mlsanityData to 14 Oct 2026

Feature Qualification by Deep Nets: A Constructive Approach

arXiv 2503.18676 ↗First posted 24 Mar 2025cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

The great success of deep learning has stimulated avid research activities in verifying the power of depth in theory, a common consensus of which is that deep net are versatile in approximating and learning numerous functions. Such a versatility certainly enhances the understanding of the power of depth, but makes it difficult to judge which data features are crucial in a specific learning task. This paper proposes a constructive approach to equip deep nets for the feature qualification purpose. Using the product-gate nature and localized approximation property of deep nets with sigmoid activation (deep sigmoid nets), we succeed in constructing a linear deep net operator that possesses optimal approximation performance in approximating smooth and radial functions. Furthermore, we provide theoretical evidences that the constructed deep net operator is capable of qualifying multiple features such as the smoothness and radialness of the target functions.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 41 references that are in the map. First posted on arXiv 24 Mar 2025.

Builds on

19 of 41 references.

References · 19

  1. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  2. 2016Error bounds for approximations with deep ReLU networkscited by 574
  3. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  4. 2017Optimal approximation of piecewise smooth functions using deep ReLU neural networkscited by 179
  5. 2018Universality of Deep Convolutional Neural Networkscited by 176
  6. 2016Why does deep and cheap learning work so well?cited by 100
  7. 2019Deep Neural Network Approximation Theorycited by 93
  8. 2016Deep vs. shallow networks : An approximation theory perspectivecited by 63
  9. 2015Provable approximation properties for deep neural networkscited by 60
  10. 2020The Global Landscape of Neural Networks: An Overviewcited by 57
  11. 2019On ADMM in Deep Learning: Convergence and Saturation-Avoidancecited by 15
  12. 2020Depth Selection for Deep ReLU Nets in Feature Extraction and Generalizationcited by 13
7 more
  1. 2018Generalization and Expressivity for Deep Netscited by 11
  2. 2019Realization of spatial sparseness by deep ReLU nets with massive datacited by 10
  3. 2019Realizing data features by deep netscited by 6
  4. 2019Deep Neural Networks Predicting Oil Movement in a Development Unitcited by 4
  5. 2021Generalization Performance of Empirical Risk Minimization on Over-parameterized Deep ReLU Netscited by 4
  6. 2023Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learningcited by 4
  7. 2024Component-based Sketching for Deep ReLU Netscited by 1

Built on by

Not cited yet.