{"ID":2867846,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18025","arxiv_id":"2509.18025","title":"Deep Learning as the Disciplined Construction of Tame Objects","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.","short_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 c...","url_abs":"https://arxiv.org/abs/2509.18025","url_pdf":"https://arxiv.org/pdf/2509.18025v1","authors":"[\"Gilles Bareilles\",\"Allen Gehret\",\"Johannes Aspman\",\"Jana Lepšová\",\"Jakub Mareček\"]","published":"2025-09-22T17:00:40Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.AI\",\"cs.LG\",\"math.LO\",\"stat.ML\"]","methods":"[]","has_code":false}