From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties

Fuente: arXiv
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Main Authors: Auricchio, Gennaro, Brigati, Giovanni, Giudici, Paolo, Toscani, Giuseppe
Format: Preprint
Published: 2025
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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
id 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