From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918093099368448 |
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| author | Auricchio, Gennaro Brigati, Giovanni Giudici, Paolo Toscani, Giuseppe |
| author_facet | Auricchio, Gennaro Brigati, Giovanni Giudici, Paolo Toscani, Giuseppe |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties Auricchio, Gennaro Brigati, Giovanni Giudici, Paolo Toscani, Giuseppe Mathematical Physics Artificial Intelligence Machine Learning Multiagent Systems 35B40, 35L60, 35K55, 35Q70, 35Q91, 35Q92 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. |
| title | From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties |
| topic | Mathematical Physics Artificial Intelligence Machine Learning Multiagent Systems 35B40, 35L60, 35K55, 35Q70, 35Q91, 35Q92 |
| url | https://arxiv.org/abs/2507.11387 |