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：个体和企业已通过包括PaLM、Gemini和ChatGPT在内的大语言模型（LLMs）在多方面显著获益。例如，LLMs能提升生产效率、降低成本，并使我们能专注于更具价值的任务。此外，LLMs具备筛选海量数据集、揭示潜在模式并提供关键洞见的能力，从而推动技术与科学的前沿发展。然而，LLMs也引发了隐私担忧。用户与LLMs的交互可能暴露其敏感的个人或公司信息。若缺乏健全的隐私保护措施与法律框架，可能导致对个人数据的无端侵入或不当处理，从而危及隐私侵犯与身份盗用风险。为确保隐私，必须最小化共享提示词与私人信息之间的关联性。已有多种随机化方法被提出以保护提示词的隐私，但与未受保护的LLMs提示相比，这些方法可能导致效用损失。因此，在实施有效保护机制时，必须评估隐私泄露风险与效用损失之间的平衡。本研究构建了一个用于推理隐私保护大语言模型（LLMs）的框架，并为审视隐私保护与效用之间的相互作用奠定了坚实的理论基础。其核心洞见被概括为一个称为NFL（即“无免费午餐”的缩写）定理的定理。