# Necessary and Sufficient Watermark for Large Language Models

arXiv: https://arxiv.org/abs/2310.00833 · HTML: https://mlsanity.com/paper/2310.00833/

## 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 26 of its 30 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## 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, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [No Language Left Behind: Scaling Human-Centered Machine Translation](https://mlsanity.com/paper/2207.04672/) (2022)
- [DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature](https://mlsanity.com/paper/2301.11305/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Defending Against Neural Fake News](https://mlsanity.com/paper/1905.12616/) (2019)
- [GLTR: Statistical Detection and Visualization of Generated Text](https://mlsanity.com/paper/1906.04043/) (2019)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (2023)
- [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)
- [Distortion Agnostic Deep Watermarking](https://mlsanity.com/paper/2001.04580/) (2020)
- [Protecting Language Generation Models via Invisible Watermarking](https://mlsanity.com/paper/2302.03162/) (2023)
- [Protecting Intellectual Property of Language Generation APIs with Lexical Watermark](https://mlsanity.com/paper/2112.02701/) (2021)
- [CATER: Intellectual Property Protection on Text Generation APIs via Conditional Watermarks](https://mlsanity.com/paper/2209.08773/) (2022)
- [Are You Copying My Model? Protecting the Copyright of Large Language Models for EaaS via Backdoor Watermark](https://mlsanity.com/paper/2305.10036/) (2023)
- [DeAR: A Deep-learning-based Audio Re-recording Resilient Watermarking](https://mlsanity.com/paper/2212.02339/) (2022)

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

- [Watermark Stealing in Large Language Models](https://mlsanity.com/paper/2402.19361/) (2024)
- [Mark My Words: Analyzing and Evaluating Language Model Watermarks](https://mlsanity.com/paper/2312.00273/) (2023)
- [Copyright Protection in Generative AI: A Technical Perspective](https://mlsanity.com/paper/2402.02333/) (2024)
- [Embarrassingly Simple Text Watermarks](https://mlsanity.com/paper/2310.08920/) (2023)
- [Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach](https://mlsanity.com/paper/2410.02890/) (2024)
- [WAPITI: A Watermark for Finetuned Open-Source LLMs](https://mlsanity.com/paper/2410.06467/) (2024)
- [PASA: A Principled Embedding-Space Watermarking Approach for LLM-Generated Text under Semantic-Invariant Attacks](https://mlsanity.com/paper/2605.10977/) (2026)
- [Building Intelligence Identification System via Large Language Model Watermarking: A Survey and Beyond](https://mlsanity.com/paper/2407.11100/) (2024)
- [SoK: Are Watermarks in LLMs Ready for Deployment?](https://mlsanity.com/paper/2506.05594/) (2025)
- [RLCracker: Evaluating the Worst-Case Vulnerability of LLM Watermarks with Adaptive RL Attacks](https://mlsanity.com/paper/2509.20924/) (2025)
- [SimKey: A Semantically Aware Key Module for Watermarking Language Models](https://mlsanity.com/paper/2510.12828/) (2025)
- [Block-wise Codeword Embedding for Reliable Multi-bit Text Watermarking](https://mlsanity.com/paper/2605.00348/) (2026)
- [Learning to Watermark: A Selective Watermarking Framework for Large Language Models via Multi-Objective Optimization](https://mlsanity.com/paper/2510.15976/) (2025)
- [Toward Copyright Integrity and Verifiability via Multi-Bit Watermarking for Intelligent Transportation Systems](https://mlsanity.com/paper/2502.05425/) (2025)
- [Semantic Differentiation for Tackling Challenges in Watermarking Low-Entropy Constrained Generation Outputs](https://mlsanity.com/paper/2601.11629/) (2026)
- [Optimal Multi-bit Generative Watermarking Schemes Under Worst-Case False-Alarm Constraints](https://mlsanity.com/paper/2604.08759/) (2026)
- [Watermarking Game-Playing Agents in Perfect-Information Extensive-Form Games](https://mlsanity.com/paper/2605.14283/) (2026)
- [CORE-BREW: LLR-Based Soft Decoding for Robust Multi-Bit LLM Watermarking](https://mlsanity.com/paper/2606.24163/) (2026)
- [Preserving Structure, Strengthening Signals: A Grammar-Driven Approach to Optimize the Trade-off Between Quality and Detectability in Code Watermarking](https://mlsanity.com/paper/2607.10210/) (2026)

## Abstract (arXiv)

In recent years, large language models (LLMs) have achieved remarkable performances in various NLP tasks. They can generate texts that are indistinguishable from those written by humans. Such remarkable performance of LLMs increases their risk of being used for malicious purposes, such as generating fake news articles. Therefore, it is necessary to develop methods for distinguishing texts written by LLMs from those written by humans. Watermarking is one of the most powerful methods for achieving this. Although existing watermarking methods have successfully detected texts generated by LLMs, they significantly degrade the quality of the generated texts. In this study, we propose the Necessary and Sufficient Watermark (NS-Watermark) for inserting watermarks into generated texts without degrading the text quality. More specifically, we derive minimum constraints required to be imposed on the generated texts to distinguish whether LLMs or humans write the texts. Then, we formulate the NS-Watermark as a constrained optimization problem and propose an efficient algorithm to solve it. Through the experiments, we demonstrate that the NS-Watermark can generate more natural texts than existing watermarking methods and distinguish more accurately between texts written by LLMs and those written by humans. Especially in machine translation tasks, the NS-Watermark can outperform the existing watermarking method by up to 30 BLEU scores.