Mathematical Mysteries of Deep Neural Networks
Abstract: Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems including images, audio signals, with spectacular results. We shall review their architecture and concentrate on the analysis of their mathematical properties which remain mostly mysterious. Applications will be shown for image and audio classification, but also for learning complex physics such as quantum chemistry.
Bio: Stéphane Mallat received the Ph.D. degree in electrical engineering from the University of Pennsylvania, in 1988. He was then Professor at the Courant Institute of Mathematical Sciences, until 1994. In 1995, he became Professor in Applied Mathematics at Ecole Polytechnique, Paris and Department Chair in 2001. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. In 2012 he joined the Computer Science Department of Ecole Normale Supérieure, in Paris. Stéphane Mallat’s research interests include learning, signal processing, and harmonic analysis. He is a member of the French Academy of sciences, an IEEE Fellow and an EUSIPCO Fellow. In 1997, he received the Outstanding Achievement Award from the SPIE Society and was a plenary lecturer at the International Congress of Mathematicians in 1998. He also received the 2004 European IST Grand prize, the 2004 INIST-CNRS prize for most cited French researcher in engineering and computer science, the 2007 EADS grand prize of the French Academy of Sciences, the 2013 Innovation medal of the CNRS, and the 2015 IEEE Signal Processing best sustaining paper award.