Towards Better Statistical Understanding of Watermarking LLMs

• 成果类型: Article
• 署名作者: Cai, Zhongze; Liu, Shang; Wang, Hanzhao; Zhong, Huaiyang; Li, Xiaocheng
• 署名单位: Imperial College London; University of Sydney; Virginia Polytechnic Institute & State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2618290
• 发表日期: 2026-01-02
• 页码: 247-258
• 关键词: Dual gradient ascent; Kullback-Leibler divergence; Large language models; Pareto optimal; Watermarking

摘要

In this article, we study the problem of watermarking large language models (LLMs). We consider the tradeoff between model distortion and detection ability and formulate it as a constrained optimization problem based on the red-green list watermarking algorithm. We show that the optimal solution to the optimization problem enjoys a nice analytical property which provides a better understanding and inspires the algorithm design for the watermarking process. We develop an online dual gradient ascent watermarking algorithm in light of this optimization formulation and prove its asymptotic Pareto optimality between model distortion and detection ability. Such a result guarantees an averaged increased green list probability and henceforth detection ability explicitly (in contrast to previous results). Moreover, we provide a systematic discussion on the choice of the model distortion metrics for the watermarking problem. We justify our choice of KL divergence and present issues with the existing criteria of distortion-free and perplexity. Finally, we empirically evaluate our algorithms on extensive datasets against benchmark algorithms. Supplementary materials for this article are available online.