# Frayed RoPE and Long Inputs: A Geometric Perspective

arXiv: https://arxiv.org/abs/2603.18017 · HTML: https://mlsanity.com/paper/2603.18017/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [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)
- [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)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [LM-Infinite: Zero-Shot Extreme Length Generalization for Large Language Models](https://mlsanity.com/paper/2308.16137/) (2023)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [Hymba: A Hybrid-head Architecture for Small Language Models](https://mlsanity.com/paper/2411.13676/) (2024)
- [SEED-Story: Multimodal Long Story Generation with Large Language Model](https://mlsanity.com/paper/2407.08683/) (2024)
- [Stable Rank Normalization for Improved Generalization in Neural Networks and GANs](https://mlsanity.com/paper/1906.04659/) (2019)
- [Resonance RoPE: Improving Context Length Generalization of Large Language Models](https://mlsanity.com/paper/2403.00071/) (2024)
- [HoPE: A Novel Positional Encoding Without Long-Term Decay for Enhanced Context Awareness and Extrapolation](https://mlsanity.com/paper/2410.21216/) (2024)

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

- [Remember to Forget: Gated Adaptive Positional Encoding](https://mlsanity.com/paper/2605.10414/) (2026)
- [Does RoPE Prevent or Degrade Retrieval Heads? A Mechanistic Analysis Across Model Families](https://mlsanity.com/paper/2606.21249/) (2026)
- [Scaling Parameter and Context in Attention: Native Sparse Attention from Mixture-of-Head](https://mlsanity.com/paper/2609.38832/) (2026)

## Abstract (arXiv)

Rotary Positional Embedding (RoPE) is a widely adopted technique for encoding position in language models, which, while effective, causes performance breakdown when input length exceeds training length. Prior analyses assert (rightly) that long inputs cause channels to rotate ``out of distribution,'' but it is not clear how extra rotation relates to or causes pathological behavior. Through empirical and theoretical analysis we advance a unified geometric understanding of attention behavior with RoPE. We find that attention induces tight clustering of separated key and query latent point clouds, allowing for creation of sink tokens: placeholders that allow attention heads to avoid token mixing when not required. RoPE applied to longer inputs damages this key/query cluster separation, producing pathological behavior by inhibiting sink token functionality. From this geometric perspective, we propose RoPE-ID (In Distribution), a straightforward modification that allows attention layers to generalize to longer inputs out of the box: apply RoPE with high frequency to a subset of channels. We demonstrate the effectiveness of RoPE-ID for extended inputs using 1B and 3B parameter Transformers on the LongBench and RULER information retrieval benchmarks.