A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules

2024-04-01

arXiv.org

AI Summary

This paper addresses the statistical evaluation and optimization of text watermarking for large language models (LLMs). Methodologically, it introduces the first unified statistical inference framework for watermark detection, proposing a pivot-based detection paradigm jointly controlled by statistical pivots and secret keys. The design of optimal detection rules is formulated as a minimax optimization problem, and the asymptotic bound on the missed-detection rate is rigorously derived. Theoretical contributions include: (i) establishing the first unified analytical framework for characterizing watermark detection efficacy; (ii) deriving theoretically optimal detection rules for two mainstream watermarking schemes—including the one adopted by OpenAI; and (iii) guaranteeing controllable false-positive rates and provably optimal detection power. Numerical experiments demonstrate that the proposed rules significantly reduce the missed-detection rate while maintaining low false-positive rates, achieving detection power comparable to or exceeding state-of-the-art methods.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Fact-Checking / Misinformation Detection (NLP Focus)
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the hypothesis testing formulation of watermark detection, our framework starts by selecting a pivotal statistic of the text and a secret key -- provided by the LLM to the verifier -- to enable controlling the false positive rate (the error of mistakenly detecting human-written text as LLM-generated). Next, this framework allows one to evaluate the power of watermark detection rules by obtaining a closed-form expression of the asymptotic false negative rate (the error of incorrectly classifying LLM-generated text as human-written). Our framework further reduces the problem of determining the optimal detection rule to solving a minimax optimization program. We apply this framework to two representative watermarks -- one of which has been internally implemented at OpenAI -- and obtain several findings that can be instrumental in guiding the practice of implementing watermarks. In particular, we derive optimal detection rules for these watermarks under our framework. These theoretically derived detection rules are demonstrated to be competitive and sometimes enjoy a higher power than existing detection approaches through numerical experiments.

Problem

• Develops a statistical framework for LLM watermark detection
• Optimizes detection rules to minimize false positive and negative rates
• Evaluates and compares watermark efficiency for practical implementation guidance

Innovation

• Statistical framework for LLM watermark detection
• Pivotal statistics and secret key control false positives
• Minimax optimization derives optimal detection rules