提出新型位置编码，更好保留图像空间结构。
GeoPE:A Unified Geometric Positional Embedding for Structured Tensors
- 用四元数扩展旋转操作，构建统一的2D空间编码。
- 在多个任务上超越现有方法，显著提升形状感知能力。
- 适合关注视觉模型几何理解的科研与工程人员。
标准视觉变换器将2D图像展平为1D序列，破坏了自然的空间拓扑。虽然旋转变换位置编码（RoPE）在1D上表现优异，但继承了这一缺陷，常将空间上远距离的图像块（如行边界处）误认为序列邻近。现有2D方法通常独立处理空间轴，无法有效区分虚假序列邻近与真实空间距离。为此，我们提出几何位置编码（GeoPE），通过四元数将旋转扩展至3D欧氏空间。为克服非交换性并保证对称性，GeoPE在李代数中计算几何均值，构建统一的旋转算子，实现空间维度的几何耦合编码。大量实验表明，GeoPE在图像分类、目标检测和3D语义分割任务中持续优于现有2D RoPE变体，并显著增强形状偏差，验证其准确捕捉真实几何结构的能力。
原文摘要 · Abstract (English)
Standard Vision Transformers flatten 2D images into 1D sequences, disrupting the natural spatial topology. While Rotary Positional Embedding (RoPE) excels in 1D, it inherits this limitation, often treating spatially distant patches (e.g., at row edges) as sequence neighbors. Existing 2D approaches typically treat spatial axes independently, failing to decouple this false sequential proximity from true spatial distance. To restore the 2D spatial manifold, we introduce Geometric Positional Embedding (GeoPE), a framework that extends rotations to 3D Euclidean space using quaternions. To overcome non-commutativity and ensure symmetry, GeoPE constructs a unified rotational operator by computing the geometric mean in the Lie algebra. This creates a geometrically coupled encoding that effectively separates spatial dimensions. Extensive experiments on image classification, object detection, and 3D semantic segmentation demonstrate that GeoPE consistently outperforms existing 2D RoPE variants and significantly enhances shape bias, confirming its ability to capture true geometric structure.
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