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

arXiv: https://arxiv.org/abs/2507.11387 · HTML: https://mlsanity.com/paper/2507.11387/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 127 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [The Cramer Distance as a Solution to Biased Wasserstein Gradients](https://mlsanity.com/paper/1705.10743/) (2017)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Fast and Smooth Interpolation on Wasserstein Space](https://mlsanity.com/paper/2010.12101/) (2020)
- [Second order models for optimal transport and cubic splines on the Wasserstein space](https://mlsanity.com/paper/1801.04144/) (2018)
- [Measure-valued spline curves: an optimal transport viewpoint](https://mlsanity.com/paper/1801.03186/) (2018)
- [Sparsifying the Fisher Linear Discriminant by Rotation](https://mlsanity.com/paper/1408.4475/) (2014)
- [Computing Kantorovich-Wasserstein Distances on d-dimensional histograms using (d+1)-partite graphs](https://mlsanity.com/paper/1805.07416/) (2018)
- [Benamou-Brenier Formulation of Optimal Transport for Nonlinear Control Systems on Rd](https://mlsanity.com/paper/2407.16088/) (2024)
- [A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient](https://mlsanity.com/paper/2101.04748/) (2021)
- [The Fourier Discrepancy Function](https://mlsanity.com/paper/2102.02979/) (2021)
- [Measuring multidimensional heterogeneity in emergent social phenomena](https://mlsanity.com/paper/2310.20483/) (2023)
- [Multivariate Gini-type discrepancies](https://mlsanity.com/paper/2411.01052/) (2024)
- [On the equivalence between static and dynamic optimal transport governed by linear control systems](https://mlsanity.com/paper/2505.17570/) (2025)

## Abstract (arXiv)

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.