Individuals and businesses have been significantly benefited by Large Language Models (LLMs) including PaLM, Gemini and ChatGPT in various ways. For example, LLMs enhance productivity, reduce costs, and enable us to focus on more valuable tasks. Furthermore, LLMs possess the capacity to sift through extensive datasets, uncover underlying patterns, and furnish critical insights that propel the frontiers of technology and science. However, LLMs also pose privacy concerns. Users' interactions with LLMs may expose their sensitive personal or company information. A lack of robust privacy safeguards and legal frameworks could permit the unwarranted intrusion or improper handling of individual data, thereby risking infringements of privacy and the theft of personal identities. To ensure privacy, it is essential to minimize the dependency between shared prompts and private information. Various randomization approaches have been proposed to protect prompts' privacy, but they may incur utility loss compared to unprotected LLMs prompting. Therefore, it is essential to evaluate the balance between the risk of privacy leakage and loss of utility when conducting effective protection mechanisms. The current study develops a framework for inferring privacy-protected Large Language Models (LLMs) and lays down a solid theoretical basis for examining the interplay between privacy preservation and utility. The core insight is encapsulated within a theorem that is called as the NFL (abbreviation of the word No-Free-Lunch) Theorem.

翻译：个人和企业已通过PaLM、Gemini和ChatGPT等大语言模型在诸多方面获得显著效益。例如，大语言模型能提升生产效率、降低成本，并使我们得以专注于更具价值的任务。此外，大语言模型具备筛选海量数据集、发现潜在模式及提供关键见解的能力，从而推动科技与科学的前沿发展。然而，大语言模型亦引发隐私隐忧。用户与大语言模型的交互可能暴露其敏感的个人或企业信息。若缺乏健全的隐私保护措施与法律框架，可能导致个人数据遭受不当侵入或违规处理，进而引发隐私侵犯与身份盗用风险。为确保隐私安全，必须最小化共享提示词与私有信息之间的关联性。现有研究已提出多种随机化方法以保护提示词隐私，但与未受保护的提示词相比，这些方法可能导致效用损失。因此，在实施有效保护机制时，必须审慎评估隐私泄露风险与效用损失之间的平衡关系。本研究构建了一个用于推理隐私保护大语言模型的框架，并为审视隐私保护与效用间的相互作用奠定了坚实的理论基础。其核心思想凝练于一项定理——即被称为NFL（"无免费午餐"的缩写）定理。