从数学角度定义模型稳定性，揭示其与函数平滑性的关系。
On the Conditions for Domain Stability for Machine Learning: a Mathematical Approach
- 用函数拓扑与度量空间理论重新定义模型稳定性
- 稳定性取决于分类集的拓扑与可测性质
- 提供可验证稳定性的等价条件，适合理论研究者
本文提出一种数学方法，重新定义机器学习模型的一种属性——稳定性，并确定其成立的充分条件。将机器学习模型视为函数，其特性依赖于函数定义域的结构，因此采用拓扑空间与度量空间理论作为基础。最终，本文给出了若干有助于证明和检验模型稳定性的等价关系。结果表明，当稳定性与函数平滑性一致时，机器学习模型的稳定性主要取决于模型定义域中分类集的特定拓扑与可测性质。
原文摘要 · Abstract (English)
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the characteristics in scope depend upon the domain of the function, what allows us to adopt topological and metric spaces theory as a basis. Finally, this work provides some equivalences useful to prove and test stability in Machine Learning models. The results suggest that whenever stability is aligned with the notion of function smoothness, then the stability of Machine Learning models primarily depends upon certain topological, measurable properties of the classification sets within the ML model domain.
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