Appears in collection : A Multiscale tour of Harmonic Analysis and Machine Learning - To Celebrate Stéphane Mallat's 60th birthday

The new wave of artificial intelligence is impacting industry, public life, and the sciences in an unprecedented manner. In mathematics, it has by now already led to paradigm changes in several areas. However, one current major drawback is the lack of reliability of such methodologies. In this talk, we will focus on the key aspects of reliability of deep neural networks, namely generalization, and explainability, and discuss a complete generalization result in the setting of graph neural networks and a novel explainability approach based on applied harmonic analysis. Finally, we will briefly touch upon limitations as well, show that from a computability viewpoint digital hardware causes a serious problem for reliability, and reveal a surprising connection to novel computing approaches such as quantum computing.