---
title: "QuantileMark: A Message-Symmetric Multi-bit Watermark for LLMs"
description: "The authors argue that such systems need message symmetry : the specific message encoded should not change text quality… 29 references."
authors: ["Junlin Zhu", "Baizhou Huang", "Xiaojun Wan"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.308/"
doi: "10.18653/v1/2026.acl-long.308"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhu-2026-quantilemark-message-symmetric-multi-bit/"
---
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# QuantileMark: A Message-Symmetric Multi-bit Watermark for LLMs

**Authors:** Junlin Zhu, Baizhou Huang and [Xiaojun Wan](https://md.research.elamur.ai/free/en/authors/xiaojun-wan/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.308/) · [PDF](https://aclanthology.org/2026.acl-long.308.pdf) · [DOI 10.18653/v1/2026.acl-long.308](https://doi.org/10.18653/v1/2026.acl-long.308) · [OpenAlex](https://openalex.org/W7166817776)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
This paper targets multi-bit watermarking of LLM output, where a provider embeds metadata such as a user ID into generated text. The authors argue that such systems need *message symmetry*: the specific message encoded should not change text quality or how reliably it can be verified. Vocabulary-partition schemes violate this in low-entropy steps. One message may get the dominant token's probability, while others must use unlikely tail tokens. QuantileMark instead works on the cumulative probability interval [0, 1). It splits this interval into M bins of equal mass and samples only from the bin mapped to the current target symbol, so every symbol always gets a 1/M probability budget. Detection assumes white-box access. The verifier replays the text under teacher forcing, rebuilds the bins, computes posteriors over latent bins, and aggregates the evidence per message position. The authors prove the scheme is message-unbiased. Experiments on C4 continuation and LFQA show better message recovery and robustness than strong baselines, with negligible quality loss. This makes the method relevant for provider-internal attribution.

## Key points
- **How messages are encoded.** Messages are split into m-bit symbols with M = 2^m values; for example, 24 bits become 12 symbols when m = 2.
- **Keyed randomness.** A secret key plus a local context window determine which symbol each step carries (position allocation) and a keyed permutation of symbols to bins.
- **Theory.** Message-unbiasedness is proven: averaging over messages recovers the base distribution. Equal-mass bins also aim to give similar evidence strength for every message.
- **Evaluation.** Experiments cover C4 continuation and LFQA, with base and instruction-tuned models, against vocabulary-based baselines such as Yoo et al. (2024). The authors report higher recovery rates and stronger detection.
- **Limitations.** Heavy paraphrasing remains a weakness, and detection requires white-box access, so public text-only verification is not possible. Code is released on GitHub.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Junlin Zhu, Baizhou Huang and Xiaojun Wan. 2026. QuantileMark: A Message-Symmetric Multi-bit Watermark for LLMs. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhu2026quantilemark,
  title = {{QuantileMark: A Message-Symmetric Multi-bit Watermark for LLMs}},
  author = {Junlin Zhu, Baizhou Huang and Xiaojun Wan},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.308},
  url = {https://doi.org/10.18653/v1/2026.acl-long.308}
}
```

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## References

29 references, 12 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Ondrej Bojar, Christian Buck, Christian Federmann, Barry Haddow, Philipp Koehn, Johannes Leveling, Christof Monz, Pavel Pecina, Matt Post, Herve Saint-Amand, Radu Soricut, Lucia Specia, and Ale s Tamchyna. 2014. [Findings of the 2014 workshop on statistical machine translation](https://md.research.elamur.ai/free/en/papers/bojar-2014-findings-2014-workshop-statistical-machine/). In Proceedings of the…
2. Patrick Chao, Yan Sun, Edgar Dobriban, and Hamed Hassani. 2025. Watermarking language models with error correcting codes. arXiv preprint arXiv:2406.10281. — [arXiv:2406.10281](https://arxiv.org/abs/2406.10281) [find](https://scholar.google.com/scholar?q=Patrick+Chao%2C+Yan+Sun%2C+Edgar+Dobriban%2C+and+Hamed+Hassani%2E+2025%2E+Watermarking+language+models+with+error+correcting+codes%2E+arXiv+preprint+arXiv%3A2406%2E10281%2E+%E2%80%94+%5BarXiv%3A2406%2E10281%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F24)
3. Sumanth Dathathri, Abigail See, Sumedh Ghaisas, Po-Sen Huang, Rob McAdam, Johannes Welbl, Vandana Bachani, Alex Kaskasoli, Robert Stanforth, Tatiana Matejovicova, Jamie Hayes, Nidhi Vyas, Majd Al Merey, Jonah Brown-Cohen, Rudy Bunel, Borja Balle, A. Taylan Cemgil, Zahra Ahmed, Kitty Stacpoole, and 5… [find](https://scholar.google.com/scholar?q=Sumanth+Dathathri%2C+Abigail+See%2C+Sumedh+Ghaisas%2C+Po%2DSen+Huang%2C+Rob+McAdam%2C+Johannes+Welbl%2C+Vandana+Bachani%2C+Alex+Kaskasoli%2C+Robert+Stanforth%2C+Tatiana+Matejovicova%2C+Jamie+Hayes%2C+Nidhi+Vyas%2C+Majd+Al+Mere)
4. Angela Fan, Yacine Jernite, Ethan Perez, David Grangier, Jason Weston, and Michael Auli. 2019. [ELI5: long form question answering](https://md.research.elamur.ai/free/en/papers/fan-2019-eli5-long-form-question-answering/). In Proceedings of the 57th Conference of the Association for Computational Linguistics, ACL 2019, Florence, Italy, July 28- August 2, 2019, Volume 1: Long Papers, pages…
5. Pierre Fernandez, Antoine Chaffin, Karim Tit, Vivien Chappelier, and Teddy Furon. 2023. Three bricks to consolidate watermarks for large language models. [find](https://scholar.google.com/scholar?q=Pierre+Fernandez%2C+Antoine+Chaffin%2C+Karim+Tit%2C+Vivien+Chappelier%2C+and+Teddy+Furon%2E+2023%2E+Three+bricks+to+consolidate+watermarks+for+large+language+models%2E)
6. In 2023 IEEE International Workshop on Information Forensics and Security (WIFS). IEEE. [find](https://scholar.google.com/scholar?q=In+2023+IEEE+International+Workshop+on+Information+Forensics+and+Security+%28WIFS%29%2E+IEEE%2E)
7. Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, Archie Sravankumar, Artem Korenev, Arthur Hinsvark, and 542 o… — [The Llama 3 Herd of Models](https://md.research.elamur.ai/free/en/papers/grattafiori-2024-llama-3-herd-models/)
8. Tianle Gu, Zongqi Wang, Kexin Huang, Yuanqi Yao, Xiangliang Zhang, Yujiu Yang, and Xiuying Chen. 2025. Invisible entropy: Towards safe and efficient low-entropy LLM watermarking. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 6727–6744, Suzhou, China… [find](https://scholar.google.com/scholar?q=Tianle+Gu%2C+Zongqi+Wang%2C+Kexin+Huang%2C+Yuanqi+Yao%2C+Xiangliang+Zhang%2C+Yujiu+Yang%2C+and+Xiuying+Chen%2E+2025%2E+Invisible+entropy%3A+Towards+safe+and+efficient+low%2Dentropy+LLM+watermarking%2E+In+Proceedings+of+the)
9. Karl Moritz Hermann, Tomas Kocisky, Edward Grefenstette, Lasse Espeholt, Will Kay, Mustafa Suleyman, and Phil Blunsom. 2015. [Teaching machines to read and comprehend](https://md.research.elamur.ai/free/en/papers/hermann-2015-teaching-machines-read-comprehend/). Advances in neural information processing systems, 28.
10. Zhengmian Hu, Lichang Chen, Xidong Wu, Yihan Wu, Hongyang Zhang, and Heng Huang. 2024. Unbiased watermark for large language models. In The Twelfth International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Zhengmian+Hu%2C+Lichang+Chen%2C+Xidong+Wu%2C+Yihan+Wu%2C+Hongyang+Zhang%2C+and+Heng+Huang%2E+2024%2E+Unbiased+watermark+for+large+language+models%2E+In+The+Twelfth+International+Conference+on+Learning+Representations)
11. Rohith Kuditipudi, John Thickstun, Tatsunori Hashimoto, and Percy Liang. 2024. [Robust distortion-free watermarks for language models](https://md.research.elamur.ai/free/en/papers/kuditipudi-2023-robust-distortion-free-watermarks-language/). Transactions on Machine Learning Research.
12. Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Veselin Stoyanov, and Luke Zettlemoyer. 2020. [Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension](https://md.research.elamur.ai/free/en/papers/lewis-2020-bart-denoising-sequence-sequence-pre/). In Proceedings of the 58th Annual Meeting of the…
13. Yinhan Liu, Jiatao Gu, Naman Goyal, Xian Li, Sergey Edunov, Marjan Ghazvininejad, Mike Lewis, and Luke Zettlemoyer. 2020. Multilingual denoising pre-training for neural machine translation. Transactions of the Association for Computational Linguistics, 8. [find](https://scholar.google.com/scholar?q=Yinhan+Liu%2C+Jiatao+Gu%2C+Naman+Goyal%2C+Xian+Li%2C+Sergey+Edunov%2C+Marjan+Ghazvininejad%2C+Mike+Lewis%2C+and+Luke+Zettlemoyer%2E+2020%2E+Multilingual+denoising+pre%2Dtraining+for+neural+machine+translation%2E+Transactio)
14. OpenAI, :, Aaron Hurst, Adam Lerer, Adam P. Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, Aleksander M adry, Alex Baker-Whitcomb, Alex Beutel, Alex Borzunov, Alex Carney, Alex Chow, Alex Kirillov, and 401 others. 2024. [Gpt-4o system card](https://md.research.elamur.ai/free/en/papers/openai-2024-gpt-4o-system-card/).…
15. OpenAI. 2022. ChatGPT: Optimizing language models for dialogue. Website. [https://openai.com/](https://openai.com/) blog/chatgpt. [↗](https://openai.com/)
16. Ya Jiang, Massieh Kordi Boroujeny, Surender Suresh Kumar, and Kai Zeng. 2026. Mirrormark: A distortion-free multi-bit watermark for large language models. Preprint, arXiv:2601.22246. — [arXiv:2601.22246](https://arxiv.org/abs/2601.22246) [find](https://scholar.google.com/scholar?q=Ya+Jiang%2C+Massieh+Kordi+Boroujeny%2C+Surender+Suresh+Kumar%2C+and+Kai+Zeng%2E+2026%2E+Mirrormark%3A+A+distortion%2Dfree+multi%2Dbit+watermark+for+large+language+models%2E+Preprint%2C+arXiv%3A2601%2E22246%2E+%E2%80%94+%5BarXiv%3A2601%2E222)
17. Shinwoo Park, Hyejin Park, Hyeseon Ahn, and Yo-Sub Han. 2025. Watermod: Modular token-rank partitioning for probability-balanced llm watermarking. Preprint, arXiv:2511.07863. — [arXiv:2511.07863](https://arxiv.org/abs/2511.07863) [find](https://scholar.google.com/scholar?q=Shinwoo+Park%2C+Hyejin+Park%2C+Hyeseon+Ahn%2C+and+Yo%2DSub+Han%2E+2025%2E+Watermod%3A+Modular+token%2Drank+partitioning+for+probability%2Dbalanced+llm+watermarking%2E+Preprint%2C+arXiv%3A2511%2E07863%2E+%E2%80%94+%5BarXiv%3A2511%2E07863%5D%28http)
18. Ya Jiang, Chuxiong Wu, Massieh Kordi Boroujeny, Brian L. Mark, and Kai Zeng. 2025. Stealthink: A multi-bit and stealthy watermark for large language models. arXiv preprint arXiv:2506.05502. — [arXiv:2506.05502](https://arxiv.org/abs/2506.05502) [find](https://scholar.google.com/scholar?q=Ya+Jiang%2C+Chuxiong+Wu%2C+Massieh+Kordi+Boroujeny%2C+Brian+L%2E+Mark%2C+and+Kai+Zeng%2E+2025%2E+Stealthink%3A+A+multi%2Dbit+and+stealthy+watermark+for+large+language+models%2E+arXiv+preprint+arXiv%3A2506%2E05502%2E+%E2%80%94+%5BarXiv%3A2)
19. Julien Piet, Chawin Sitawarin, Vivian Fang, Norman Mu, and David Wagner. 2023. Mark my words: Analyzing and evaluating language model watermarks. arXiv preprint arXiv:2312.00273. — [arXiv:2312.00273](https://arxiv.org/abs/2312.00273) [find](https://scholar.google.com/scholar?q=Julien+Piet%2C+Chawin+Sitawarin%2C+Vivian+Fang%2C+Norman+Mu%2C+and+David+Wagner%2E+2023%2E+Mark+my+words%3A+Analyzing+and+evaluating+language+model+watermarks%2E+arXiv+preprint+arXiv%3A2312%2E00273%2E+%E2%80%94+%5BarXiv%3A2312%2E00273%5D%28)
20. John Kirchenbauer, Jonas Geiping, Yuxin Wen, Jonathan Katz, Ian Miers, and Tom Goldstein. 2023. [A watermark for large language models](https://md.research.elamur.ai/free/en/papers/kirchenbauer-2023-watermark-large-language-models/). In Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pages 17061–17084. PMLR.
21. Wenjie Qu, Dong Yin, Zixin He, Wei Zou, Tianyang Tao, Jinyuan Jia, and Jiaheng Zhang. 2024. Provably Robust Multi-bit Watermarking for AI-generated Text via Error Correction Code. arXiv preprint arXiv:2401.16820. — [arXiv:2401.16820](https://arxiv.org/abs/2401.16820) [find](https://scholar.google.com/scholar?q=Wenjie+Qu%2C+Dong+Yin%2C+Zixin+He%2C+Wei+Zou%2C+Tianyang+Tao%2C+Jinyuan+Jia%2C+and+Jiaheng+Zhang%2E+2024%2E+Provably+Robust+Multi%2Dbit+Watermarking+for+AI%2Dgenerated+Text+via+Error+Correction+Code%2E+arXiv+preprint+arXiv)
22. John Kirchenbauer, Jonas Geiping, Yuxin Wen, Manli Shu, Khalid Saifullah, Kezhi Kong, Kasun Fernando, Aniruddha Saha, Micah Goldblum, and Tom Goldstein. 2024. [On the reliability of watermarks for large language models](https://md.research.elamur.ai/free/en/papers/kirchenbauer-2023-reliability-watermarks-large-language-models/). In ICLR.
23. Massieh Kordi Boroujeny, Ya Jiang, Kai Zeng, and Brian Mark. 2024. Multi-Bit Distortion-Free Watermarking for Large Language Models. arXiv preprint arXiv:2402.16578. — [arXiv:2402.16578](https://arxiv.org/abs/2402.16578) [find](https://scholar.google.com/scholar?q=Massieh+Kordi+Boroujeny%2C+Ya+Jiang%2C+Kai+Zeng%2C+and+Brian+Mark%2E+2024%2E+Multi%2DBit+Distortion%2DFree+Watermarking+for+Large+Language+Models%2E+arXiv+preprint+arXiv%3A2402%2E16578%2E+%E2%80%94+%5BarXiv%3A2402%2E16578%5D%28https%3A%2F%2Farxiv)
24. Kalpesh Krishna, Yixiao Song, Marzena Karpinska, John Wieting, and Mohit Iyyer. 2023. [Paraphrasing evades detectors of ai-generated text, but retrieval is an effective defense](https://md.research.elamur.ai/free/en/papers/krishna-2023-paraphrasing-evades-detectors-ai-generated/). In Proceedings of the 37th International Conference on Neural Information Processing Systems, NIPS ’23, Red Hook, NY, USA.…
25. Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu. 2020. [Exploring the limits of transfer learning with a unified text-to-text transformer](https://md.research.elamur.ai/free/en/papers/raffel-2019-exploring-limits-transfer-learning-unified/). Journal of machine learning research, 21(140).
26. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, and 1 others. 2023. [Llama 2: Open foundation and fine-tuned chat models](https://md.research.elamur.ai/free/en/papers/touvron-2023-llama-2-open-foundation-fine/). arXiv preprint arXiv:2307.09288.
27. Lean Wang, Wenkai Yang, Deli Chen, Hao Zhou, Yankai Lin, Fandong Meng, Jie Zhou, and Xu Sun. 2024. Towards codable watermarking for injecting multi-bits information to LLMs. In The Twelfth International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Lean+Wang%2C+Wenkai+Yang%2C+Deli+Chen%2C+Hao+Zhou%2C+Yankai+Lin%2C+Fandong+Meng%2C+Jie+Zhou%2C+and+Xu+Sun%2E+2024%2E+Towards+codable+watermarking+for+injecting+multi%2Dbits+information+to+LLMs%2E+In+The+Twelfth+Internation)
28. Yihan Wu, Zhengmian Hu, Hongyang Zhang, and Heng Huang. 2024. Dipmark: A stealthy, efficient and resilient watermark for large language models. In Proceedings of the 41st International Conference on Machine Learning. step index: fix a context h and the corresponding base distribution p 0 (· \| h). Th… [find](https://scholar.google.com/scholar?q=Yihan+Wu%2C+Zhengmian+Hu%2C+Hongyang+Zhang%2C+and+Heng+Huang%2E+2024%2E+Dipmark%3A+A+stealthy%2C+efficient+and+resilient+watermark+for+large+language+models%2E+In+Proceedings+of+the+41st+International+Conference+on+M)
29. KiYoon Yoo, Wonhyuk Ahn, and Nojun Kwak. 2024. Advancing beyond identification: Multi-bit watermark for large language models. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pa… [find](https://scholar.google.com/scholar?q=KiYoon+Yoo%2C+Wonhyuk+Ahn%2C+and+Nojun+Kwak%2E+2024%2E+Advancing+beyond+identification%3A+Multi%2Dbit+watermark+for+large+language+models%2E+In+Proceedings+of+the+2024+Conference+of+the+North+American+Chapter+of+th)

*Updated 2 November 2026*