  Text watermarking has emerged as a pivotal technique for identifying
machine-generated text. However, existing methods often rely on arbitrary
vocabulary partitioning during decoding to embed watermarks, which compromises
the availability of suitable tokens and significantly degrades the quality of
responses. This study assesses the impact of watermarking on different
capabilities of large language models (LLMs) from a cognitive science lens. Our
finding highlights a significant disparity; knowledge recall and logical
reasoning are more adversely affected than language generation. These results
suggest a more profound effect of watermarking on LLMs than previously
understood. To address these challenges, we introduce Watermarking with Mutual
Exclusion (WatME), a novel approach leveraging linguistic prior knowledge of
inherent lexical redundancy in LLM vocabularies to seamlessly integrate
watermarks. Specifically, WatME dynamically optimizes token usage during the
decoding process by applying a mutually exclusive rule to the identified
lexical redundancies. This strategy effectively prevents the unavailability of
appropriate tokens and preserves the expressive power of LLMs. We provide both
theoretical analysis and empirical evidence showing that WatME effectively
preserves the diverse capabilities of LLMs while ensuring watermark
detectability.
