Towards Anytime-Valid Statistical Watermarking

2026-02-19

AI Summary

This work addresses the limitations of existing large language model watermarking methods, which lack principled sampling mechanisms and rely on fixed-horizon hypothesis testing, thereby hindering effective early stopping. The authors propose Anchored E-Watermarking, the first e-value–based watermarking framework that approximates the target model via an anchor distribution to construct a test supermartingale. This enables statistically valid inference at any time and supports optional stopping while rigorously controlling Type I error. By introducing anytime-valid inference to watermarking for the first time and optimizing the worst-case log growth rate for improved efficiency, the method achieves notable gains in sample efficiency. Experiments on standard benchmarks show a 13–15% reduction in the average number of tokens required for detection compared to the current state-of-the-art.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Computer Vision: Large Vision Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

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.

Problem

• statistical watermarking
• anytime-valid inference
• sampling distribution
• hypothesis testing
• LLM-generated text

Innovation

• e-value
• anytime-valid inference
• statistical watermarking
• test supermartingale
• anchor distribution