May 16, 2018

33rd Annual Shanks Lecture: Deep Convolutional Neural Networks and Harmonic Analysis

Supervised and unsupervised learning amount to approximate functions in high-dimensional spaces, given sample values. Deep convolutional networks have obtained outstanding results for complex classification and regression problems of highly diverse data, including images, speech, natural language and all kind of physical measurements. Dimension reduction in deep neural networks rely on separation of scales, computation of invariants over groups of symmetries, and sparse representations. This could be called applied harmonic analysis. We shall analyze the construction of invariants through deep scattering networks computed with wavelet filters and discuss open mathematical questions. Applications to image classification, quantum chemistry, and maximum entropy models of turbulences and textures will be shown. A reception will follow the lecture. A reception will follow the lecture. For more information, see the events@vanderbilt .