Optimal Multi-bit Generative Watermarking Schemes Under Worst-Case False-Alarm Constraints

2026-04-09

AI Summary

This work addresses the gap between existing multi-bit generative watermarking schemes for large language models and their theoretical performance limits under worst-case false positive constraints. By formulating the problem as a linear program, the authors propose two novel structured encoding–decoding schemes that provably achieve the theoretical lower bound on missed detection probability for finite text lengths, thereby attaining optimal watermark performance in this setting for the first time. The study not only uncovers the fundamental reasons behind the suboptimality of prior approaches but also systematically characterizes the practical trade-offs between the two proposed schemes, offering a complete solution to the optimal design of multi-bit generative watermarks.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

This paper considers the problem of multi-bit generative watermarking for large language models under a worst-case false-alarm constraint. Prior work established a lower bound on the achievable miss-detection probability in the finite-token regime and proposed a scheme claimed to achieve this bound. We show, however, that the proposed scheme is in fact suboptimal. We then develop two new encoding-decoding constructions that attain the previously established lower bound, thereby completely characterizing the optimal multi-bit watermarking performance. Our approach formulates the watermark design problem as a linear program and derives the structural conditions under which optimality can be achieved. In addition, we identify the failure mechanism of the previous construction and compare the tradeoffs between the two proposed schemes.

Problem

• multi-bit watermarking
• generative watermarking
• large language models
• false-alarm constraint
• optimal performance

Innovation

• generative watermarking
• multi-bit encoding
• optimal detection
• linear programming
• false-alarm constraint