Towards Better Statistical Understanding of Watermarking LLMs

• URL: http://arxiv.org/abs/2403.13027v1
• Date: Tue, 19 Mar 2024 01:57:09 GMT
• Title: Towards Better Statistical Understanding of Watermarking LLMs
• Authors: Zhongze Cai, Shang Liu, Hanzhao Wang, Huaiyang Zhong, Xiaocheng Li,
• Abstract summary: In this paper, we study the problem of watermarking large language models (LLMs) We consider the trade-off between model distortion and detection ability and it as a constrained optimization problem based on the green-red list of Kirchenbauer et al. We develop an online dual gradient ascent watermarking algorithm in light of this optimization formulation and prove its optimality between model distortion and detection ability.
• Score: 7.68488211412916
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the problem of watermarking large language models (LLMs). We consider the trade-off between model distortion and detection ability and formulate it as a constrained optimization problem based on the green-red algorithm of Kirchenbauer et al. (2023a). 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.

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