# Efficient Matrix Implementation for Rotary Position Embedding

arXiv: https://arxiv.org/abs/2604.09742 · HTML: https://mlsanity.com/paper/2604.09742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models](https://mlsanity.com/paper/2411.05007/) (2024)
- [Step-Video-T2V Technical Report: The Practice, Challenges, and Future of Video Foundation Model](https://mlsanity.com/paper/2502.10248/) (2025)
- [SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration](https://mlsanity.com/paper/2410.02367/) (2024)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [SageAttention2: Efficient Attention with Thorough Outlier Smoothing and Per-thread INT4 Quantization](https://mlsanity.com/paper/2411.10958/) (2024)
- [SageAttention3: Microscaling FP4 Attention for Inference and An Exploration of 8-Bit Training](https://mlsanity.com/paper/2505.11594/) (2025)
- [Sparser is Faster and Less is More: Efficient Sparse Attention for Long-Range Transformers](https://mlsanity.com/paper/2406.16747/) (2024)
- [PAROAttention: Pattern-Aware ReOrdering for Efficient Sparse and Quantized Attention in Visual Generation Models](https://mlsanity.com/paper/2506.16054/) (2025)
- [KV-Latent: Dimensional-level KV Cache Reduction with Frequency-aware Rotary Positional Embedding](https://mlsanity.com/paper/2507.11273/) (2025)

## Abstract (arXiv)

Rotary Position Embedding (RoPE) has become a core component of modern Transformer architectures across language, vision, and 3D domains. However, existing implementations rely on vector-level split and merge operations that introduce non-negligible computational overhead, often overlooked in attention optimization. The problem is further amplified in multi-dimensional settings (e.g., 2D and 3D RoPE), where additional vector operations and uneven feature partitions degrade hardware utilization. To overcome these limitations, we propose RoME (Rotary Matrix position Embedding), a mathematically equivalent yet computationally efficient reformulation of RoPE that replaces vector operations with unified matrix transformations. RoME eliminates dimension-specific operations, simplifies implementation, and enables fused parallel execution across Cube and Vector units on modern NPUs. Experiments show that RoME delivers substantial acceleration at both the operator and full-model levels. The implementation is available at https://gitcode.com/cann/ops-transformer/blob/master/experimental/posembedding/rope_matrix/README.md.