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cs.LGJul 1, 2018
16
citations (OpenAlex)
authors
  • Weinan E
  • Qingcan Wang
arXiv abstractPDF
paper

Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions

arXiv:1807.00297

Abstract

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

References in corpus (2)

  • The Expressive Power of Neural Networks: A View from the Width
  • Benefits of depth in neural networks

Cited by in corpus (14)

  • PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
  • Deep Network Approximation for Smooth Functions
  • Neural Network Approximation: Three Hidden Layers Are Enough
  • Nonlinear Approximation and (Deep) ReLU Networks
  • Nonlinear Approximation via Compositions
  • Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
  • Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
  • Full error analysis for the training of deep neural networks
  • Structure Probing Neural Network Deflation
  • The gap between theory and practice in function approximation with deep neural networks
  • Reproducing Activation Function for Deep Learning
  • Selection dynamics for deep neural networks
  • Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data
  • Analytic Continuation of Noisy Data Using Adams Bashforth ResNet
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