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

Gennaro Auricchio, Giovanni Brigati, Paolo Giudici, Giuseppe Toscani
7/15/2025
math-phcs.AIcs.LG

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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.

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Cite this paper

@article{auricchio2025from,
  title  = {From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties},
  author = {Gennaro Auricchio and Giovanni Brigati and Paolo Giudici and Giuseppe Toscani},
  year   = {2025},
  eprint = {2507.11387},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2507.11387v1}
}

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