Episode 6 — Annual highlights

Christian Fleischhack | Mathematical Physics
General relativity and quantum theory have not been merged into a consistent theory of quantum gravity yet. Unfortunately, to date, there are no experiments available that may disclose parts of the unified theory. Nevertheless, mathematics is already in a position to provide us with rigorous statements on how quantum gravity may look like.

Guido Montúfar | ERC Research Group Mathematical Machine Learning
This project develops mathematical theory for deep learning, critical in making these enormously successful machine learning methods more broadly applicable, efficient, interpretable, safe, and reliable. Concretely, we seek to clarify the interplay between the representational power of artificial neural networks as parametric sets of hypotheses, the properties and consequences of the parameter optimization procedures that are employed in order to select a hypothesis based on data, and the performance of trained neural networks at test time on new data.