旋转注意力中的相位结构：语义连续性和执行边界治理的谱框架
Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance
- ENTRUST AI（ENTRUST人工智能公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究Transformer语言模型中旋转注意力的相位结构，通过定义有效域、推导分数和引入函数构建谱框架，可区分表征连续性与执行边界可接受性，为相关研究提供理论和方法程序。
AI中文摘要：
Transformer语言模型通常通过向量几何进行分析，然而有序上下文和旋转位置编码在查询-键交互中引入了明确的相位结构。本文开发了一个有界谱框架，用于研究旋转相位对齐、隐藏状态连续性和语义漂移，而无需将语言模型视为实际的物理波系统。首先将有序隐藏状态序列而非词汇索引确定为谱分解的有效域，推导旋转位置嵌入（RoPE）注意力分数为幅度加权余弦项之和并证明局部稳定性引理。为将相位分析扩展到原生RoPE坐标之外，定义复模态坐标并引入隐藏状态轨迹的加权相干函数。该框架有助于区分表征连续性和执行边界可接受性，为确定谱结构何时解释连续性以及治理何时必须作为执行的外部谓词提供理论和方法程序。
英文摘要：
Transformer language models are usually analyzed through vector geometry, yet ordered context and rotary position encoding introduce explicit phase structure into query-key interactions. This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift without treating language models as literal physical wave systems. It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition. It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma: uniformly bounded phase displacement limits degradation of the corresponding pre-softmax score. To extend phase analysis beyond native RoPE coordinates, the paper defines complex modal coordinates over fixed orthonormal direction pairs and introduces a weighted coherence functional for hidden-state trajectories. These constructions support a strict distinction between representational continuity and execution-boundary admissibility. Internal coherence may describe preservation of task-relevant relations, but it cannot authorize a consequential transition. Positioned against existing geometric, spectral, phase-modulation, representation-analysis, and mechanistic-interpretability accounts, the framework contributes a theoretical and methodological program for determining when spectral structure explains continuity and when governance must remain an external predicate over execution.
