Optimal Approximation and Learning Rates for Deep Convolutional Neural Networks
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Abstract (arXiv)
This paper focuses on approximation and learning performance analysis for deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate r-smooth function, the approximation rates of deep convolutional neural networks with depth L are of order (L2/log L)-2r/d , which is optimal up to a logarithmic factor. Furthermore, we deduce almost optimal learning rates for implementing empirical risk minimization over deep convolutional neural networks.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 13 of its 24 references that are in the map. First posted on arXiv 7 Aug 2023.
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13 of 24 references.
References · 13
- 2016Error bounds for approximations with deep ReLU networkscited by 574
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
- 2018Universality of Deep Convolutional Neural Networkscited by 176
- 2020Deep Network Approximation for Smooth Functionscited by 164
- 2017Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activationscited by 104
- 2019The phase diagram of approximation rates for deep neural networkscited by 88
- 2020Theory of Deep Convolutional Neural Networks II: Spherical Analysiscited by 22
- 2021Theory of Deep Convolutional Neural Networks III: Approximating Radial Functionscited by 22
- 2021Universal Consistency of Deep Convolutional Neural Networkscited by 16
- 2020Depth Selection for Deep ReLU Nets in Feature Extraction and Generalizationcited by 13
- 2019Realization of spatial sparseness by deep ReLU nets with massive datacited by 10
- 2019Realizing data features by deep netscited by 6
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Citing papers per year: 2024: 1.
1 paper.
- 2024Component-based Sketching for Deep ReLU Netscited by 1
- 2024Component-based Sketching for Deep ReLU Nets21 Sep 2024