Conference highlights advances in theory and applications
Organized by the Institute for Data Science Foundations under the direction of Prof. Nihat Ay, the Conference on Mathematics of Machine Learning took place at the Hamburg University of Technology. With this conference, the organizing team consisting of Nihat Ay (TUHH, Hamburg, and SFI, USA), Martin Burger (DESY, Hamburg), Benjamin Gess (TU Berlin and MPI MiS Leipzig), and Guido Montúfar (UCLA, USA, and MPI MiS Leipzig) continued a series of events that was initiated in 2021 at the Center for Interdisciplinary Research (ZiF) at Bielefeld University.
In recent years, the field of machine learning has made significant progress in theory and applications. This success is based on the mutual symbiosis of mathematical findings and experimental studies. Over 190 scientists participated in the public conference. During the four days of the conference, they discussed the different approaches of current research.
The scientists engaged in lively discussions related to the fascinating interplay of theory and application. On the one hand, mathematics enables the conceptualization and formalization of core problems within learning theory, which leads, for example, to performance limits for learning algorithms. On the other hand, experimental studies confirm theoretical predictions and set new directions for theoretical research. The aim of this meeting was to discuss the interaction between theory and practice, with a focus on the current gaps between the two.
A central topic of the conference was diffusion models of generative artificial intelligence. These are currently an important subject of mathematical research, in which the influence of different geometries on performance is being investigated. Numerous scientists gave presentations on this topic, in particular Francis Bach (INRIA Paris Centre, France), Gabriele Steidl (TU Berlin), Kenji Fukumizu (ISM, Japan), and Markos Katsoulakis (UMass Amherst, USA). Another central topic of the conference was large language models, which have had a major impact on our everyday lives in recent years. These are based on the transformer architecture of deep neural networks and represent another fascinating subject of mathematical research. Presentations on this topic were given by Misha Belkin (UC San Diego, USA), Lénaïc Chizat (EPFL, Switzerland), Stefanie Jegelka (MIT, USA, and TU Munich), and Matus Telgarsky (NYU, USA). Gitta Kutyniok (LMU Munich) gave a visionary presentation in which she highlighted the limitations of current AI in terms of reliability and energy consumption and outlined a mathematical perspective. As an interdisciplinary field, geometry was a recurring theme throughout the conference. Jürgen Jost (MPI MiS Leipzig) and Frank Nielsen (Sony CSL, Japan) gave presentations specifically on this topic.
The Institute for Data Science Foundations pursues a holistic approach in which key aspects of intelligent systems are researched in a unified manner. In particular, concepts and methods from the fields of machine learning, deep neural networks, reinforcement learning, and embodied intelligence are integrated. The development of mathematical theories plays a central role in this and is supported and guided by experimental work in a robotics lab.
