Sobolev-type embeddings for neural network approximation spaces

DOI10.1007/S00365-022-09598-XOpenAlexW3208427634MaRDI QIDQ2700875

Philipp Grohs, Felix Voigtlaender

Publication date: 27 April 2023

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.15304

zbMATH Keywords

Hölder spacesapproximation spacesembedding theoremsdeep neural networksoptimal learning algorithms

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Numerical interpolation (65D05)

Related Items (1)

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Cites Work

• Approximation spaces of deep neural networks
• Universal approximation bounds for superpositions of a sigmoidal function
• Deep Neural Network Approximation Theory
• The Modern Mathematics of Deep Learning
• Neural network approximation
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