Optimal Watermark Generation under Type I and Type II Errors

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ID: 324715
2026
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Abstract
Abstract Watermarking has recently emerged as a crucial tool for protecting the intellectual property of generative models and for distinguishing AI-generated content from human-generated data. Despite its practical success, most existing watermarking schemes are empirically driven and lack a theoretical understanding of the fundamental trade-off between detection power and generation fidelity. To address this gap, we formulate watermarking as a statistical hypothesis testing problem between a null distribution and its watermarked counterpart. Under explicit constraints on false-positive and false-negative rates, we derive a tight lower bound on the achievable fidelity loss, measured by a general f-divergence, and characterize the optimal watermarked distribution that attains this bound. We further develop a corresponding sampling rule that provides an optimal mechanism for inserting watermarks with minimal fidelity distortion. Our result establishes a simple yet broadly applicable principle linking hypothesis testing, information divergence, and watermark generation.
Reference Key
openalex_W4417142420 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Hengzhi He, Shirong Xu, Alexander Nemecek, J. Li, Erman Ayday, Guang Cheng
Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag049
URL
https://doi.org/10.1093/biomet/asag049
Keywords Keywords not found

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