Stéphane Mallat is an applied mathematician, Professor at the Collège de France on the chair of Data Sciences. He is a member of the French Academy of Sciences, the Academy of Technologies and a Foreign Member of the US National Academy of Engineering. He was Professor at the Courant Institute of NYU in New York for 10 years, then at Ecole Polytechnique and Ecole Normale Supérieure in Paris. He also was the co-founder and CEO of a semiconductor start-up company. Stéphane Mallat's research interests include machine learning, signal processing and harmonic analysis. He developed the multiresolution wavelet theory with applications to image processing and sparse representations. He now works on mathematical understanding of deep neural networks, and their applications. ABSTRACT: Deep neural networks obtain impressive results for image, sound and language recognition or to address complex problems in physics. They are partly responsible of the renewal of artificial intelligence. Yet, we do not understand why they can work so well and why they fail sometimes, which raises many problems of robustness and explainability. Recognizing or classifying data amounts to approximate phenomena which depend on a very large number of variables. The combinatorial explosion of possibilities makes it potentially impossible to solve. One can learn from data only if the problem is highly structured. Deep neural networks appear to take advantage of these unknown structures. Understanding this "architecture of complexity" involves many branches of mathematics and is related to open questions in physics. I will discuss some approaches and show applications. Register in advance for this ICTP Colloquium at the following link: https://zoom.us/webinar/register/WN_IFSyVfu2RDm_EIipvwFzBQ After registering, you will receive a confirmation email containing information about joining the talk. Should you not be able to join the talk, the Colloquium is also available in live streaming at: ictp.it/livestream All are welcome to attend.