PhD Position F/M Distributional perspective of self-supervised learning

The Inria Rennes - Bretagne Atlantique Centre is one of Inria's eight centres and has more than thirty research teams. The Inria Center is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative PMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute, etc.

With the joint progress in collecting increasingly complex and massive datasets and the rapid rise of
large foundation models, it has become crucial to design methods that can adapt to multiple tasks and
data modalities. This raises a fundamental challenge: how can we learn versatile and informative
data representations that can be effectively reused across diverse downstream applications?
To address this issue, self-supervised learning (SSL) has emerged as a key paradigm [Gui+24].
SSL involves training models—typically neural networks—on unlabeled data by solving pretext tasks, such
as denoising corrupted inputs or distinguishing between perturbed and clean samples. These approaches
have achieved remarkable performance, in some cases even surpassing fully supervised methods [Li+25].
However, the mechanisms underlying such success remain only partially understood. In particular, why
do SSL representations generalize so well, and what are the key principles driving this behavior?
A first step toward understanding SSL’s performance lies in examining its connections with di-
mensionality reduction and optimal transport (OT). SSL indeed exhibits strong conceptual and
mathematical ties with classical dimensionality reduction techniques such as PCA [AW10], t-SNE [VH08],
and UMAP [MHM18], especially in the use of related loss functions and optimization strategies [Dam+23].
On the other hand, dimensionality reduction itself is deeply connected to optimal transport theory—indeed,
it can even be interpreted as a special case of OT.
Recent studies of the supervisors [Van+25] have demonstrated that SSL and OT share several key
principles, suggesting a unifying theoretical framework. OT now plays a central role in a wide range
of modern machine learning applications, from generative modeling and domain adaptation to cellular
dynamics analysis, neural networks, and graph-based models (see [PC+19] for a detailed overview).
Understanding SSL through the lens of OT could thus provide valuable theoretical insights and lead to
more principled and efficient algorithms for representation learning.

Based on these recent connections, the objectives of this thesis are twofold — theoretical and practical.
From a theoretical perspective, the work will build upon the recent research conducted by the supervisors
to understand the theoretical foundations of modern SSL methods through the lens of OT
and to develop new, efficient SSL techniques inspired by these findings. For example: can we
use OT to force interesting distribution in the embedding space ? Can we derive theoretical analysis
suggesting that some SSL framework are more interesting in certain regime ?
The practical component of the thesis will focus on implementing and applying these algorithms to
the analysis of single-cell data, in collaboration with Franck Picard (CNRS, ENS Lyon). Since the
late 2010s, major technological advances in molecular and cellular biology have given rise to single-cell
biology, a field enabling genome-wide analysis of molecular data, such as DNA, RNA, and proteins—at
the resolution of individual cells. Single-cell datasets typically comprise large multivariate distributions,
with thousands to millions of cell and thousands of molecular features. Finally, the thesis will also provide
an opportunity to contribute to the Python library

We are looking for a highly motivated student with a background in mathematics (optimization,
probability and statistics) and/or electrical engineering (signal/image processing, harmonic analysis).
Strong abilities in computer sciences will be appreciated. Experience with Python is also desirable.
The thesis is financed by the ANR JCJC CALME (ANR-25-CE23-4419).
The thesis is expected to start in october 2026 and will be hosted at Inria Rennes, within the
COMPACT research team. The this will be supervised by Titouan Vayer (Inria) Do not hesitate to
contact for more information.

background in mathematics (optimization,
probability and statistics) and/or electrical engineering (signal/image processing, harmonic analysis).
Strong abilities in computer sciences will be appreciated

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

2 300€ per month