Theory of deep convolutional neural networks. II: Spherical analysis
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Publication:2057723
DOI10.1016/j.neunet.2020.07.029zbMath1475.68313arXiv2007.14285OpenAlexW3047620219WikidataQ98384792 ScholiaQ98384792MaRDI QIDQ2057723
Ding-Xuan Zhou, Han Feng, Zhiying Fang, Shuo Huang
Publication date: 7 December 2021
Published in: Neural Networks (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.14285
Artificial neural networks and deep learning (68T07) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)
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Cites Work
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- Consistency analysis of an empirical minimum error entropy algorithm
- The best approximation of the classes of functions \(W_ p^{\alpha}(S^ n)\) by polynomials in spherical harmonics
- Provable approximation properties for deep neural networks
- Distributed kernel-based gradient descent algorithms
- Approximation properties of a multilayered feedforward artificial neural network
- Limitations of the approximation capabilities of neural networks with one hidden layer
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Theory of deep convolutional neural networks: downsampling
- Error bounds for approximations with deep ReLU networks
- Universality of deep convolutional neural networks
- Neural network with unbounded activation functions is universal approximator
- Fully discrete needlet approximation on the sphere
- A lower bound for the worst-case cubature error on spheres of arbitrary dimension
- Learning theory estimates via integral operators and their approximations
- Learning rates for the risk of kernel-based quantile regression estimators in additive models
- Universal approximation bounds for superpositions of a sigmoidal function
- Deep distributed convolutional neural networks: Universality
- Approximation by Combinations of ReLU and Squared ReLU Ridge Functions With <inline-formula> <tex-math notation="LaTeX">$\ell^1$ </tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\ell^0$ </tex-math> </inline-formula> Controls
- Approximation Theory and Harmonic Analysis on Spheres and Balls
- Optimal Approximation with Sparsely Connected Deep Neural Networks
- Equivalence of approximation by convolutional neural networks and fully-connected networks
- Thresholded spectral algorithms for sparse approximations
- A Fast Learning Algorithm for Deep Belief Nets