Аннотация:
Deep neural networks are remarkably successful hybrid classifiers, first trained on large data bases
of unlabeled examples, and then optimized with a discriminative supervised classi er. They provide state of the art results in computer vision, speech recognition, music and bio-medical classification, with little mathematical understanding of their performance. We introduce a mathematical model of deep neural networks with scattering transforms, which cascade complex valued unitary operators and a contractive modulus. In this framework, unsupervised learning amounts to optimize a contraction of the space, while maximizing the volume occupied by representations of unlabeled examples. These deep scattering provides new models of stochastic processes, whose properties are analyzed. Wavelet unitary operators appear to be nearly optimal for the first network layers of many audio and image classifiers. Applications will be discussed and shown on images and sounds.
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