Mathematical Mysteries of Deep Neural Networks, by Prof. Dr. Stéphane Mallat (École Normale Supérieur)

Mathematical Mysteries of Deep Neural Networks”: by Prof. Dr. Stéphane Mallat (École Normale Supérieur)

Abstract:

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.

Please send an email to office@bimos.tu-berlin.de <mailto:office@bimos.tu-berlin.de> to register, if you would like to attend.