Descartes versus Bayes: Harmonic Analysis and Deep Net Theories

Is high-dimensional learning about function approximation or Bayes probability estimation ? Algorithmic 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?  This lecture outlines harmonic analysis challenges raised by classification and data models with deep convolutional neural networks. We consider applications to statistical physics models and image classification with ImageNet.