Master Internship on Deep Statistical Manifolds


The internship aims to explore the usefulness of the Fisher-Ráo [1] metric combined with deep probabilistic models [2]. 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 [3].


Your task will be to design an 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 learn new mathematical concepts. The implementation of these experiments will require knowledge in Python and in PyTorch.


You will join RobotLearn, an international team of researchers, students, and engineers at Inria Grenoble. The team has a strong background in machine learning for audio-visual computation and its application to robotics, and in particular with deep generative models. The team is headed by Xavier Alameda-Pineda, who will be your supervisor, together with Xiaoyu Lin (PhD student).


Our main requirements are 1) motivation, 2) general knowledge about Machine Learning and Mathematics, and 3) knowledge in Python programming. Knowledge in Riemannian geometry or differential geometry in general is a plus but it is NOT mandatory.


The internship should start in the second half of 2023. It has a duration of 5 to 6 months. There will be a compensation of 500 – 600 Euro per month. Additionally, you will receive subsidized lunch meals (one lunch costs 2 – 4 Euro). You will have a dedicated working space at Inria with a workstation that has a GPU. Moreover, you will have access to one CPU and two GPU clusters to run experiments.


Please send an e-mail to including a paragraph about your motivation, your CV, and a recent transcript of your grades.


[1] Fisher-Ráo metric in wikipedia:
[2] Girin, Laurent, et al. “Dynamical variational autoencoders: A comprehensive review.” Foundations and Trends in Machine Learning, 2021.
[3] Statistical manifolds in wikipedia:

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