Orateur
Description
Many classification and reconstruction tasks in physics rely on learned latent representations of the data. When networks are trained with a notion of locality, they encode task-specific similarity as closeness in the latent space. Differential geometry, particularly information geometry, is a powerful tool to uncover the learned information in these latent representations and thereby retrace the decision-making of the network. With a jet tagging task in mind, we construct an information geometry on the learned latent space of a variational autoencoder with a classifier head. We show how the classifier likelihood links high-level physics observables to the learned latent geometry via the Fisher information metric. We supplement the Fisher information by advanced differential geometric concepts such as curvature and geodesic paths and use them to assess the importance of different features for the classification decision. We realize the importance of the likelihood’s skewness contribution as a geometric nonmetricity tensor and use it to construct coordinate-invariant measures of class separation.