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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

06-04-2025

Dr. Hidde Schönberger receives award from Sparkasse Ingolstadt Eichstätt for the best dissertation

As part of this year's Dies Academicus, Dr. Hidde Schönberger received the award for the best dissertation for his work titled "Nonlocal gradients within variational models: Existence theories and asymptotic analysis." The dissertation, written under the supervision of Prof. Dr. Carolin Kreisbeck at the Chair of Mathematics – Analysis, consists of 6 research articles and was previously honored with the prestigious Klaus-Körper Prize of the Society for Applied Mathematics and Mechanics (GAMM).

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. As opposed to classical models in the literature based on local quantities like the derivative, the nonlocal analogues allow for discontinuities to emerge, which is of relevance for studying when materials fracture. His work establishes that solutions of these nonlocal variational problems exist and identifies their dependence on crucial parameters in the model. Since these solutions cannot be computed explicitly, proving that they exist is important not only from a theoretical point, but also from an applied point of view where they need to be approximated with the computer. Furthermore, the asymptotic analysis shows, in particular, that the nonlocal models are consistent with their local counterparts that have already been used for many decades. The concepts introduced in the thesis represent a significant contribution to the understanding and advancement of nonlocal variational principles. A crucial tool that is introduced allows the analysis of the more intractable nonlocal gradients to be reduced to their simpler local versions, and this provides a methodology that can help solve many other problems in the nonlocal setting as well.

Dr. Hidde Schönberger completed his BSc and MSc in mathematics cum laude at Utrecht University, after which he continued as/became a doctoral researcher at KU in 2021 During that time, he presented his work at various conferences and completed a research visit to Universidad Autonoma de Madrid in Spain. Since September 2024, he is a postdoc at the Institute for Analysis and Scientific Computing at TU Wien, where he continues his research on nonlocal problems in the calculus of variations.

We sincerely congratulate Dr. Schönberger on this well-deserved award and wish him continued success in his future career!

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.