Connectionists: [Master Internship] Deep Statistical Manifolds at Inria Grenoble, France

[Chris Reinke]

Deep Statistical Manifolds
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#project>Project

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].
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#task>Task

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.
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#team>Team

You will join the RobotLearn team [4], an international team of
researchers, students, and engineers at Inria Grenoble [5]. 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 [6], who will be your supervisor,
together with Xiaoyu Lin (PhD student) [7].
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#requirements>Requirements

Our main requirements are 1) motivation, 2) general knowledge of Machine
Learning and Mathematics, and 3) knowledge of Python programming. Knowledge
of Riemannian geometry or differential geometry in general is a plus but it
is NOT mandatory.
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#conditions>Conditions

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.
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#application>Application

Please send an e-mail to xavier.alameda-pineda at inria.fr including a
paragraph about your motivation, your CV, and a recent transcript of your
grades.
<https://notes.inria.fr/t0bx4VaNSHiyMPPa9P2OZw#references>References

[1] Fisher-Ráo metric in Wikipedia:
https://en.wikipedia.org/wiki/Fisher_information_metric
[2] Girin, Laurent, et al. “Dynamical variational autoencoders: A
comprehensive review.” Foundations and Trends in Machine Learning, 2021.
[3] Statistical manifolds in Wikipedia:
https://en.wikipedia.org/wiki/Statistical_manifold
[4] https://team.inria.fr/robotlearn/
[5] https://www.inria.fr/fr/centre-inria-grenoble-rhone-alpes
[6] http://xavirema.eu/
[7] https://team.inria.fr/robotlearn/team-members/xiaoyu-lin/
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