Optimal Watermark Localization in Mixed-Source Large Language Model Texts

[2608.14906] Optimal Watermark Localization in Mixed-Source Large Language Model Texts Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2608.14906 (stat) [Submitted on 14 Aug 2026] Title: Optimal Watermark Localization in Mixed-Source Large Language Model Texts Authors: Jose H. Blanchet , T. Tony Cai , Xiang Li , Hao Liu , Qi Long , Weijie J. Su View a PDF of the paper titled Optimal Watermark Localization in Mixed-Source Large Language Model Texts, by Jose H. Blanchet and 5 other authors View PDF HTML (experimental) 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: 66 pages, 13 figures 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:2608.14906v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2608.14906 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hao Liu [ view email ] [v1] Fri, 14 Aug 2026 21:41:50 UTC (2,253 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Watermark Localization in Mixed-Source Large Language Model Texts, by Jose H. Blanchet and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-08 Change to browse by: cs cs.CL cs.LG stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• A Watermark for Large Language Models#16582
• Watermarking Diffusion Language Models#1014549
• Topic-Based Watermarks for Large Language Models#144201
• Fusion Training for Mathematical Generalization in Large Language Models#441828
• The Probabilistic Structure of Large Language Models#1051627