Towards Anytime-Valid Statistical Watermarking

TL;DR

This paper introduces a new e-value-based watermarking framework for LLMs that allows for efficient, anytime-valid detection of machine-generated text, overcoming limitations of fixed-horizon methods.

Contribution

It develops the first principled, anytime-valid watermarking method using e-values, enabling adaptive detection with improved sample efficiency.

Findings

Reduces token budget for detection by 13-15% compared to baselines.

Provides a theoretical foundation for optimal sampling and stopping time.

Demonstrates effectiveness through simulations and benchmark evaluations.

Abstract

The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.