语言完整性与统计水印：保留意义变换的内蕴几何

中文摘要 AI 辅助

语言模型的统计水印存在于能指的自由度中：它们在意义近乎等价的 token 中进行选择，因此会被那些改变文本形式但保留内容的变换所侵蚀。现有文献通过变换的终点，即原文与改写文本间的语义相似度，来衡量这类变换。我们证明终点是错误的统计量。通过适配语言环的形式体系，我们证明保留意义变换链的不变量可典范分解为终点部分和初始状态稳定子中的完整部分，而语义缺陷无法察觉后者；环旋转是嵌入空间单位球上的平行运输，因此与威尔逊环的类比成为定理而非比喻。在检测器一侧，我们证明一个精确恒等式：残差统计量与种子窗口完整保留的位置数成正比，由此独立编辑推论得出衰减律 ρ^(h+1)。该恒等式有一个令人不安的结论，我们以三位小数证实：在相同保留率下，存活信号可能是原始信号的一半、四分之一，或完全为零，仅取决于编辑发生的位置。

英文摘要

Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by exactly those transformations which move the form of a text while leaving its content in place. The literature measures such transformations by their endpoint, through the semantic similarity between the original and the rewritten text. We show that the endpoint is the wrong statistic. Adapting the formalism of linguistic loops, we prove that the invariant of a chain of meaning-preserving transformations factorises canonically into an endpoint part and a holonomy in the stabiliser of the initial state, the second of which the semantic deficit cannot see; the loop rotation is parallel transport on the unit sphere of the embedding space, so that the analogy with the Wilson loop becomes a theorem rather than a figure of speech. On the side of the detector we prove an exact identity: the residual statistic is proportional to the number of positions whose seeding window survived intact, from which the decay law $ρ^{h+1}$ follows as the independent-edit corollary. The identity has a disconcerting consequence, which we confirm to three decimal places: at one and the same retention rate the surviving signal may be one half of the original, one quarter of it, or exactly nothing, according only to where the edits fall.

发表机构

• Instituto Superior Técnico（高等技术学院）
• Universidade do Algarve（阿尔加维大学）

机构由 AI 辅助整理，请以论文原文为准。