arXiv cs.CL· Jose H. Blanchet, T. Tony Cai, Xiang Li, Hao Liu, Qi Long, Weijie J. Su·· 2 天前AI 评分22
混合来源大语言模型文本中的最优水印定位
Optimal Watermark Localization in Mixed-Source Large Language Model Texts
AI 导读
研究将水印定位形式化为基于枢轴统计量的 token 级多重检验问题，用隐变量记录每个位置的水印依赖是否在改写、插入、删除或改写后存活。理论推导给出全局检测的锐利边界，以及发现与分类的相变，证明发现严格难于检测、一致分类在该参数区间内不可能。作者提出自适应阈值方法，无需已知稀疏指数或时变下一 token 分布，即可达到最优发现边界。
正文 · 原文
Abstract:Watermarking provides a principled way to authenticate text generated by large language models (LLMs). In practice, however, the final text may be mixed-source, with watermark evidence surviving at only a subset of token positions after rewriting, insertion, deletion, or paraphrasing. Although prior work has studied global detection of watermark signals, when such signals can be localized remains unclear. We formulate watermark localization as a token-level multiple-testing problem based on pivotal statistics, with a latent indicator recording whether watermark dependence survives at each position. Under an asymptotic regime indexed by exponents for signal sparsity, next-token concentration, and effective-vocabulary growth, we derive a sharp boundary for global detection and phase transitions for discovery and classification within the class of coordinatewise pivot-based localization rules. We show that discovery is strictly harder than detection and that consistent classification is impossible across the parameter regime within this class. We then develop an adaptive thresholding method that does not require knowledge of the exponents or time-varying next-token distributions, but uses a data-driven estimate of the surviving watermark fraction. The method attains the optimal discovery boundary and near-optimal discovery power relative to homogeneous pivot-based rules. Simulations support the theoretical phase transitions, while experiments on model-generated texts demonstrate practical localization performance under common edit mechanisms.
| Comments: | 73 pages, 13 figures. Updated experiments and supplementary material |
| Subjects: | Methodology (stat.ME); Computation and Language (cs.CL); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2608.14906 [stat.ME] |
| (or arXiv:2608.14906v2 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2608.14906 arXiv-issued DOI via DataCite |
Submission history
From: Hao Liu [view email]
[v1]
Fri, 14 Aug 2026 21:41:50 UTC (2,253 KB)
[v2]
Thu, 15 Oct 2026 17:29:07 UTC (881 KB)
来源：arXiv cs.CL · arxiv.org