Felix VoigtländerView profile
Professor
Felix Voigtländer is a mathematics professor at Catholic University Eichstätt-Ingolstadt specializing in the theoretical foundations of machine learning and neural networks. His research focuses on Barron spaces and their applications in understanding neural network approximation capabilities. Voigtländer's primary research interests lie in mathematical analysis of neural networks, particularly examining how Barron spaces (functions with finite Fourier moments) relate to neural network approximation properties. His work demonstrates that functions in these spaces can be approximated by shallow neural networks with rates that don't severely deteriorate with dimension, providing mathematical justification for neural networks' effectiveness in high-dimensional problems. His recent publications analyze sampling numbers of Fourier-type Barron spaces and neural network performance for classification problems with Barron-class boundaries. These works establish important theoretical connections between function approximation theory and practical neural network performance, showing how dimensionality affects approximation and sampling rates in these specialized function spaces. Voïgtländer's research contributes significantly to the mathematical understanding of why neural networks can overcome the curse of dimensionality for certain function classes, with implications for both theoretical machine learning and practical neural network design.






