Pseudo- vs. True-Randomness: Rethinking Distortion-Free Watermarks of Language Models under Watermark Key Collisions

Yihan Wu, Ruibo Chen, Zhengmian Hu, Yanshuo Chen, Junfeng Guo, Hongyang Zhang, Heng Huang

Keywords: LLM watermarking

Abstract: Language model (LM) watermarking techniques inject a statistical signal into LM-generated content by substituting the random sampling process with pseudo-random sampling, using watermark keys as the random seed. Among these statistical watermarking approaches, distortion-free watermarks are particularly crucial because they embed watermarks into LM-generated content without compromising generation quality. However, one notable limitation of pseudo-random sampling compared to true-random sampling is that, under the same watermark keys (i.e., key collision), the results of pseudo-random sampling exhibit correlations. This limitation could potentially undermine the distortion-free property. Our studies reveal that key collisions are inevitable due to the limited availability of watermark keys, and existing distortion-free watermarks exhibit a significant distribution bias toward the original LM distribution in the presence of key collisions. Moreover, we go beyond the key collision condition and prove that achieving a perfect distortion-free watermark is impossible. To study the trade-off between watermark strength and its distribution bias, we introduce a new family of distortion-free watermarks--beta-watermark. Experimental results support that the beta-watermark can effectively reduce the distribution bias under key collisions.

Primary Area: generative models

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Submission Number: 4867