Hodson Hall Board Room
Mathematical Mysteries of Deep Neural Networks
Classification and regression require to approximate functions in high dimensional spaces. Avoiding the dimensionality curse opens many questions in statistics, probability, harmonic analysis and geometry. Convolutional deep neural networks can obtain spectacular results for image analysis, speech understanding, natural languages and many other problems. We shall review their architecture and analyze their mathematical properties, with many open questions. We show that the architectures implement multiscale contractions, where wavelets have an important role, and they can learn groups of symmetries. This will be illustrated through applications to image and audio classification, but also to statistical physics and computations of molecular energies in quantum chemistry.
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 ofMathematical 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, foreign member of the US National Academy of Engineering, an IEEE Fellow and a 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 receivedthe 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.n