Optimal Watermark Localization in Mixed-Source Large Language Model Texts

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.

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BibTeX RIS

BibTeX

@misc{blanchet2026optimal,
  title = {{Optimal Watermark Localization in Mixed-Source Large Language Model Texts}},
  author = {Jose H. Blanchet and T. Tony Cai and Xiang Li and Hao Liu and Qi Long and Weijie J. Su},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.14906},
  eprint = {2608.14906},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.14906},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Optimal Watermark Localization in Mixed-Source Large Language Model Texts
AU  - Jose H. Blanchet
AU  - T. Tony Cai
AU  - Xiang Li
AU  - Hao Liu
AU  - Qi Long
AU  - Weijie J. Su
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.14906
UR  - https://arxiv.org/abs/2608.14906
AB  - 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.
ER  -

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