The internship aims to explore the usefulness of the Fisher-Ráo metric combined with deep probabilistic models. The main question is whether or not this metric has some relationship with the training of deep generative models. In plain, we would like to understand if the training and/or fine-tuning of such probabilistic models follow optimal paths on the manifold of probability distributions. Your task will be to design and implement an experimental framework allowing to measure what kind of paths are followed on the manifold of probability distributions when such deep probabilistic models are trained. To that aim, one must first be able to measure distances in this manifold, and here is where the Fisher-Ráo metric comes in the game. The candidate does not need to be familiar with the specific concepts of Fisher-Ráo metric, but needs to be open to learning new mathematical concepts. The implementation of these experiments will require knowledge in Python and in PyTorch.