---
OA_place: repository
OA_type: green
_id: '21504'
abstract:
- lang: eng
  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.
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)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gennaro
  full_name: Auricchio, Gennaro
  last_name: Auricchio
- first_name: Giovanni
  full_name: Brigati, Giovanni
  id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  last_name: Brigati
- first_name: Paolo
  full_name: Giudici, Paolo
  last_name: Giudici
- first_name: Giuseppe
  full_name: Toscani, Giuseppe
  last_name: Toscani
citation:
  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;36(6):1185-1233. doi:<a href="https://doi.org/10.1142/S0218202526410010">10.1142/S0218202526410010</a>'
  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>'
  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>, vol. 36, no. 6. World Scientific Publishing,
    pp. 1185–1233, 2026.'
  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. 36(6), 1185–1233.'
  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>, vol. 36, no. 6, World Scientific Publishing, 2026, pp. 1185–233,
    doi:<a href="https://doi.org/10.1142/S0218202526410010">10.1142/S0218202526410010</a>.'
  short: G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and
    Methods in Applied Sciences 36 (2026) 1185–1233.
das_tickbox: '0'
date_created: 2026-03-29T22:07:08Z
date_published: 2026-06-01T00:00:00Z
date_updated: 2026-07-27T12:11:38Z
day: '01'
department:
- _id: JaMa
doi: 10.1142/S0218202526410010
ec_funded: 1
external_id:
  arxiv:
  - '2507.11387'
intvolume: '        36'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2507.11387
mathsc:
- 35B40
- 35L60
- 35K55
- 35Q70
- 35Q91
- 35Q92
month: '06'
oa: 1
oa_version: Preprint
page: 1185-1233
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  eissn:
  - 1793-6314
  issn:
  - 0218-2025
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: 'From kinetic theory to AI: A rediscovery of high-dimensional divergences and
  their properties'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2026'
...