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The research group "Reliable Machine Learning" studies the properties of machine learning algorithms.
In view of the recent success of deep learning methods in applications like image recognition, speech recognition, and automatic translation, the group especially focuses on properties of deep neural networks.

Although a neural network trained e.g. for an image classification task might work well on "real inputs", it has been repeatedly shown empirically that such networks are vulnerable to adversarial examples:
a minimal perturbation (impercetible to a human) of the input data can cause the network to misclassify the input.
Thus, an important research area of the group is to mathematically understand the reasons for the existence of such adversarial examples (i.e., the instability of trained neural networks),
and - building on that understanding - to develop improved methods that yield provably robust neural networks.

The research group is supported by the Emmy Noether project "Stability and Solvability in Deep Learning".

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Math News

03-28-2025

Dr.-Klaus-Körper Prize 2025 for dissertation of Dr. Schönberger

Dr. Hidde Schönberger has been selected for the Dr.-Klaus-Körper Prize 2025, awarded by the International Association of Applied Mathematics and Mechanics (GAMM). He received this honor for his doctoral thesis titled “Nonlocal gradients within variational models: Existence theories and asymptotic analysis”, which he completed at the Chair of Analysis under the supervision of Prof. Carolin Kreisbeck.

In his dissertation, Dr. Schönberger investigates mathematical models involving nonlocal gradients—a highly topical subject in variational calculus, particularly relevant in the modeling of material behavior. His work develops new existence theories and provides a thorough asymptotic analysis of such models. The concepts introduced in the thesis represent a significant contribution to the understanding and advancement of nonlocal variational principles.

Dr. Schönberger is currently a postdoctoral researcher at TU Wien, where he continues his research in this field, among other activities.

The Dr.-Klaus-Körper Prize is awarded annually to young researchers under the age of 35 for an outstanding dissertation in applied mathematics or mechanics. It is funded by the Dr.-Klaus-Körper Foundation and conferred by the GAMM Executive Board. Dr. Schönberger was presented with the award during the GAMM Annual Meeting, which took place from April 7–11, 2025, in Poznań, Poland.

The entire Department of Mathematics congratulates Dr. Schönberger on this recognition!

MIDS Seminar

Mathematical Institute for Machine Learning and Data Science

The Chair of Reliable Maschine Learning is part of the Mathematical Institute for Machine Learning and Data Science, MIDS.
Learn more about MIDS here.