{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.11387","open_access":"1"}],"day":"14","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"date_updated":"2026-03-30T06:56:35Z","article_processing_charge":"No","citation":{"chicago":"Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>.","ieee":"G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties,” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026.","short":"G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and Methods in Applied Sciences (2026).","ama":"Auricchio G, Brigati G, Giudici P, Toscani G. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026. doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>","ista":"Auricchio G, Brigati G, Giudici P, Toscani G. 2026. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. Mathematical Models and Methods in Applied Sciences.","apa":"Auricchio, G., Brigati, G., Giudici, P., &#38; Toscani, G. (2026). From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>","mla":"Auricchio, Gennaro, et al. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>."},"arxiv":1,"doi":"10.1142/S0218202526410010","acknowledgement":"This work has been written within the activities of GNCS and GNFM groups of INdAM (Italian\r\nNational Institute of High Mathematics). G.B. has been funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. P.G. has been funded by the European Union - NextGenerationEU, in the framework of the GRINSGrowing Resilient, INclusive and Sustainable (GRINS PE00000018).","title":"From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties","publisher":"World Scientific Publishing","ec_funded":1,"department":[{"_id":"JaMa"}],"date_created":"2026-03-29T22:07:08Z","article_type":"original","abstract":[{"text":"Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback–Leibler (KL) divergence, originally introduced in kinetic theory as a measure of relative entropy between probability distributions. Just as in machine learning, the ability to quantify the proximity of probability distributions plays a central role in kinetic theory. In this paper, we present a comparative review of divergence measures rooted in kinetic theory, highlighting their theoretical foundations and exploring their potential applications in machine learning and artificial intelligence.","lang":"eng"}],"oa":1,"publication_status":"epub_ahead","year":"2026","_id":"21504","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"oa_version":"Preprint","date_published":"2026-03-14T00:00:00Z","OA_type":"green","language":[{"iso":"eng"}],"month":"03","external_id":{"arxiv":["2507.11387"]},"author":[{"first_name":"Gennaro","last_name":"Auricchio","full_name":"Auricchio, Gennaro"},{"first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"last_name":"Giudici","first_name":"Paolo","full_name":"Giudici, Paolo"},{"first_name":"Giuseppe","last_name":"Toscani","full_name":"Toscani, Giuseppe"}],"type":"journal_article","scopus_import":"1","publication":"Mathematical Models and Methods in Applied Sciences","OA_place":"repository","quality_controlled":"1"}