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We introduce a sparse scattering deep convolutional neural network, whichprovides a simple model to analyze properties of deep representation learningfor classification. Learning a single dictionary matrix with a classifieryields a higher classification accuracy than AlexNet over the ImageNet 2012dataset. The network first applies a scattering transform that linearizesvariabilities due to geometric transformations such as translations and smalldeformations. A sparse $\ell^1$ dictionary coding reduces intra-classvariability while preserving class separation through projections over unionsof linear spaces. It is implemented in a deep convolutional network with ahomotopy algorithm having an exponential convergence. A convergence proof isgiven in a general framework that includes ALISTA. Classification results areanalyzed on ImageNet.

Deep Network Classification by Scattering and Homotopy Dictionary Learning