1. CA Special Issue on Neural Network Approximation

   • Wolfgang Dahmen
   • Ronald A. DeVore
   • Philipp Grohs

   Guest Editorial Open access 06 August 2021 Pages: 1 - 2

2. DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

   • Dennis Elbrächter
   • Philipp Grohs
   • Christoph Schwab

   OriginalPaper Open access 06 May 2021 Pages: 3 - 71

3. A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

   • Gitta Kutyniok
   • Philipp Petersen
   • Reinhold Schneider

   OriginalPaper Open access 02 June 2021 Pages: 73 - 125

4. Nonlinear Approximation and (Deep) \(\mathrm {ReLU}\) Networks

   • I. Daubechies
   • R. DeVore
   • G. Petrova

   OriginalPaper 26 April 2021 Pages: 127 - 172

   

5. Neural Network Identifiability for a Family of Sigmoidal Nonlinearities

   • Verner Vlačić
   • Helmut Bölcskei

   OriginalPaper Open access 07 May 2021 Pages: 173 - 224

   

6. Depth Separations in Neural Networks: What is Actually Being Separated?

   • Itay Safran
   • Ronen Eldan
   • Ohad Shamir

   OriginalPaper 02 June 2021 Pages: 225 - 257

   

7. Approximation Spaces of Deep Neural Networks

   • Rémi Gribonval
   • Gitta Kutyniok
   • Felix Voigtlaender

   OriginalPaper 05 May 2021 Pages: 259 - 367

   

8. The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

   • Weinan E
   • Chao Ma
   • Lei Wu

   OriginalPaper 24 May 2021 Pages: 369 - 406

9. Universal Approximations of Invariant Maps by Neural Networks

   • Dmitry Yarotsky

   OriginalPaper 30 April 2021 Pages: 407 - 474

   

10. Robust and Resource-Efficient Identification of Two Hidden Layer Neural Networks

    • Massimo Fornasier
    • Timo Klock
    • Michael Rauchensteiner

    OriginalPaper Open access 30 June 2021 Pages: 475 - 536

    

11. Exponential ReLU DNN Expression of Holomorphic Maps in High Dimension

    • J. A. A. Opschoor
    • Ch. Schwab
    • J. Zech

    OriginalPaper Open access 23 April 2021 Pages: 537 - 582

12. Best k-Layer Neural Network Approximations

    • Lek-Heng Lim
    • Mateusz Michałek
    • Yang Qi

    OriginalPaper 07 June 2021 Pages: 583 - 604