Reliable AI: Successes, Challenges, and Limitations

Abstract - 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 diagnostics or molecular dynamics. However, one current major drawback is the lack of reliability of such methodologies.
In this lecture we will take a mathematical viewpoint towards this problem, showing the power of such approaches to reliability. We will first provide an introduction into this vibrant research area, focussing specifically on deep neural networks. We will then survey recent advances, in particular, concerning generalization guarantees and explainability. Finally, we will discuss fundamental limitations of deep neural networks and related approaches in terms of computability, which seriously affects their reliability.

Bio - Gitta Kutyniok currently holds 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, and was a Nachdiplomslecturer at ETH Zurich in 2014. 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 holds an Adjunct Professorship in Machine Learning at the University of Tromso since 2019.
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, the lecturer of the London Mathematical Society (LMS) Invited Lecture Series in 2022, and an invited lecturer at both the International Congress of Mathematicians 2022 and the International Congress on Industrial and Applied Mathematics 2023. Moreover, she became a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017, a SIAM Fellow in 2019, and a member of the European Academy of Sciences in 2022. In addition, she was honored by a Francqui Chair of the Belgian Francqui Foundation in 2020. She was Chair of the SIAM Activity Group on Imaging Sciences from 2018-2019 and Vice Chair of the new SIAM Activity Group on Data Science in 2021, and currently serves as Vice President-at-Large of SIAM. She is also the spokesperson of the Research Focus "Next Generation AI" at the Center for Advanced Studies at LMU, and serves as LMU-Director of the Konrad Zuse School of Excellence in Reliable AI.
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.