Convergence rates for shallow neural networks learned by gradient descent

DOI10.3150/23-bej1605arXiv2107.09550OpenAlexW4388506988MaRDI QIDQ6137712

Alina Braun, Sophie Langer, Harro Walk, Michael Kohler

Publication date: 16 January 2024

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.09550

zbMATH Keywords

rate of convergenceneural networksgradient descentdeep learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximation and estimation bounds for artificial neural networks
• Optimal global rates of convergence for nonparametric regression
• A distribution-free theory of nonparametric regression
• Over-parametrized deep neural networks minimizing the empirical risk do not generalize well
• Analysis of a two-layer neural network via displacement convexity
• On the rate of convergence of fully connected deep neural network regression estimates
• Gradient descent optimizes over-parameterized deep ReLU networks
• Nonparametric regression using deep neural networks with ReLU activation function
• On deep learning as a remedy for the curse of dimensionality in nonparametric regression
• Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
• Geometric Upper Bounds on Rates of Variable-Basis Approximation
• Universal approximation bounds for superpositions of a sigmoidal function
• Theoretical issues in deep networks
• Estimation of a Function of Low Local Dimensionality by Deep Neural Networks
• Nonparametric Regression Based on Hierarchical Interaction Models
• Neural tangent kernel: convergence and generalization in neural networks (invited paper)
• Approximation bounds for random neural networks and reservoir systems