研究团队从群论中汲取灵感，创新性地将"群作用"概念引入位置编码领域。该数学工具擅长描述对称变换规律，例如正方形的四种旋转方式保持图形不变性。基于这一理论突破，GRAPE框架构建出乘法与加法两大编码体系，分别对应旋转与平移两种空间变换方式。

在人工智能领域，位置编码技术的最新突破引发了广泛关注。由清华大学及其他多所顶尖高校联合研发的GRAPE（Group Representational Position Encoding）框架，成功将现有的旋转位置编码（RoPE）和线性偏差编码（ALiBi）等技术整合进一个统一的数学体系。这一成果为Transformer架构在位置信息处理上开辟了新的路径，标志着AI技术的又一重要进步。

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Abstract: Neural Radiance Fields (NeRF) has been a milestone in 3D reconstruction. However, researchers seldom explore the influence of positional encoding, which is counted in the NeRF. Thus, we ...