{"ID":2894445,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11387","arxiv_id":"2507.11387","title":"From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.11387","url_pdf":"https://arxiv.org/pdf/2507.11387v1","authors":"[\"Gennaro Auricchio\",\"Giovanni Brigati\",\"Paolo Giudici\",\"Giuseppe Toscani\"]","published":"2025-07-15T14:56:25Z","proceeding":"math-ph","tasks":"[\"math-ph\",\"cs.AI\",\"cs.LG\",\"cs.MA\"]","methods":"[]","has_code":false}