Optimized Couplings for Watermarking Large Language Models
This work addresses the need for effective watermarking to distinguish AI-generated text, but it is incremental as it builds on existing hypothesis testing frameworks.
The paper tackles the problem of watermarking large language models by analyzing the trade-off between detection power and text quality distortion, providing a closed-form expression for detection rate and showing numerical comparisons with existing schemes.
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