Conference VIP Talk

Title: Multiscale Models for Data Generation and Inverse Problems with Deep Networks

Speaker: Stéphane Mallat

Abstract:

Generating signals and images or solving inverse problems requires to build models of high-dimensional data distributions. Spectacular results have been obtained by deep neural networks, particularly with score diffusion models.  A major issue is to understand how come such models can be estimated in high dimesion. We show that many signals and images have local dependencies across scales, allowing to circumvent the curse of dimensionality. Similarly to Wilson renormalisation group in physics, we demonstrate that probability distributions can be factorised into conditional probabilities of wavelet coefficients across scales, which are local. It defines low-dimensional models of complex physical fields, but also of structured images. Applications are shown for image generation, noise removal and super-resolution recovery. We shall also relate these questions to classification and regression problems with deep neural networks. 

Bio:

Stéphane Mallat was Professor at NYU in computer science, until 1994, then at Ecole Polytechnique in Paris and Department Chair. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company.  Since 2017, he holds the “Data Sciences” chair at the Collège de France. He is a member of the French Academy of sciences, of the Academy of Technologies, and a foreign member of the US National Academy of Engineering.

Stéphane Mallat’s research interests include machine learning, signal processing and harmonic analysis. He developed the multiresolution wavelet theory and algorithms at the origin of the compression standard JPEG-2000, and sparse signal representations in dictionaries through matching pursuits. He currently works on mathematical models of deep neural networks, for data analysis and physics.