# Debiasing Watermarks for Large Language Models via Maximal Coupling

arXiv: https://arxiv.org/abs/2411.11203 · HTML: https://mlsanity.com/paper/2411.11203/

## Key facts

- Cited by 19 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 25 of its 53 references that are in the map.
- First posted on arXiv 17 Nov 2024.

## 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, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [ELI5: Long Form Question Answering](https://mlsanity.com/paper/1907.09190/) (2019)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models](https://mlsanity.com/paper/2311.04378/) (2023)
- [Three Bricks to Consolidate Watermarks for Large Language Models](https://mlsanity.com/paper/2308.00113/) (2023)
- [Mark My Words: Analyzing and Evaluating Language Model Watermarks](https://mlsanity.com/paper/2312.00273/) (2023)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [Tracing Text Provenance via Context-Aware Lexical Substitution](https://mlsanity.com/paper/2112.07873/) (2021)
- [WaterBench: Towards Holistic Evaluation of Watermarks for Large Language Models](https://mlsanity.com/paper/2311.07138/) (2023)
- [Towards Optimal Statistical Watermarking](https://mlsanity.com/paper/2312.07930/) (2023)
- [Towards Better Statistical Understanding of Watermarking LLMs](https://mlsanity.com/paper/2403.13027/) (2024)
- [The I/O Complexity of Attention, or How Optimal is Flash Attention?](https://mlsanity.com/paper/2402.07443/) (2024)
- [Higher criticism: p-values and criticism](https://mlsanity.com/paper/1411.1437/) (2014)

## Built on by (most cited first, 19 of 19)

- [A Comparison of DeepSeek and Other LLMs](https://mlsanity.com/paper/2502.03688/) (2025)
- [Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework](https://mlsanity.com/paper/2502.18049/) (2025)
- [Detecting LLM-Generated Text with Performance Guarantees](https://mlsanity.com/paper/2601.06586/) (2026)
- [Optimized Couplings for Watermarking Large Language Models](https://mlsanity.com/paper/2505.08878/) (2025)
- [A note on conditional PAC-efficient reasoning in large language model routing](https://mlsanity.com/paper/2512.03057/) (2025)
- [A Visual Semantic Adaptive Watermark grounded by Prefix-Tuning for Large Vision-Language Model](https://mlsanity.com/paper/2601.07291/) (2026)
- [Towards Robust Content Watermarking Against Removal and Forgery Attacks](https://mlsanity.com/paper/2604.06662/) (2026)
- [Perturbation is All You Need for Extrapolating Language Models](https://mlsanity.com/paper/2605.04344/) (2026)
- [HeavyWater and SimplexWater: Distortion-Free LLM Watermarks for Low-Entropy Next-Token Predictions](https://mlsanity.com/paper/2506.06409/) (2025)
- [Robust Spectral Watermark for Synthetic Tabular Data](https://mlsanity.com/paper/2511.21600/) (2025)
- [Improving the Trade-off Between Watermark Strength and Speculative Sampling Efficiency for Language Models](https://mlsanity.com/paper/2602.01428/) (2026)
- [Linear Ensembles Wash Away Watermarks: On the Fragility of Distributional Perturbations in LLMs](https://mlsanity.com/paper/2605.30501/) (2026)
- [Geometric Reciprocity: Unlocking Self-Supervision for Stereoscopic Video Generation](https://mlsanity.com/paper/2607.05354/) (2026)
- [Adaptive Testing for Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2511.06645/) (2025)
- [MarkTune: Improving the Quality-Detectability Trade-off in Open-Weight LLM Watermarking](https://mlsanity.com/paper/2512.04044/) (2025)
- [ADD for Multi-Bit Image Watermarking](https://mlsanity.com/paper/2604.11491/) (2026)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)
- [Detecting LLM-Generated Tokens in Human--LLM Coauthored Text](https://mlsanity.com/paper/2607.21458/) (2026)
- [textGrain watermarking is harder to detect: can sum-tests still do it optimally?](https://mlsanity.com/paper/2610.17655/) (2026)

## Abstract (arXiv)

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. We present a novel green/red list watermarking approach that partitions the token set into ``green'' and ``red'' lists, subtly increasing the generation probability for green tokens. To correct token distribution bias, our method employs maximal coupling, using a uniform coin flip to decide whether to apply bias correction, with the result embedded as a pseudorandom watermark signal. Theoretical analysis confirms this approach's unbiased nature and robust detection capabilities. Experimental results show that it outperforms prior techniques by preserving text quality while maintaining high detectability, and it demonstrates resilience to targeted modifications aimed at improving text quality. This research provides a promising watermarking solution for language models, balancing effective detection with minimal impact on text quality.