Résumé : The statistical problem of estimating a Sobolev function using a deep network is studied using the Neuberger theorem and recent approximation results by Gurhing Kutyniok and Petersen. The problem is addressed by decoupling the statistical and the approximation problems and is shown to boil down to the computation of the Sobolev norm of bump functions.

Keywords : deep learning; generalisation; Sobolev spaces