# GumbelSoft: Diversified Language Model Watermarking via the GumbelMax-trick

arXiv: https://arxiv.org/abs/2402.12948 · HTML: https://mlsanity.com/paper/2402.12948/

## Key facts

- Cited by 37 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 31 of its 51 references that are in the map.
- First posted on arXiv 20 Feb 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, 30 of 31)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature](https://mlsanity.com/paper/2301.11305/) (2023)
- [Defending Against Neural Fake News](https://mlsanity.com/paper/1905.12616/) (2019)
- [Release Strategies and the Social Impacts of Language Models](https://mlsanity.com/paper/1908.09203/) (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)
- [Fast-DetectGPT: Efficient Zero-Shot Detection of Machine-Generated Text via Conditional Probability Curvature](https://mlsanity.com/paper/2310.05130/) (2023)
- [DetectLLM: Leveraging Log Rank Information for Zero-Shot Detection of Machine-Generated Text](https://mlsanity.com/paper/2306.05540/) (2023)
- [DNA-GPT: Divergent N-Gram Analysis for Training-Free Detection of GPT-Generated Text](https://mlsanity.com/paper/2305.17359/) (2023)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [A Survey of Text Watermarking in the Era of Large Language Models](https://mlsanity.com/paper/2312.07913/) (2023)
- [On the Possibilities of AI-Generated Text Detection](https://mlsanity.com/paper/2304.04736/) (2023)
- [Robust Multi-bit Natural Language Watermarking through Invariant Features](https://mlsanity.com/paper/2305.01904/) (2023)
- [A Robust Semantics-based Watermark for Large Language Model against Paraphrasing](https://mlsanity.com/paper/2311.08721/) (2023)
- [CATER: Intellectual Property Protection on Text Generation APIs via Conditional Watermarks](https://mlsanity.com/paper/2209.08773/) (2022)
- [Publicly-Detectable Watermarking for Language Models](https://mlsanity.com/paper/2310.18491/) (2023)
- [A Survey on Detection of LLMs-Generated Content](https://mlsanity.com/paper/2310.15654/) (2023)
- [Multiscale Positive-Unlabeled Detection of AI-Generated Texts](https://mlsanity.com/paper/2305.18149/) (2023)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Tracing Text Provenance via Context-Aware Lexical Substitution](https://mlsanity.com/paper/2112.07873/) (2021)
- [Origin Tracing and Detecting of LLMs](https://mlsanity.com/paper/2304.14072/) (2023)
- [GPT-who: An Information Density-based Machine-Generated Text Detector](https://mlsanity.com/paper/2310.06202/) (2023)
- [The Threat of Offensive AI to Organizations](https://mlsanity.com/paper/2106.15764/) (2021)
- [Smaller Language Models are Better Black-box Machine-Generated Text Detectors](https://mlsanity.com/paper/2305.09859/) (2023)
- [Efficient Detection of LLM-generated Texts with a Bayesian Surrogate Model](https://mlsanity.com/paper/2305.16617/) (2023)

## Built on by (most cited first, 30 of 37)

- [Watermarking Makes Language Models Radioactive](https://mlsanity.com/paper/2402.14904/) (2024)
- [SoK: Watermarking for AI-Generated Content](https://mlsanity.com/paper/2411.18479/) (2024)
- [Watermarking Techniques for Large Language Models: A Survey](https://mlsanity.com/paper/2409.00089/) (2024)
- [Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach](https://mlsanity.com/paper/2410.02890/) (2024)
- [Dataset Protection via Watermarked Canaries in Retrieval-Augmented LLMs](https://mlsanity.com/paper/2502.10673/) (2025)
- [In-Context Watermarks for Large Language Models](https://mlsanity.com/paper/2505.16934/) (2025)
- [On Protecting Agentic Systems' Intellectual Property via Watermarking](https://mlsanity.com/paper/2602.08401/) (2026)
- [Position: LLM Watermarking Should Align Stakeholders' Incentives for Practical Adoption](https://mlsanity.com/paper/2510.18333/) (2025)
- [PASA: A Principled Embedding-Space Watermarking Approach for LLM-Generated Text under Semantic-Invariant Attacks](https://mlsanity.com/paper/2605.10977/) (2026)
- [On the Empirical Power of Goodness-of-Fit Tests in Watermark Detection](https://mlsanity.com/paper/2510.03944/) (2025)
- [Lost in Overlap: Exploring Logit-based Watermark Collision in LLMs](https://mlsanity.com/paper/2403.10020/) (2024)
- [Addressing Tokenization Inconsistency in Steganography and Watermarking Based on Large Language Models](https://mlsanity.com/paper/2508.20718/) (2025)
- [Enhancing Watermarking Quality for LLMs via Contextual Generation States Awareness](https://mlsanity.com/paper/2506.07403/) (2025)
- [Multi-use LLM Watermarking and the False Detection Problem](https://mlsanity.com/paper/2506.15975/) (2025)
- [MirrorMark: Generalizable Mirrored Sampling for Multi-bit LLM Watermarking](https://mlsanity.com/paper/2601.22246/) (2026)
- [SoK: Are Watermarks in LLMs Ready for Deployment?](https://mlsanity.com/paper/2506.05594/) (2025)
- [SimKey: A Semantically Aware Key Module for Watermarking Language Models](https://mlsanity.com/paper/2510.12828/) (2025)
- [LLM-Text Watermarking based on Lagrange Interpolation](https://mlsanity.com/paper/2505.05712/) (2025)
- [HeavyWater and SimplexWater: Distortion-Free LLM Watermarks for Low-Entropy Next-Token Predictions](https://mlsanity.com/paper/2506.06409/) (2025)
- [Improving the Trade-off Between Watermark Strength and Speculative Sampling Efficiency for Language Models](https://mlsanity.com/paper/2602.01428/) (2026)
- [Watermark Smoothing Attacks against Language Models](https://mlsanity.com/paper/2407.14206/) (2024)
- [Watermarking Generative Categorical Data](https://mlsanity.com/paper/2411.10898/) (2024)
- [Disappearing Ink: Obfuscation Breaks N-gram Code Watermarks in Theory and Practice](https://mlsanity.com/paper/2507.05512/) (2025)
- [Adaptive Testing for Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2511.06645/) (2025)
- [UniMark: Artificial Intelligence Generated Content Identification Toolkit](https://mlsanity.com/paper/2512.12324/) (2025)
- [CODE ACROSTIC: Robust Watermarking for Code Generation](https://mlsanity.com/paper/2512.14753/) (2025)
- [WorldCup Sampling for Multi-bit LLM Watermarking](https://mlsanity.com/paper/2602.01752/) (2026)
- [On Google's SynthID-Text LLM Watermarking System: Theoretical Analysis and Empirical Validation](https://mlsanity.com/paper/2603.03410/) (2026)
- [Rethinking LLM Watermark Detection in Black-Box Settings: A Non-Intrusive Third-Party Framework](https://mlsanity.com/paper/2603.14968/) (2026)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excellently generate human-like text, but also raise concerns about misuse in fake news and academic dishonesty. Decoding-based watermark, particularly the GumbelMax-trick-based watermark(GM watermark), is a standout solution for safeguarding machine-generated texts due to its notable detectability. However, GM watermark encounters a major challenge with generation diversity, always yielding identical outputs for the same prompt, negatively impacting generation diversity and user experience. To overcome this limitation, we propose a new type of GM watermark, the Logits-Addition watermark, and its three variants, specifically designed to enhance diversity. Among these, the GumbelSoft watermark (a softmax variant of the Logits-Addition watermark) demonstrates superior performance in high diversity settings, with its AUROC score outperforming those of the two alternative variants by 0.1 to 0.3 and surpassing other decoding-based watermarking methods by a minimum of 0.1.