发表机构
Dartmouth College; Geisel School of Medicine at Dartmouth（达特茅斯学院; 达特茅斯盖泽尔医学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于图灵测试与统计决策理论，用全变差距离量化AI文本检测的理论极限，指出完美检测需分布不重叠，并强调实际中分布变化、基础比率及人机混合使检测更复杂，且区分性、归属等是不同任务。
AI 中文摘要
一篇完成的文本能揭示其产生过程的哪些信息？本文借鉴图灵的模仿游戏和统计决策理论，探讨了将AI文本检测视为从已完成对象推断未观测历史这一过程的局限性。对于两个先验概率相等的已知源分布，一个标准恒等式给出了最小平均分类误差为其概率重叠的一半。该重叠等于一减去它们的全变差距离。因此，完美检测要求分布不重叠；而有用的区分则不需要。在实践中，问题更为困难：人类和机器写作构成不断变化的分布族，后验概率依赖于基础比率，当人类和软件共同贡献于同一文本时，“AI撰写的”变得模糊。图灵的询问者可以提出另一个问题；而仅限于成品散文的检测器则不能。可区分性、来源归属、认证和合规性是不同的推断任务。论文自身有记录的人机共同创作来源展示了生产历史能揭示而二元标签不能揭示的内容。
英文摘要
What can a finished text reveal about the process that produced it? Drawing on Turing's imitation game and statistical decision theory, this article examines the limits of AI-text detection as an inference from a completed object to an unobserved history. For two known source distributions with equal prior probabilities, a standard identity gives the minimum average classification error as half their probability overlap. This overlap is one minus their total variation distance. Perfect detection therefore requires nonoverlapping distributions; useful discrimination does not. In practice, the problem is harder: human and machine writing form changing families of distributions, posterior probabilities depend on base rates, and ``AI-written'' becomes ambiguous when people and software contribute to the same text. Turing's interrogator can ask another question; a detector restricted to finished prose cannot. Distinguishability, source attribution, authentication, and compliance are different inferential tasks. The paper's own documented human-AI provenance shows what a production history can reveal that a binary label cannot.
Comments18 pages; 2 figures, expository article for a broad mathematical readership
