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

TL;DR

This paper analyzes multi-bit generative watermarking for large language models, identifying suboptimality in prior schemes and proposing two new optimal encoding-decoding methods under false-alarm constraints.

Contribution

It develops two new watermarking schemes that achieve the theoretical lower bound, fully characterizing optimal performance and analyzing their structural conditions.

Findings

Prior scheme is suboptimal under worst-case false-alarm constraints.

Two new schemes attain the established lower bound on miss-detection probability.

The paper provides a linear programming formulation for optimal watermark design.

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.