{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T05:10:45Z","timestamp":1788757845470,"version":"build-2803163510"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T00:00:00Z","timestamp":1788739200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T00:00:00Z","timestamp":1788739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["Grant 62472122"],"award-info":[{"award-number":["Grant 62472122"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100019033","name":"Key Research and Development Program of Liaoning Province","doi-asserted-by":"publisher","award":["Grant No. 2024YFB31NL00101"],"award-info":[{"award-number":["Grant No. 2024YFB31NL00101"]}],"id":[{"id":"10.13039\/501100019033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["Grant No. U22A2036"],"award-info":[{"award-number":["Grant No. U22A2036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["Grant No. HIT.OCEF.2021007"],"award-info":[{"award-number":["Grant No. HIT.OCEF.2021007"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Existing generative watermarking methods rely on fixed or heuristic entropy thresholds in cross-task generation scenarios, leading to redundant watermark injection, detection noise, and degraded generation quality. To address these limitations, we propose GAMark, a\n                    <jats:bold>G<\/jats:bold>\n                    aussian Mixture Model (GMM)-based semantics-aware\n                    <jats:bold>A<\/jats:bold>\n                    daptive entropy threshold water\n                    <jats:bold>Mark<\/jats:bold>\n                    ing framework. Motivated by the manifold hypothesis in the logits space, GAMark adopts an offline semantic modeling and online frozen inference paradigm. A GMM is trained offline to characterize multimodal latent semantic states, while during generation, entropy thresholds are dynamically synthesized via Bayesian posterior aggregation over semantic states, enabling automatic avoidance of low-entropy sensitive regions and effective watermark embedding in high-entropy regions. At the detection stage, we further introduce an entropy-weighted statistical test based on state inference, which improves robustness against noise introduced by the inclusion of semantically deterministic tokens. Extensive experiments demonstrate that GAMark consistently improves cross-task generation quality and functional correctness, while maintaining detection accuracy and enhancing watermark robustness and inference efficiency.\n                  <\/jats:p>","DOI":"10.1186\/s42400-026-00607-1","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T04:20:27Z","timestamp":1788754827000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Gamark: adaptive entropy-threshold watermarking via gaussian mixture modeling for large language models"],"prefix":"10.1186","volume":"9","author":[{"given":"Jing","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongwei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hengji","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weizhe","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"607_CR24","unstructured":"Austin J, Odena A, Nye M, Bosma M, Michalewski H, Dohan D, Jiang E, Cai C, Terry M, Le Q (2021) Program synthesis with large language models. arXiv:2108.07732"},{"key":"607_CR17","doi-asserted-by":"crossref","unstructured":"Chang Y, Krishna K, Houmansadr A, Wieting JF, Iyyer M (2024) Postmark: A robust blackbox watermark for large language models. 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