Papers › Deep Network Classification by Scattering and Homotopy Dictionary Learning

Deep Network Classification by Scattering and Homotopy Dictionary Learning

8 Oct 2019ICLR 2020 1arXiv:1910.03561archive 2025-07-28

John Zarka, Louis Thiry, Tomás Angles, Stéphane Mallat

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 ℓ¹ 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.

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