Optimal Watermark Generation under Type I and Type II Errors
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917127285374976 |
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| author | He, Hengzhi Xu, Shirong Nemecek, Alexander Li, Jiping Ayday, Erman Cheng, Guang |
| author_facet | He, Hengzhi Xu, Shirong Nemecek, Alexander Li, Jiping Ayday, Erman Cheng, Guang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Watermark Generation under Type I and Type II Errors He, Hengzhi Xu, Shirong Nemecek, Alexander Li, Jiping Ayday, Erman Cheng, Guang Methodology 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. |
| title | Optimal Watermark Generation under Type I and Type II Errors |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.05333 |