Abstract
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.
Abstract (translated)
可以将深度学习模型视为所谓的“温和几何”（tame geometry）中的函数组合。在这篇阐述性笔记中，我们概述了处于温和几何学（又称o-最小性）、优化理论以及深度学习理论与实践交汇处的一些主题。为此，我们将逐步介绍用于在一般非光滑、非凸但符合温和条件的框架下构建随机梯度下降收敛保证的概念和工具。这说明了温和几何如何成为研究AI系统特别是深度学习系统的自然数学框架。
URL
https://arxiv.org/abs/2509.18025
