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

PhD Position F/M Distributional perspective of self-supervised learning Download job offer in PDF format Contract type : Fixed-term contract Level of qualifications required : Graduate degree or equivalent Fonction : PhD Position About the research centre or Inria department 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. Context 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. Assignment 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 Main activities 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. Skills background in mathematics (optimization, probability and statistics) and/or electrical engineering (signal/image processing, harmonic analysis). Strong abilities in computer sciences will be appreciated Benefits package • 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 Remuneration 2 300€ per month Apply for this position Share • Facebook • Linkedin • Twitter • Email General Information • Theme/Domain : Optimization, machine learning and statistical methods Statistics (Big data) (BAP E) • Town/city : Rennes • Inria Center : Centre Inria de l'Université de Rennes • Starting date : 2026-10-01 • Duration of contract : 3 years • Deadline to apply : 2026-08-31 Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed. Instruction to apply Please submit your CV, cover letter, and any recommandations online Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment. Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities. Contacts • Inria Team : COMPACT • PhD Supervisor : Vayer Titouan / titouan.vayer@inria.fr The keys to success The successful candidate should demonstrate scientific curiosity, autonomy, and a strong interest in research at the interface of mathematics and machine learning. We are looking for a motivated person who enjoys tackling theoretical questions while developing methods with meaningful real-world applications. The ability to work independently, take initiative, and engage with open-ended research problems will be highly valued. An interest in scientific collaboration, and intellectual exchanges will also be an important asset for successfully carrying out this PhD project. About Inria Inria, the French national institute for research in digital science and technology, supports the French government in national research and innovation strategies in the digital field, acting as Digital Programs Agency. Inria leads over 300 research and innovation projects with its 3,500 scientists, engineers, and support staff, in partnership with universities and the digital ecosystem (businesses, entrepreneurs, and public stakeholders). Together, we explore strategic fields such as artificial intelligence, cybersecurity, quantum computing, cloud technologies, digital transformation in healthcare, digital twins, and digital technologies for defence. We develop practical solutions such as software, tech startups, partnerships with national companies, and cutting-edge training programmes. Our goal is to drive scientific, technological, and industrial excellence to ensure France’s digital sovereignty.