{"paper":{"title":"Covert Multi-bit LLM Watermarking: An Information Theory and Coding Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Multi-bit covert watermarking for LLMs has an exactly characterized capacity that supports practical embedding at 0.375 bits per token.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Matthieu R. Bloch, Sidong Guo, Teodora Baluta, Tyler Kann","submitted_at":"2026-05-15T23:46:22Z","abstract_excerpt":"We study the problem of multi-bit watermarking for large language models (LLMs). We introduce a block-autoregressive model inspired by multi-token prediction, in which the encoder has limited non-causal access to token distributions within each block. This formulation enables an information-theoretic characterization of multi-bit watermarking capacity, by which the knowledge of LLM cover statistics is leveraged to enable a multi-bit covert embedding. We study the information-theoretic limits of the model by combining Gelfand-Pinsker and channel synthesis coding techniques and obtain an exact c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We study the information-theoretic limits of the model by combining Gelfand-Pinsker and channel synthesis coding techniques and obtain an exact characterization of the capacity. Our algorithm achieves a bit-error rate below 10 percent with a rate of 0.375 bits/token over short token lengths with negligible perplexity and distortion degradation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The formulation assumes the encoder has limited non-causal access to token distributions within each block and that LLM cover statistics are known and can be leveraged for covert embedding; if this access or knowledge is unavailable in fully causal real-world sampling, the capacity characterization and performance claims would not apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Characterizes the exact capacity of multi-bit covert LLM watermarking via Gelfand-Pinsker and channel synthesis, then gives a polar-code algorithm achieving 0.375 bits/token at under 10% BER with negligible perplexity impact.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multi-bit covert watermarking for LLMs has an exactly characterized capacity that supports practical embedding at 0.375 bits per token.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"190b28217324e749ac6618e98c9efbb20c774b968b0c1480fc386e63ad3e633b"},"source":{"id":"2605.16709","kind":"arxiv","version":1},"verdict":{"id":"06c5a49d-0dc0-4a0d-b094-8a88ed0f1b74","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:19:36.931891Z","strongest_claim":"We study the information-theoretic limits of the model by combining Gelfand-Pinsker and channel synthesis coding techniques and obtain an exact characterization of the capacity. Our algorithm achieves a bit-error rate below 10 percent with a rate of 0.375 bits/token over short token lengths with negligible perplexity and distortion degradation.","one_line_summary":"Characterizes the exact capacity of multi-bit covert LLM watermarking via Gelfand-Pinsker and channel synthesis, then gives a polar-code algorithm achieving 0.375 bits/token at under 10% BER with negligible perplexity impact.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The formulation assumes the encoder has limited non-causal access to token distributions within each block and that LLM cover statistics are known and can be leveraged for covert embedding; if this access or knowledge is unavailable in fully causal real-world sampling, the capacity characterization and performance claims would not apply.","pith_extraction_headline":"Multi-bit covert watermarking for LLMs has an exactly characterized capacity that supports practical embedding at 0.375 bits per token."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16709/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:32:32.044280Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.210416Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.360689Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.483087Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b63fc0d71e1c74275c7c8ff6d1c98aee3c8b37d82edbe0d5e6de56bf42a07a39"},"references":{"count":46,"sample":[{"doi":"","year":2023,"title":"A watermark for large language models,","work_id":"daa02d2d-650a-4faa-b61e-fc4dc5ace0a6","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Undetectable watermarks for language models,","work_id":"21ab8221-481a-447a-9e38-bd0702708b96","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Heavywater and simplexwater: Distortion- free llm watermarks for low-entropy distributions,","work_id":"38348e92-4c65-4c63-b36c-4513a67f56cd","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Provable robust watermarking for AI-generated text","work_id":"ad6da7f1-2fd9-4768-bbd8-0568dc11215f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Robust content-dependent high- fidelity watermark for tracking in digital cinema,","work_id":"b131c990-560b-4a55-9035-420a5748c73d","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":46,"snapshot_sha256":"d89bb85282acd8290cd4ab471478f2a27a5e9a1eb960c0dee22f3cac794cca88","internal_anchors":3},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4e57282d7070d4b170a6277eebf6ee4fdb62e9f9d2393fccbbb3e2aa521adc39"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}