# Optimal Watermark Localization in Mixed-Source Large Language Model Texts

arXiv: https://arxiv.org/abs/2608.14906 · HTML: https://mlsanity.com/paper/2608.14906/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 7 of its 63 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Placed in

- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 7 of 7)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Large Language Models as Markov Chains](https://mlsanity.com/paper/2410.02724/) (2024)
- [Optimal Estimation of Watermark Proportions in Hybrid AI-Human Texts](https://mlsanity.com/paper/2506.22343/) (2025)
- [Towards Anytime-Valid Statistical Watermarking](https://mlsanity.com/paper/2602.17608/) (2026)

## Built on by (most cited first, 1 of 1)

- [textGrain watermarking is harder to detect: can sum-tests still do it optimally?](https://mlsanity.com/paper/2610.17655/) (2026)

## Abstract (arXiv)

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.