  We introduce a sparse scattering deep convolutional neural network, which
provides a simple model to analyze properties of deep representation learning
for classification. Learning a single dictionary matrix with a classifier
yields a higher classification accuracy than AlexNet over the ImageNet 2012
dataset. The network first applies a scattering transform that linearizes
variabilities due to geometric transformations such as translations and small
deformations. A sparse $\ell^1$ dictionary coding reduces intra-class
variability while preserving class separation through projections over unions
of linear spaces. It is implemented in a deep convolutional network with a
homotopy algorithm having an exponential convergence. A convergence proof is
given in a general framework that includes ALISTA. Classification results are
analyzed on ImageNet.
