Artificial intelligence is currently leading to one breakthrough after the other, both in public life with, for instance, autonomous driving and speech recognition, and in the sciences in areas such as medical imaging or molecular dynamics. However, one  current major drawback worldwide, in particular, in light of regulations such as the EU AI Act and the G7 Hiroshima AI  Process, is the lack of reliability of such methodologies.

In this lecture, we will provide an introduction into this vibrant research area, focussing specifically on deep neural networks.  We will discuss the role of a theoretical perspective to this highly topical research direction, and survey the current state of the art in areas such as explainability. Finally, we will also touch upon fundamental limitations of deep neural networks in terms of computability, which seriously affects their reliability, and reveal an intriguing connection to neuromorphic and quantum computing.

Gitta Kutyniok (https://www.ai.math.lmu.de/kutyniok) currently has a Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at the Ludwig-Maximilians-Universität München. She received her Diploma in Mathematics and Computer Science as well as her Ph.D. degree from the Universität Paderborn in Germany, and her Habilitation in Mathematics in 2006 at the Justus-Liebig Universität Gießen. From 2001 to 2008 she held visiting positions at several US institutions, including Princeton University, Stanford University, Yale University, Georgia Institute of Technology, and Washington University in St. Louis. In 2008, she became a full professor of mathematics at the Universität Osnabrück, and moved to Berlin three years later, where she held an Einstein Chair in the Institute of Mathematics at the Technische Universität Berlin and a courtesy appointment in the Department of Computer Science and Engineering until 2020. In addition, Gitta Kutyniok held an Adjunct Professorship in Machine Learning at the University of Tromso from 2019 until 2023.

Gitta Kutyniok has received various awards for her research such as an award from the Universität Paderborn in 2003, the Research Prize of the Justus-Liebig Universität Gießen and a Heisenberg-Fellowship in 2006, and the von Kaven Prize by the DFG in 2007. She was invited as the Noether Lecturer at the ÖMG-DMV Congress in 2013, a plenary lecturer at the 8th European Congress of Mathematics (8ECM) in 2021, and the lecturer of the London Mathematical Society (LMS) Invited Lecture Series in 2022. She was also honored by invited lectures at both the International Congress of Mathematicians 2022
(ICM 2022) and the International Congress on Industrial and Applied Mathematics (ICIAM 2023). Moreover, she was elected as a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017 and of the European Academy of Sciences in 2022, and became a SIAM Fellow in 2019 and an IEEE Fellow in 2024. She currently acts as LMU-Director of the Konrad Zuse School of Excellence in Reliable AI (relAI) in Munich, serves as Vice President-at-Large of SIAM, and is spokesperson of the DFG-Priority Program "Theoretical Foundations of Deep Learning" and of the AI-HUB@LMU, which is the interdisciplinary platform for research and teaching in AI and data science at LMU.

Gitta Kutyniok's research work covers, in particular, the areas of applied and computational harmonic analysis, artificial intelligence, compressed sensing, deep learning, imaging sciences, inverse problems, and applications to life sciences, robotics, and telecommunication.