Title: Deep Learning as the Disciplined Construction of Tame Objects

Abstract: This expository note explores the intersection of deep learning theory and practice, optimization theory, and tame geometry (also referred to as o-minimality). By viewing deep-learning models as compositions of functions situated within tame geometry, we provide a comprehensive overview of key topics at this interface. To achieve this, we progressively introduce the concepts and analytical tools necessary to establish convergence guarantees for stochastic gradient descent in a general setting that is nonsmooth, nonconvex, yet tame. This approach highlights how tame geometry serves as a natural mathematical framework for investigating AI systems, particularly within the domain of Deep Learning.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC