Artificial intelligence holds a central and plurithematic position within Laboratoire J. A. Dieudonné recognized internationally for theoretical and applied research.
The laboratory conducts both theoretical and applied research in AI, in collaboration with 3IA Côte d’Azur, with several chairholders, and Inria. Its members regularly publish in leading international conferences such as NeurIPS, ICML, and ICLR, as well as in specialized venues in optimization, probability, statistics, scientific computing and various AI applications.
Research activities cover several key areas:
Mathematical structures and AI:
Ongoing work investigates the links between AI and mathematical logic, proof systems, and game theory. Topics include formal reasoning with the help of machine learning and the study of learning dynamics through mean field game theory. These activities are part of major European projects such as the ERC Synergy project MALINCA and the ERC Advanced project ELISA.
Applications with other scientific fields
The laboratory develops AI methods for environmental sciences, neuroscience, archaeology, hydrology, and historical research. These efforts include participation in national programs such as the PEPR IRIMA initiative.
Foundations and algorithms for machine learning
Research focuses on optimization methods for machine learning, including bilevel optimization, graph learning, and automatic differentiation. Some projects explore the use of mathematical tools such as free probability to better understand learning dynamics. This includes contributions to research projects such as the ANR project MAD.
Model learning for simulation
Research includes developing hydrological simulations and projections for shallow aquifers under climate scenarios, employing hybrid modeling tools that combine physics-based methods and deep learning. The laboratory is also a partner of the PEPR PDE-AI project.
Robustness, fairness, and uncertainty
Several lines of research address statistical robustness, algorithmic fairness, and the treatment of uncertainty in machine learning. This includes works on distributionally robust optimization, latent variable models, and model-based clustering in probabilistic frameworks.