Deep Learning as the Disciplined Construction of Tame Objects

• URL: http://arxiv.org/abs/2509.18025v1
• Date: Mon, 22 Sep 2025 17:00:40 GMT
• Title: Deep Learning as the Disciplined Construction of Tame Objects
• Authors: Gilles Bareilles, Allen Gehret, Johannes Aspman, Jana Lepšová, Jakub Mareček,
• Abstract summary: One can see deep-learning as compositions of functions within the so-called tame geometry.<n>In this note, we give an overview of tame interface theory (also as o-minimality) and deep learning theory.
• Score: 0.9786690381850356
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

Related papers

• Deep sequence models tend to memorize geometrically; it is unclear why [42.53849315139079]
  We argue that the rise of such a geometry, despite optimizing over mere local associations, cannot be straightforwardly attributed to typical architectural or optimizational pressures.<n>We demonstrate how the geometry stems from a spectral bias that -- in contrast to prevailing theories -- indeed arises naturally despite the lack of various pressures.
  arXiv  Detail & Related papers  (2025-10-30T17:40:22Z)
• Geometric Origins of Bias in Deep Neural Networks: A Human Visual System Perspective [1.7315645623674356]
  Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge.<n>Inspired by the human visual system, we propose a geometric analysis framework linking the geometric complexity of class-specific perceptual Manifolds to model bias.<n>To support this analysis, we present the Perceptual-Manifold-Geometry library, designed for calculating the geometric properties of perceptual Manifolds.
  arXiv  Detail & Related papers  (2025-02-17T13:54:02Z)
• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• Geometric Constraints in Deep Learning Frameworks: A Survey [12.021629185200807]
  The classic geometric technique of Shape from Stereo is built on using geometry to define constraints on scene and camera deep learning.<n>We compare and contrast geometry enforcing constraints integrated into deep learning frameworks for depth estimation and other closely related vision tasks.<n>We present a new taxonomy for prevalent geometry enforcing constraints used in modern deep learning frameworks.
  arXiv  Detail & Related papers  (2024-03-19T04:41:09Z)
• Fundamental Components of Deep Learning: A category-theoretic approach [0.0]
  This thesis develops a novel mathematical foundation for deep learning based on the language of category theory. We also systematise many existing approaches, placing many existing constructions and concepts under the same umbrella.
  arXiv  Detail & Related papers  (2024-03-13T01:29:40Z)
• A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
  Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
  arXiv  Detail & Related papers  (2023-12-12T18:44:19Z)
• Exploring Data Geometry for Continual Learning [64.4358878435983]
  We study continual learning from a novel perspective by exploring data geometry for the non-stationary stream of data. Our method dynamically expands the geometry of the underlying space to match growing geometric structures induced by new data. Experiments show that our method achieves better performance than baseline methods designed in Euclidean space.
  arXiv  Detail & Related papers  (2023-04-08T06:35:25Z)
• Is Distance Matrix Enough for Geometric Deep Learning? [24.307433184938127]
  We show that Vanilla DisGNN is geometrically incomplete. We then propose $k$-DisGNNs, which can effectively exploit the rich geometry contained in the distance matrix. Our $k$-DisGNNs achieve many new state-of-the-art results on MD17.
  arXiv  Detail & Related papers  (2023-02-11T16:54:20Z)
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges [50.22269760171131]
  The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. This text is concerned with exposing pre-defined regularities through unified geometric principles. It provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers.
  arXiv  Detail & Related papers  (2021-04-27T21:09:51Z)
• Fusing the Old with the New: Learning Relative Camera Pose with Geometry-Guided Uncertainty [91.0564497403256]
  We present a novel framework that involves probabilistic fusion between the two families of predictions during network training. Our network features a self-attention graph neural network, which drives the learning by enforcing strong interactions between different correspondences. We propose motion parmeterizations suitable for learning and show that our method achieves state-of-the-art performance on the challenging DeMoN and ScanNet datasets.
  arXiv  Detail & Related papers  (2021-04-16T17:59:06Z)
• DSG-Net: Learning Disentangled Structure and Geometry for 3D Shape Generation [98.96086261213578]
  We introduce DSG-Net, a deep neural network that learns a disentangled structured and geometric mesh representation for 3D shapes. This supports a range of novel shape generation applications with disentangled control, such as of structure (geometry) while keeping geometry (structure) unchanged. Our method not only supports controllable generation applications but also produces high-quality synthesized shapes, outperforming state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-08-12T17:06:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.