Missions

In recent years, we have witnessed major breakthroughs in the field of artificial intelligence (AI). Computers are now capable of understanding human language, transcribing text, recognizing patterns, and even driving vehicles. At the core of these advances lies machine learning — a field concerned with how machines can learn from data.

Despite these impressive technological achievements, our theoretical understanding of modern machine learning models remains limited. Classical statistical analysis, developed in the early 20th century, struggles to address the modern regime in which the number of model parameters is often of the same order as the amount of available data — a phenomenon commonly referred to as the curse of dimensionality (CoD). Understanding why algorithms used in everyday practice work so well despite the CoD is therefore a major theoretical challenge, and key to enabling the broader adoption of these methods in sensitive domains such as medicine and healthcare.

This project focuses on a central aspect of this issue: the role played by data structure in the success of machine learning algorithms.

The postdoctoral researcher will focus on a specific case of structured data: data with temporal correlations, studied within the framework of simple, mathematically tractable models. To this end, they will employ a combination of classical tools — such as high-dimensional probability and random matrix theory — along with techniques from the statistical physics of disordered systems. The goal of the project is to advance our theoretical understanding of the interplay between feature learning and the learning of underlying structure in machine learning problems.

Activities

Main responsibilities:
Develop a research project on the role of data structure — in particular, data exhibiting temporal correlations (e.g., arising from stochastic processes or time series) — in the context of statistical learning.

Secondary responsibilities:
Lead scientific discussions within the Centre for Data Science (CSD), present project results at national and international conferences, and actively contribute to the scientific and community life of the CSD.

Skills

- PhD in applied mathematics, computer science, or theoretical physics.
- Strong background in probability and statistics, particularly in concepts from non-equilibrium statistical physics and stochastic processes.
- Proficiency in Python and machine learning frameworks (NumPy, PyTorch, SciPy, etc.).
- Comfortable with writing scientific papers.
- Good command of spoken and written English.
- Ability to work in a team within a multidisciplinary environment.

Work Context

The postdoctoral researcher will work under the supervision of Bruno Loureiro and will be part of the DATA team in the Computer Science Department at École Normale Supérieure. They will be based at the Centre for Data Science (CSD), a multidisciplinary initiative bringing together researchers from the Departments of Computer Science, Mathematics, Cognitive Science, and Physics at ENS.