No Free Lunch Theorem for Privacy-Preserving LLM Inference

2024-05-31

arXiv.org

AI Summary

This work addresses privacy leakage risks in large language model (LLM) inference, focusing on the fundamental trade-off between privacy protection and model utility. Method: We develop a formal information-theoretic and statistical inference framework that integrates randomized prompt design with adversarial risk modeling to rigorously analyze privacy–utility interplay. Contribution/Results: We propose and prove the first “No-Free-Lunch” theorem for LLM inference, establishing that any randomization mechanism reducing dependence between prompts and private inputs necessarily degrades utility, with a universal, unavoidable lower bound. Our analysis provides the first theoretical limits for privacy-preserving LLM inference, refuting the common assumption that strong privacy guarantees can be achieved without utility loss. The results offer foundational insights for trustworthy LLM deployment.

Technology Category

• Machine Learning: Privacy
• Natural Language Processing: (Large) Language Models
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Privacy concerns in LLM interactions
• Balance privacy protection and utility
• Framework for privacy-preserving LLM inference

Innovation

• Privacy-preserving LLM inference framework
• Balancing privacy and utility loss
• NFL Theorem for privacy protection