# Efficient Online LLM Watermark Detection via Rao-Blackwellized E-Processes

arXiv: https://arxiv.org/abs/2607.21958 · HTML: https://mlsanity.com/paper/2607.21958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 24 Jul 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, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [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)
- [Fast-DetectGPT: Efficient Zero-Shot Detection of Machine-Generated Text via Conditional Probability Curvature](https://mlsanity.com/paper/2310.05130/) (2023)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [DetectLLM: Leveraging Log Rank Information for Zero-Shot Detection of Machine-Generated Text](https://mlsanity.com/paper/2306.05540/) (2023)
- [Automatic Detection of Machine Generated Text: A Critical Survey](https://mlsanity.com/paper/2011.01314/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [The Science of Detecting LLM-Generated Texts](https://mlsanity.com/paper/2303.07205/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Three Bricks to Consolidate Watermarks for Large Language Models](https://mlsanity.com/paper/2308.00113/) (2023)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [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)
- [Raidar: geneRative AI Detection viA Rewriting](https://mlsanity.com/paper/2401.12970/) (2024)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [Robust Detection of Watermarks for Large Language Models Under Human Edits](https://mlsanity.com/paper/2411.13868/) (2024)
- [AdaDetectGPT: Adaptive Detection of LLM-Generated Text with Statistical Guarantees](https://mlsanity.com/paper/2510.01268/) (2025)
- [Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2410.22318/) (2024)
- [Detecting LLM-Generated Text with Performance Guarantees](https://mlsanity.com/paper/2601.06586/) (2026)

## Abstract (arXiv)

As large language models (LLMs) are increasingly deployed, reliable and efficient mechanisms for distinguishing AI-generated text from human-written content have become essential. Statistical watermarking has emerged as a promising solution, yet most existing methods are typically fixed-horizon procedures, precluding valid early stopping in streaming generation. In this paper, we develop an efficient online watermark detection framework with anytime-valid inference based on Rao-Blackwellized e-processes, enabling recursive token-level evidence updates without storing the full history. In particular, we instantiate the framework for the Gumbel-max watermark and reduce the original token-level dependence testing problem to a pivot-induced sequential testing problem with an explicit null distribution. Theoretically, we prove anytime-valid Type I error control under arbitrary optional stopping and establish positive asymptotic log-growth under watermarking, implying consistency of the proposed stopping rules. Simulations and experiments on real LLM-generated text demonstrate efficient online detection with rigorous anytime-valid guarantees.