Deep Learning aus der Per- spektive von Wahrscheinlichkeit und Geometrie

01/07/2024 to 30/06/2027

Laplace approximations have re-emerged as a potent and efficient tool for deep learning. They combine the two powerful paradigms of automatic differentiation and numerical linear algebra to enable functionality that had previously become niche due its high computational cost. In particular, Laplace approximations yield a Bayesian formalism for deep learning, effectively turning any deep neural network into an approximate Gaussian process. But they also define a metric, and an associated mani- fold to the deep network and its parameter space. This project hopes to expand recent results both in a theoretical and algorithmic direction. On the theoretical side, the project aims to leverage differential geometry to improve understanding of the computational complexity of Bayesian deep training. As a direct outcome, the project will then develop new algorithms and functional extensions of deep learning through re-parametrization, to provide better calibrated uncertainty quantification in deep learning.