10 papers
Selection, Representation, and Execution in Sparse Fourier Neural Operators
Abdul Qadir Ibrahim, Martin Burger
Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives are not equivalent or do not…
A neural operator view on U-Nets for inverse imaging problems
Alexander Auras, Martin Burger, Samira Kabri +2
Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging. Yet, very few works have studied their behavior…
Allure of Craquelure: A Variational-Generative Approach to Crack Detection in Paintings
Laura Paul, Holger Rauhut, Martin Burger +2
Recent advances in imaging technologies, deep learning and numerical performance have enabled non-invasive detailed analysis of artworks, supporting their documentation and conserv…
Explainable Learning Based Regularization of Inverse Problems
Martin Burger, Samira Kabri, Gitta Kutyniok +2
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infan…
Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference
Simon Welker, Lorenz Kuger, Tim Roith +4
In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions…
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
Martin Burger, Samira Kabri, Yury Korolev +2
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns…
Adversarial flows: A gradient flow characterization of adversarial attacks
Lukas Weigand, Tim Roith, Martin Burger
A popular method to perform adversarial attacks on neuronal networks is the so-called fast gradient sign method and its iterative variant. In this paper, we interpret this method a…
Analysis of Primal-Dual Langevin Algorithms
Martin Burger, Matthias J. Ehrhardt, Lorenz Kuger +1
We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions in with a Lebesgue density of the form $μ^\ast…
Learning a Sparse Representation of Barron Functions with the Inverse Scale Space Flow
Tjeerd Jan Heeringa, Tim Roith, Christoph Brune +1
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an function , the inverse scale space flow is used to find a spar…
Learned Regularization for Inverse Problems: Insights from a Spectral Model
Martin Burger, Samira Kabri
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction oper…