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1W-MINDS: Stéphane Mallat, July 2, 2020, Descartes versus Bayes: Harmonic Analysis for High...

Is high-dimensional learning about function approximation or Bayes probability estimation? We shall argue that solutions go through finding discriminative variables which concentrate, according to Bayes and statistical physics. Harmonic analysis gives a mathematical framework to define and analyze such variables from prior information on symmetries. The results of deep neural network architectures are opening new horizons beyond Fourier, wavelets and sparsity. What is being learned through optimization? Phase was long forgotten and is making its way back. This lecture outlines harmonic analysis challenges raised by classification and data generation with deep convolutional neural networks. We consider applications to image generation and classification, including ImageNet.