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.

翻译：本研究提出一种数学方法，用于（重新）定义机器学习模型的一种性质——稳定性，并确定验证该性质的充分条件。我们将机器学习模型表示为函数，其特性范围取决于函数的定义域，这使得我们可以采用拓扑和度量空间理论作为基础。最后，本研究提供了一些等价关系，可用于证明和测试机器学习模型的稳定性。结果表明，当稳定性与函数光滑性概念一致时，机器学习模型的稳定性主要取决于其定义域内分类集的某些拓扑可测性质。