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Our normalization is minimally constraining and allows the underlying architecture to maintain higher expressiveness compared to other techniques which aim to either control the Lipschitz constant of the model or ensure its monotonicity. We show how the algorithm was used to train a powerful, robust, and interpretable discriminator for heavy-flavor-quark decays, which has been adopted for use as the primary data-selection algorithm in the LHCb real-time data-processing system in the current LHC data-taking period known as Run 3. In addition, our algorithm has also achieved state-of-the-art performance on benchmarks in medicine, finance, and other applications.<\/jats:p>","DOI":"10.1088\/2632-2153\/aced80","type":"journal-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T22:31:29Z","timestamp":1691188289000},"page":"035020","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Robust and provably monotonic networks"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9695-8165","authenticated-orcid":false,"given":"Ouail","family":"Kitouni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2536-4209","authenticated-orcid":false,"given":"Niklas","family":"Nolte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8285-3346","authenticated-orcid":true,"given":"Mike","family":"Williams","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2023,8,17]]},"reference":[{"key":"mlstaced80bib1","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/s41781-020-00039-7","article-title":"Allen: a high level trigger on GPUs for LHCb","volume":"4","author":"Aaij","year":"2020","journal-title":"Comput. 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