从物理理论重探信息距离，为机器学习提供新度量思路
From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
- 基于动能理论对比多种信息距离度量方法
- 揭示高维空间中信息差异的数学特性
- 适合研究模型泛化与分布对齐的学者参考
选择合适的差异度量是机器学习中的关键问题，直接影响模型性能。其中最常用的包括来自动能理论的相对熵度量——即Kullback-Leibler（KL）散度。在动能理论中，量化概率分布间的接近程度同样具有核心地位。本文对源自动能理论的差异度量进行对比综述，强调其理论基础，并探讨其在机器学习与人工智能中的潜在应用。
原文摘要 · Abstract (English)
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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