The Modern Mathematics of Artificial Intelligence: From Reliable AI to Quantum Computing

Abstract

Artificial intelligence is currently changing our society in an unprecedented manner. A similarly strong impact can be witnessed on basically any area of science. However, one current major drawback is the lack of reliability of such methodologies. It is therefore crucial to develop a profound mathematical foundation of artificial intelligence. In this lecture we will first provide an introduction into this exciting research field. We will then survey several high impact results in this realm, ranging from expressivity over generalization to explainability of such methods. Finally, we will discuss fundamental limitations in terms of computability, which seriously affects reliability of artificial intelligence approaches, and reveal a connection with quantum computing.

Our Speaker

Gitta Kutyniok currently is 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 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, 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. She is currently the main coordinator of the Research Focus "Next Generation AI" at the Center for Advanced Studies at LMU and the DFG-Priority Program "Theoretical Foundations of Deep Learning", serves as Vice President-at-Large of SIAM, and acts as Co-Director of the Konrad Zuse School of Excellence in Reliable AI (relAI) in Munich. 

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.