# Fractional Rotation, Full Potential? Investigating Performance and Convergence of Partial RoPE

arXiv: https://arxiv.org/abs/2603.11611 · HTML: https://mlsanity.com/paper/2603.11611/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [Base of RoPE Bounds Context Length](https://mlsanity.com/paper/2405.14591/) (2024)
- [Rope to Nope and Back Again: A New Hybrid Attention Strategy](https://mlsanity.com/paper/2501.18795/) (2025)
- [Signal and Noise: A Framework for Reducing Uncertainty in Language Model Evaluation](https://mlsanity.com/paper/2508.13144/) (2025)
- [Hubble: a Model Suite to Advance the Study of LLM Memorization](https://mlsanity.com/paper/2510.19811/) (2025)
- [When Precision Meets Position: BFloat16 Breaks Down RoPE in Long-Context Training](https://mlsanity.com/paper/2411.13476/) (2024)

## Built on by (most cited first, 4 of 4)

- [Disentangling the Expressivity of RoPE](https://mlsanity.com/paper/2608.11909/) (2026)
- [Does RoPE Prevent or Degrade Retrieval Heads? A Mechanistic Analysis Across Model Families](https://mlsanity.com/paper/2606.21249/) (2026)
- [NeoMME: A Single-Tower Multimodal-Native Multilingual Foundation Encoder for Efficient Fine-Tuning and Inference](https://mlsanity.com/paper/2609.01657/) (2026)
- [Shifting Mechanisms: How Positional Encoding Choice Shapes In-Context Retrieval](https://mlsanity.com/paper/2609.38530/) (2026)

## Abstract (arXiv)

Rotary Positional Embedding (RoPE) is widely used in transformers to encode relative positional information, yet the effect of applying RoPE to only a subset of hidden dimensions remains underexplored. This design choice can substantially reduce memory usage, especially at long context lengths. We show that partial RoPE achieves up to 10× memory savings over standard RoPE cache while maintaining comparable final loss. We systematically study its impact on training dynamics and convergence across architectures, model sizes, sequence lengths, and datasets. Our results reveal that: (1) applying RoPE to only a small fraction of dimensions (around 10%) matches the convergence of full RoPE; (2) these trends remain consistent across settings; and (3) NoPE (No Positional Encoding) can produce loss spikes, which are mitigated by minimal RoPE usage or QK-Norm application. Overall, our findings highlight partial RoPE as an effective trade-off between efficiency and stability.