Semantic-level watermarking (SWM) for large language models (LLMs) enhances watermarking robustness against text modifications and paraphrasing attacks by treating the sentence as the fundamental unit. However, existing methods still lack strong theoretical guarantees of robustness, and reject-sampling-based generation often introduces significant distribution distortions compared with unwatermarked outputs. In this work, we introduce a new theoretical framework on SWM through the concept of proxy functions (PFs) $\unicode{x2013}$ functions that map sentences to scalar values. Building on this framework, we propose PMark, a simple yet powerful SWM method that estimates the PF median for the next sentence dynamically through sampling while enforcing multiple PF constraints (which we call channels) to strengthen watermark evidence. Equipped with solid theoretical guarantees, PMark achieves the desired distortion-free property and improves the robustness against paraphrasing-style attacks. We also provide an empirically optimized version that further removes the requirement for dynamical median estimation for better sampling efficiency. Experimental results show that PMark consistently outperforms existing SWM baselines in both text quality and robustness, offering a more effective paradigm for detecting machine-generated text. Our code will be released at [this URL](https://github.com/PMark-repo/PMark).

翻译：针对大型语言模型（LLM）的语义级水印（SWM）通过将句子作为基本单元，增强了水印对文本修改和转述攻击的鲁棒性。然而，现有方法仍缺乏坚实的鲁棒性理论保证，且基于拒绝采样的生成方式相较于无水印输出常引入显著的分布失真。本文通过代理函数（PF）——将句子映射为标量值的函数——这一概念，提出了一个新的语义级水印理论框架。基于此框架，我们提出PMark，一种简洁而强大的语义级水印方法。该方法通过采样动态估计下一句的PF中值，同时施加多重PF约束（我们称之为信道）以增强水印证据。凭借坚实的理论保证，PMark实现了理想的无失真特性，并提升了对转述式攻击的鲁棒性。我们还提供了一个经验优化的版本，进一步消除了动态中值估计的需求，从而提高了采样效率。实验结果表明，PMark在文本质量和鲁棒性方面均持续优于现有的语义级水印基线方法，为检测机器生成文本提供了一种更有效的范式。我们的代码将在[此网址](https://github.com/PMark-repo/PMark)发布。