/2401.16421/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 57 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 30 of 42)

- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (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)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [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)
- [The NarrativeQA Reading Comprehension Challenge](https://mlsanity.com/paper/1712.07040/) (2017)
- [A Dataset of Information-Seeking Questions and Answers Anchored in Research Papers](https://mlsanity.com/paper/2105.03011/) (2021)
- [QMSum: A New Benchmark for Query-based Multi-domain Meeting Summarization](https://mlsanity.com/paper/2104.05938/) (2021)
- [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)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [QuALITY: Question Answering with Long Input Texts, Yes!](https://mlsanity.com/paper/2112.08608/) (2021)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [SCROLLS: Standardized CompaRison Over Long Language Sequences](https://mlsanity.com/paper/2201.03533/) (2022)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [ContractNLI: A Dataset for Document-level Natural Language Inference for Contracts](https://mlsanity.com/paper/2110.01799/) (2021)
- [LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning](https://mlsanity.com/paper/2401.01325/) (2024)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)

## Built on by (most cited first, 24 of 24)

- [Training-Free Long-Context Scaling of Large Language Models](https://mlsanity.com/paper/2402.17463/) (2024)
- [SepLLM: Accelerate Large Language Models by Compressing One Segment into One Separator](https://mlsanity.com/paper/2412.12094/) (2024)
- [DAPE: Data-Adaptive Positional Encoding for Length Extrapolation](https://mlsanity.com/paper/2405.14722/) (2024)
- [Sample Complexity and Representation Ability of Test-time Scaling Paradigms](https://mlsanity.com/paper/2506.05295/) (2025)
- [Let the Code LLM Edit Itself When You Edit the Code](https://mlsanity.com/paper/2407.03157/) (2024)
- [DAPE V2: Process Attention Score as Feature Map for Length Extrapolation](https://mlsanity.com/paper/2410.04798/) (2024)
- [SoLoPO: Unlocking Long-Context Capabilities in LLMs via Short-to-Long Preference Optimization](https://mlsanity.com/paper/2505.11166/) (2025)
- [HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models](https://mlsanity.com/paper/2509.05218/) (2025)
- [Position Bias Mitigates Position Bias:Mitigate Position Bias Through Inter-Position Knowledge Distillation](https://mlsanity.com/paper/2508.15709/) (2025)
- [Born a Transformer -- Always a Transformer? On the Effect of Pretraining on Architectural Abilities](https://mlsanity.com/paper/2505.21785/) (2025)
- [Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding](https://mlsanity.com/paper/2501.00712/) (2025)
- [SAS: Simulated Attention Score](https://mlsanity.com/paper/2507.07694/) (2025)
- [Context-aware Biases for Length Extrapolation](https://mlsanity.com/paper/2503.08067/) (2025)
- [On the Ability of Transformers to Verify Plans](https://mlsanity.com/paper/2603.19954/) (2026)
- [Two are better than one: Context window extension with multi-grained self-injection](https://mlsanity.com/paper/2410.19318/) (2024)
- [Softplus Attention with Re-weighting Boosts Length Extrapolation in Large Language Models](https://mlsanity.com/paper/2501.13428/) (2025)
- [LexPro-1.0 Technical Report](https://mlsanity.com/paper/2503.06949/) (2025)
- [Beyond Isolated Capabilities: Bridging Long CoT Reasoning and Long-Context Understanding](https://mlsanity.com/paper/2507.14849/) (2025)
- [Position as Probability: Self-Supervised Transformers that Think Past Their Training for Length Extrapolation](https://mlsanity.com/paper/2506.00920/) (2025)
- [On the Limitations and Capabilities of Position Embeddings for Length Generalization](https://mlsanity.com/paper/2510.04130/) (2025)
- [Stacked from One: Multi-Scale Self-Injection for Context Window Extension](https://mlsanity.com/paper/2603.04759/) (2026)
- [A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits](https://mlsanity.com/paper/2605.19944/) (2026)
- [Give it Space! Explicit Disentangling of Positional and Semantic Representations in Encoders](https://mlsanity.com/paper/2605.30022/) (2026)
- [Length Generalization Needs Proper Regularization](https://mlsanity.com/paper/2610.04518/) (2026)

## Abstract (arXiv)

In this work, we leverage the intrinsic segmentation of language sequences and design a new positional encoding method called Bilevel Positional Encoding (BiPE). For each position, our BiPE blends an intra-segment encoding and an inter-segment encoding. The intra-segment encoding identifies the locations within a segment and helps the model capture the semantic information therein via absolute positional encoding. The inter-segment encoding specifies the segment index, models the relationships between segments, and aims to improve extrapolation capabilities via relative positional encoding. Theoretical analysis shows this disentanglement of positional information makes learning more effective. The empirical results also show that our BiPE has superior length extrapolation capabilities across a wide range of tasks in diverse text modalities.