A Watermark for Low-entropy and Unbiased Generation in Large Language Models

Recent advancements in large language models (LLMs) have highlighted the risk of misusing them, raising the need for accurate detection of LLM-generated content. In response, a viable solution is to inject imperceptible identifiers into LLMs, known as watermarks. Previous work demonstrates that unbiased watermarks ensure unforgeability and preserve text quality by maintaining the expectation of the LLM output probability distribution. However, previous unbiased watermarking methods suffer from one or more of the following issues: (1) requiring access to white-box LLMs during detection, (2) incurring long detection time, (3) being not robust against simple watermarking attacks, (4) failing to provide statistical guarantees for the type II error of watermark detection, and (5) being not statistically unbiased for low-entropy scenarios, which hinder their deployment in practice. This study proposes the Sampling One Then Accepting (STA-1) method, a watermark that can address all of these issues. Moreover, we discuss the tradeoff between watermark strength and text quality for unbiased watermarks. We show that in low-entropy scenarios, unbiased watermarks face a tradeoff between watermark strength and the risk of unsatisfactory outputs. Experimental results on both low-entropy and high-entropy datasets demonstrate that STA-1 achieves text quality and watermark strength comparable to existing unbiased watermarks, with a low risk of unsatisfactory outputs. Implementation codes for this study are available online.