Theoretical issues in deep networks

DOI10.1073/pnas.1907369117zbMath1485.68235OpenAlexW2995896684WikidataQ96229123 ScholiaQ96229123MaRDI QIDQ5073211

Andrzej Banburski, Qianli Liao, Tomaso Poggio

Publication date: 5 May 2022

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.1907369117

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07)

Related Items (10)

Locality defeats the curse of dimensionality in convolutional teacher–student scenarios* ⋮ The unreasonable effectiveness of deep learning in artificial intelligence ⋮ Theoretical issues in deep networks ⋮ Estimation of a regression function on a manifold by fully connected deep neural networks ⋮ The generalized extreme learning machines: tuning hyperparameters and limiting approach for the Moore-Penrose generalized inverse ⋮ Theory of deep convolutional neural networks. III: Approximating radial functions ⋮ Towards understanding theoretical advantages of complex-reaction networks ⋮ Convergence rates for shallow neural networks learned by gradient descent ⋮ On the influence of over-parameterization in manifold based surrogates and deep neural operators ⋮ An analytic layer-wise deep learning framework with applications to robotics

Cites Work

• Approximation properties of a multilayered feedforward artificial neural network
• Limitations of the approximation capabilities of neural networks with one hidden layer
• Nonlinear approximation and (deep) ReLU networks
• Optimal approximation of piecewise smooth functions using deep ReLU neural networks
• Just interpolate: kernel ``ridgeless regression can generalize
• Error bounds for approximations with deep ReLU networks
• Deep vs. shallow networks: An approximation theory perspective
• Neural Networks for Localized Approximation
• Two Models of Double Descent for Weak Features
• The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve
• Theoretical issues in deep networks
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