Faculty, Staff and Student Publications
Language
English
Publication Date
2-1-2025
Journal
Annals of Statistics
DOI
10.1214/24-aos2468
PMID
41018122
PMCID
PMC12467635
PubMedCentral® Posted Date
2-13-2026
PubMedCentral® Full Text Version
Author MSS
Abstract
Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the hypothesis testing formulation of watermark detection, our framework starts by selecting a pivotal statistic of the text and a secret key-provided by the LLM to the verifier-to control the false positive rate (the error of mistakenly detecting human-written text as LLM-generated). Next, this framework allows one to evaluate the power of watermark detection rules by obtaining a closed-form expression of the asymptotic false negative rate (the error of incorrectly classifying LLM-generated text as human-written). Our framework further reduces the problem of determining the optimal detection rule to solving a minimax optimization program. We apply this framework to two representative watermarks-one of which has been internally implemented at OpenAI-and obtain several findings that can be instrumental in guiding the practice of implementing watermarks. In particular, we derive optimal detection rules for these watermarks under our framework. These theoretically derived detection rules are demonstrated to be competitive and sometimes enjoy a higher power than existing detection approaches through numerical experiments.
Published Open-Access
yes
Recommended Citation
Li, Xiang; Ruan, Feng; Wang, Huiyuan; et al., "A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules" (2025). Faculty, Staff and Student Publications. 930.
https://digitalcommons.library.tmc.edu/uthshis_docs/930