Optimized Couplings for Watermarking Large Language Models

TL;DR

This paper analyzes the fundamental trade-offs in watermarking large language models, proposing an optimal coupling strategy that balances detection accuracy and text quality preservation, with theoretical and numerical validation.

Contribution

It introduces a novel coupling-based watermarking scheme optimized for worst-case LLM distributions, providing closed-form detection rates and practical comparisons.

Findings

Optimal coupling strategy enhances watermark detection

Proposed scheme approaches theoretical detection limits

Numerical results validate effectiveness on synthetic and real data

Abstract

Large-language models (LLMs) are now able to produce text that is, in many cases, seemingly indistinguishable from human-generated content. This has fueled the development of watermarks that imprint a ``signal'' in LLM-generated text with minimal perturbation of an LLM's output. This paper provides an analysis of text watermarking in a one-shot setting. Through the lens of hypothesis testing with side information, we formulate and analyze the fundamental trade-off between watermark detection power and distortion in generated textual quality. We argue that a key component in watermark design is generating a coupling between the side information shared with the watermark detector and a random partition of the LLM vocabulary. Our analysis identifies the optimal coupling and randomization strategy under the worst-case LLM next-token distribution that satisfies a min-entropy constraint. We provide a closed-form expression of the resulting detection rate under the proposed scheme and quantify the cost in a max-min sense. Finally, we provide an array of numerical results, comparing the proposed scheme with the theoretical optimum and existing schemes, in both synthetic data and LLM watermarking. Our code is available at https://github.com/Carol-Long/CC_Watermark