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Published online by Cambridge University Press: 29 November 2022
In this chapter we describe scattering representations, a signal representation built using wavelet multiscale decompositions with a deep convolutional architecture. Its construction highlights the fundamental role of geometric stability in deep learning representations, and provides a mathematical basis to study CNNs. We describe its main mathematical properties, its applications to computer vision, speech recognition and physical sciences, as well as its extensions to Lie Groups and non-Euclidean domains. Finally, we discuss recent applications to modeling high-dimensional probability densities.
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