Eur. Phys. J. C (2025) 85: 1360
https://doi.org/10.1140/epjc/s10052-025-14713-w

Regular Article - Computing, Software and Data Science

Development of systematic uncertainty-aware neural network trainings for binned-likelihood analyses at the LHC

¹ Yerevan Physics Institute, Yerevan, Armenia
² Institut für Hochenergiephysik, Vienna, Austria
³ Universiteit Antwerpen, Antwerpen, Belgium
⁴ Vrije Universiteit Brussel, Brussels, Belgium
⁵ Université Libre de Bruxelles, Brussels, Belgium
⁶ Ghent University, Ghent, Belgium
⁷ Université Catholique de Louvain, Louvain-la-Neuve, Belgium
⁸ Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
⁹ Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
¹⁰ Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
¹¹ Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
¹² University of Sofia, Sofia, Bulgaria
¹³ Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
¹⁴ Beihang University, Beijing, China
¹⁵ Department of Physics, Tsinghua University, Beijing, China
¹⁶ Institute of High Energy Physics, Beijing, China
¹⁷ State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
¹⁸ Guangdong Provincial Key Laboratory of Nuclear Science and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou, China
¹⁹ Sun Yat-Sen University, Guangzhou, China
²⁰ University of Science and Technology of China, Hefei, China
²¹ Nanjing Normal University, Nanjing, China
²² Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) - Fudan University, Shanghai, China
²³ Zhejiang University, Hangzhou, Zhejiang, China
²⁴ Universidad de Los Andes, Bogotá, Colombia
²⁵ Universidad de Antioquia, Medellin, Colombia
²⁶ Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
²⁷ Faculty of Science, University of Split, Split, Croatia
²⁸ Institute Rudjer Boskovic, Zagreb, Croatia
²⁹ University of Cyprus, Nicosia, Cyprus
³⁰ Charles University, Prague, Czech Republic
³¹ Escuela Politecnica Nacional, Quito, Ecuador
³² Universidad San Francisco de Quito, Quito, Ecuador
³³ Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
³⁴ Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
³⁵ National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
³⁶ Department of Physics, University of Helsinki, Helsinki, Finland
³⁷ Helsinki Institute of Physics, Helsinki, Finland
³⁸ Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
³⁹ IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
⁴⁰ Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
⁴¹ CNRS, IPHC UMR 7178, Université de Strasbourg, Strasbourg, France
⁴² Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France
⁴³ Institut de Physique des 2 Infinis de Lyon (IP2I), Villeurbanne, France
⁴⁴ Georgian Technical University, Tbilisi, Georgia
⁴⁵ RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
⁴⁶ RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
⁴⁷ RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
⁴⁸ Deutsches Elektronen-Synchrotron, Hamburg, Germany
⁴⁹ University of Hamburg, Hamburg, Germany
⁵⁰ Karlsruher Institut fuer Technologie, Karlsruhe, Germany
⁵¹ Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
⁵² National and Kapodistrian University of Athens, Athens, Greece
⁵³ National Technical University of Athens, Athens, Greece
⁵⁴ University of Ioánnina, Ioánnina, Greece
⁵⁵ HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
⁵⁶ MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
⁵⁷ Faculty of Informatics, University of Debrecen, Debrecen, Hungary
⁵⁸ HUN-REN ATOMKI-Institute of Nuclear Research, Debrecen, Hungary
⁵⁹ Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
⁶⁰ Panjab University, Chandigarh, India
⁶¹ University of Delhi, Delhi, India
⁶² Saha Institute of Nuclear Physics, HBNI, Kolkata, India
⁶³ Indian Institute of Technology Madras, Madras, India
⁶⁴ Tata Institute of Fundamental Research-A, Mumbai, India
⁶⁵ Tata Institute of Fundamental Research-B, Mumbai, India
⁶⁶ National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
⁶⁷ Indian Institute of Science Education and Research (IISER), Pune, India
⁶⁸ Isfahan University of Technology, Isfahan, Iran
⁶⁹ Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
⁷⁰ University College Dublin, Dublin, Ireland
⁷¹ INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
⁷² INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
⁷³ INFN Sezione di Catania, Università di Catania, Catania, Italy
⁷⁴ INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
⁷⁵ INFN Laboratori Nazionali di Frascati, Frascati, Italy
⁷⁶ INFN Sezione di Genova, Università di Genova, Genoa, Italy
⁷⁷ INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
⁷⁸ INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy; Scuola Superiore Meridionale (SSM), Naples, Italy
⁷⁹ INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
⁸⁰ INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
⁸¹ INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
⁸² INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
⁸³ INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
⁸⁴ INFN Sezione di Torino, Università di Torino, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
⁸⁵ INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
⁸⁶ Kyungpook National University, Daegu, Korea
⁸⁷ Department of Mathematics and Physics - GWNU, Gangneung, Korea
⁸⁸ Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
⁸⁹ Hanyang University, Seoul, Korea
⁹⁰ Korea University, Seoul, Korea
⁹¹ Department of Physics, Kyung Hee University, Seoul, Korea
⁹² Sejong University, Seoul, Korea
⁹³ Seoul National University, Seoul, Korea
⁹⁴ University of Seoul, Seoul, Korea
⁹⁵ Department of Physics, Yonsei University, Seoul, Korea
⁹⁶ Sungkyunkwan University, Suwon, Korea
⁹⁷ College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
⁹⁸ Kuwait University-College of Science-Department of Physics, Safat, Kuwait
⁹⁹ Riga Technical University, Riga, Latvia
¹⁰⁰ University of Latvia (LU), Riga, Latvia
¹⁰¹ Vilnius University, Vilnius, Lithuania
¹⁰² National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
¹⁰³ Universidad de Sonora (UNISON), Hermosillo, Mexico
¹⁰⁴ Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
¹⁰⁵ Universidad Iberoamericana, Mexico City, Mexico
¹⁰⁶ Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
¹⁰⁷ University of Montenegro, Podgorica, Montenegro
¹⁰⁸ University of Canterbury, Christchurch, New Zealand
¹⁰⁹ National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
¹¹⁰ AGH University of Krakow, Kraków, Poland
¹¹¹ National Centre for Nuclear Research, Swierk, Poland
¹¹² Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
¹¹³ Warsaw University of Technology, Warsaw, Poland
¹¹⁴ Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
¹¹⁵ Faculty of Physics, University of Belgrade, Belgrade, Serbia
¹¹⁶ VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
¹¹⁷ Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
¹¹⁸ Universidad Autónoma de Madrid, Madrid, Spain
¹¹⁹ Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Universidad de Oviedo, Oviedo, Spain
¹²⁰ Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
¹²¹ University of Colombo, Colombo, Sri Lanka
¹²² Department of Physics, University of Ruhuna, Matara, Sri Lanka
¹²³ CERN, European Organization for Nuclear Research, Geneva, Switzerland
¹²⁴ PSI Center for Neutron and Muon Sciences, Villigen, Switzerland
¹²⁵ ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
¹²⁶ Universität Zürich, Zurich, Switzerland
¹²⁷ National Central University, Chung-Li, Taiwan
¹²⁸ National Taiwan University (NTU), Taipei, Taiwan
¹²⁹ High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
¹³⁰ Tunis El Manar University, Tunis, Tunisia
¹³¹ Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
¹³² Physics Department, Middle East Technical University, Ankara, Turkey
¹³³ Bogazici University, Istanbul, Turkey
¹³⁴ Istanbul Technical University, Istanbul, Turkey
¹³⁵ Istanbul University, Istanbul, Turkey
¹³⁶ Yildiz Technical University, Istanbul, Turkey
¹³⁷ Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
¹³⁸ National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
¹³⁹ University of Bristol, Bristol, UK
¹⁴⁰ Rutherford Appleton Laboratory, Didcot, UK
¹⁴¹ Imperial College, London, UK
¹⁴² Brunel University, Uxbridge, UK
¹⁴³ Baylor University, Waco, TX, USA
¹⁴⁴ Catholic University of America, Washington, DC, USA
¹⁴⁵ The University of Alabama, Tuscaloosa, AL, USA
¹⁴⁶ Boston University, Boston, MA, USA
¹⁴⁷ Brown University, Providence, RI, USA
¹⁴⁸ University of California, Davis, Davis, CA, USA
¹⁴⁹ University of California, Los Angeles, CA, USA
¹⁵⁰ University of California, Riverside, Riverside, CA, USA
¹⁵¹ University of California, San Diego, La Jolla, CA, USA
¹⁵² Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
¹⁵³ California Institute of Technology, Pasadena, CA, USA
¹⁵⁴ Carnegie Mellon University, Pittsburgh, PA, USA
¹⁵⁵ University of Colorado Boulder, Boulder, CO, USA
¹⁵⁶ Cornell University, Ithaca, NY, USA
¹⁵⁷ Fermi National Accelerator Laboratory, Batavia, IL, USA
¹⁵⁸ University of Florida, Gainesville, FL, USA
¹⁵⁹ Florida State University, Tallahassee, FL, USA
¹⁶⁰ Florida Institute of Technology, Melbourne, FL, USA
¹⁶¹ University of Illinois Chicago, Chicago, IL, USA
¹⁶² The University of Iowa, Iowa City, IA, USA
¹⁶³ Johns Hopkins University, Baltimore, MD, USA
¹⁶⁴ The University of Kansas, Lawrence, KS, USA
¹⁶⁵ Kansas State University, Manhattan, KS, USA
¹⁶⁶ University of Maryland, College Park, MD, USA
¹⁶⁷ Massachusetts Institute of Technology, Cambridge, MA, USA
¹⁶⁸ University of Minnesota, Minneapolis, MN, USA
¹⁶⁹ University of Nebraska-Lincoln, Lincoln, NE, USA
¹⁷⁰ State University of New York at Buffalo, Buffalo, NY, USA
¹⁷¹ Northeastern University, Boston, MA, USA
¹⁷² Northwestern University, Evanston, IL, USA
¹⁷³ University of Notre Dame, Notre Dame, IN, USA
¹⁷⁴ The Ohio State University, Columbus, OH, USA
¹⁷⁵ Princeton University, Princeton, NJ, USA
¹⁷⁶ University of Puerto Rico, Mayaguez, PR, USA
¹⁷⁷ Purdue University, West Lafayette, IN, USA
¹⁷⁸ Purdue University Northwest, Hammond, IN, USA
¹⁷⁹ Rice University, Houston, TX, USA
¹⁸⁰ University of Rochester, Rochester, NY, USA
¹⁸¹ Rutgers, The State University of New Jersey, Piscataway, NJ, USA
¹⁸² University of Tennessee, Knoxville, TN, USA
¹⁸³ Texas A&M University, College Station, TX, USA
¹⁸⁴ Texas Tech University, Lubbock, TX, USA
¹⁸⁵ Vanderbilt University, Nashville, TN, USA
¹⁸⁶ University of Virginia, Charlottesville, VA, USA
¹⁸⁷ Wayne State University, Detroit, MI, USA
¹⁸⁸ University of Wisconsin-Madison, Madison, WI, USA
¹⁸⁹ Authors Affiliated with an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
¹⁹⁰ Authors Affiliated with an Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
¹⁹¹ Yerevan State University, Yerevan, Armenia
¹⁹² TU Wien, Vienna, Austria
¹⁹³ Ghent University, Ghent, Belgium
¹⁹⁴ Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
¹⁹⁵ FACAMP-Faculdades de Campinas, Sao Paulo, Brazil
¹⁹⁶ Universidade Estadual de Campinas, Campinas, Brazil
¹⁹⁷ Federal University of Rio Grande do Sul, Porto Alegre, Brazil
¹⁹⁸ University of Chinese Academy of Sciences, Beijing, China
¹⁹⁹ China Center of Advanced Science and Technology, Beijing, China
²⁰⁰ University of Chinese Academy of Sciences, Beijing, China
²⁰¹ China Spallation Neutron Source, Guangdong, China
²⁰² Henan Normal University, Xinxiang, China
²⁰³ University of Shanghai for Science and Technology, Shanghai, China
²⁰⁴ The University of Iowa, Iowa City, IA, USA
²⁰⁵ An Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²⁰⁶ Cairo University, Cairo, Egypt
²⁰⁷ Suez University, Suez, Egypt
²⁰⁸ British University in Egypt, Cairo, Egypt
²⁰⁹ Purdue University, West Lafayette, IN, USA
²¹⁰ Université de Haute Alsace, Mulhouse, France
²¹¹ Istinye University, Istanbul, Turkey
²¹² An International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²¹³ The University of the State of Amazonas, Manaus, Brazil
²¹⁴ University of Hamburg, Hamburg, Germany
²¹⁵ RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
²¹⁶ Bergische University Wuppertal (BUW), Wuppertal, Germany
²¹⁷ Brandenburg University of Technology, Cottbus, Germany
²¹⁸ Forschungszentrum Jülich, Juelich, Germany
²¹⁹ CERN, European Organization for Nuclear Research, Geneva, Switzerland
²²⁰ HUN-REN ATOMKI-Institute of Nuclear Research, Debrecen, Hungary
²²¹ Universitatea Babes-Bolyai-Facultatea de Fizica, Cluj-Napoca, Romania
²²² MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
²²³ HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
²²⁴ Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
²²⁵ Punjab Agricultural University, Ludhiana, India
²²⁶ University of Visva-Bharati, Santiniketan, India
²²⁷ Indian Institute of Science (IISc), Bangalore, India
²²⁸ Amity University Uttar Pradesh, Noida, India
²²⁹ IIT Bhubaneswar, Bhubaneswar, India
²³⁰ Institute of Physics, Bhubaneswar, India
²³¹ University of Hyderabad, Hyderabad, India
²³² Deutsches Elektronen-Synchrotron, Hamburg, Germany
²³³ Isfahan University of Technology, Isfahan, Iran
²³⁴ Sharif University of Technology, Tehran, Iran
²³⁵ Department of Physics, University of Science and Technology of Mazandaran, Behshahr, Iran
²³⁶ Department of Physics, Faculty of Science, Arak University, Arak, Iran
²³⁷ Helwan University, Cairo, Egypt
²³⁸ Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Bologna, Italy
²³⁹ Centro Siciliano di Fisica Nucleare e di Struttura Della Materia, Catania, Italy
²⁴⁰ Università degli Studi Guglielmo Marconi, Rome, Italy
²⁴¹ Scuola Superiore Meridionale, Università di Napoli ’Federico II’, Naples, Italy
²⁴² Fermi National Accelerator Laboratory, Batavia, IL, USA
²⁴³ Lulea University of Technology, Lulea, Sweden
²⁴⁴ Laboratori Nazionali di Legnaro dell’INFN, Legnaro, Italy
²⁴⁵ Consiglio Nazionale delle Ricerche-Istituto Officina dei Materiali, Perugia, Italy
²⁴⁶ Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
²⁴⁷ Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia
²⁴⁸ Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
²⁴⁹ Trincomalee Campus, Eastern University, Nilaveli, Sri Lanka
²⁵⁰ Saegis Campus, Nugegoda, Sri Lanka
²⁵¹ National and Kapodistrian University of Athens, Athens, Greece
²⁵² Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
²⁵³ Universität Zürich, Zurich, Switzerland
²⁵⁴ Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
²⁵⁵ Laboratoire d’Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France
²⁵⁶ Near East University, Research Center of Experimental Health Science, Mersin, Turkey
²⁵⁷ Konya Technical University, Konya, Turkey
²⁵⁸ Izmir Bakircay University, Izmir, Turkey
²⁵⁹ Adiyaman University, Adiyaman, Turkey
²⁶⁰ Bozok Universitetesi Rektörlügü, Yozgat, Turkey
²⁶¹ Marmara University, Istanbul, Turkey
²⁶² Milli Savunma University, Istanbul, Turkey
²⁶³ Kafkas University, Kars, Turkey
²⁶⁴ Istanbul Okan University, Istanbul, Turkey
²⁶⁵ Hacettepe University, Ankara, Turkey
²⁶⁶ Erzincan Binali Yildirim University, Erzincan, Turkey
²⁶⁷ Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
²⁶⁸ Yildiz Technical University, Istanbul, Turkey
²⁶⁹ School of Physics and Astronomy, University of Southampton, Southampton, UK
²⁷⁰ IPPP Durham University, Durham, UK
²⁷¹ Faculty of Science, Monash University, Clayton, Australia
²⁷² Università di Torino, Turin, Italy
²⁷³ Bethel University, St. Paul, MN, USA
²⁷⁴ Karamanoğlu Mehmetbey University, Karaman, Turkey
²⁷⁵ California Institute of Technology, Pasadena, CA, USA
²⁷⁶ United States Naval Academy, Annapolis, MD, USA
²⁷⁷ Ain Shams University, Cairo, Egypt
²⁷⁸ Bingol University, Bingol, Turkey
²⁷⁹ Georgian Technical University, Tbilisi, Georgia
²⁸⁰ Sinop University, Sinop, Turkey
²⁸¹ Erciyes University, Kayseri, Turkey
²⁸² Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania
²⁸³ Another Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²⁸⁴ Texas A&M University at Qatar, Doha, Qatar
²⁸⁵ Kyungpook National University, Daegu, Korea
²⁸⁶ Yerevan Physics Institute, Yerevan, Armenia
²⁸⁷ Another International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²⁸⁸ Imperial College, London, UK
²⁸⁹ Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
²⁹⁰ Another Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland
²⁹¹ CERN, Geneva, Switzerland

^a cms-publication-committee-chair@cern.ch

Received: 28 August 2025
Accepted: 29 August 2025
Published online: 26 November 2025

Abstract

We propose a neural network training method capable of accounting for the effects of systematic variations of the data model in the training process and describe its extension towards neural network multiclass classification. The procedure is evaluated on the realistic case of the measurement of Higgs boson production via gluon fusion and vector boson fusion in the $\mathrm{\tau }\mathrm{\tau }$ decay channel at the CMS experiment. The neural network output functions are used to infer the signal strengths for inclusive production of Higgs bosons as well as for their production via gluon fusion and vector boson fusion. We observe improvements of 12 and 16% in the uncertainty in the signal strengths for gluon and vector-boson fusion, respectively, compared with a conventional neural network training based on cross-entropy.