title: Understanding deep convolutional networks.
abstract: Deep convolutional networks provide state-of-the-art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and nonlinearities. A mathematical framework is introduced to analyse their properties. Computations of invariants involve multiscale contractions with wavelets, the linearization of hierarchical symmetries and sparse separations. Applications are discussed.
authors.affiliation: École Normale Supérieure, CNRS, PSL, 45 rue d'Ulm, Paris, France stephane.mallat@ens.fr.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Mallat
keywords: deep convolutional neural networks; learning; wavelets