Deep Learning as the Disciplined Construction of Tame Objects
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916072942206976 |
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| author | Bareilles, Gilles Gehret, Allen Aspman, Johannes Lepšová, Jana Mareček, Jakub |
| author_facet | Bareilles, Gilles Gehret, Allen Aspman, Johannes Lepšová, Jana Mareček, Jakub |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Learning as the Disciplined Construction of Tame Objects Bareilles, Gilles Gehret, Allen Aspman, Johannes Lepšová, Jana Mareček, Jakub Optimization and Control Artificial Intelligence Machine Learning Logic 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. |
| title | Deep Learning as the Disciplined Construction of Tame Objects |
| topic | Optimization and Control Artificial Intelligence Machine Learning Logic |
| url | https://arxiv.org/abs/2509.18025 |