{
  "abstract": "A watermark verifier may hold many modes, i.e., secret keys, and a document may mix spans of different modes with unwatermarked text. Directly reporting the mode with the largest pivotal statistic (pivot) inflates the Type I error, and restoring the nominal level reduces power as candidate modes are added. We formulate token-level multi-mode attribution for the Gumbel-max watermark as maximizing correct-label power under a Type I error constraint given a mode prior. We show that the optimal rule reports the mode with the largest prior-weighted alternative density and rejects when this density exceeds one common threshold. Based on this rule, we propose the Belief-weighted Likelihood Attribution with Density Estimation (BLADE) detector. It estimates the mode prior from neighboring pivots and the alternative density from reference token probabilities. Under a conditional product model of the pivots, it keeps the exact Type I error. We further show that BLADE approaches the optimal rule as its prior and density estimates improve, with a sharp coefficient on the density error. On OPT-1.3B and other open-weight large language models, BLADE attains higher correct-label power than the compared detectors across candidate counts, token-substitution rates, generation temperatures and generator models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23601",
  "author_total": 4,
  "authors": [
    {
      "name": "Rui Zhou"
    },
    {
      "name": "Licheng Zhao"
    },
    {
      "name": "Chao Shen"
    },
    {
      "name": "Wenqiang Pu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgm5pwnq3042a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23601",
  "fulltext_url": null,
  "id": "dgm5pwnq3042a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23601",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "openalex",
      "1707|Advanced Steganography and Watermarking Techniques"
    ]
  ],
  "openalex": "W7222987793",
  "pdf_url": "https://arxiv.org/pdf/2610.23601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgm5pwnq3042a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2610.23601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23601"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Token-Level Attribution of Multi-Mode LLM Watermarks: Optimal Rule and Belief Weighting",
  "title_text": "Token-Level Attribution of Multi-Mode LLM Watermarks: Optimal Rule and Belief Weighting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/dgm5pwnq3042a",
  "venue": "arXiv",
  "versions": []
}