I am a Research Scientist (tenured Associate Professor) at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, in the Quantitative Life Sciences and Mathematics sections, and a member of the Theoretical and Scientific Data Science group at SISSA. Before moving to Trieste I did my PhD at ENS Paris and a postdoc at EPFL. I serve on the editorial boards of Information and Inference: a Journal of the IMA, Transactions on Machine Learning Research and Advances in Theoretical and Mathematical Physics.
The ICTP is a UNESCO institute whose mission is not only the research excellence, but also teaching and scientific capacity building for the developing world: ICTP really is a special place to do top research and make a positive impact, worldwide.
My group is funded by the ERC Starting Grant CHORAL (Computational Hardness Of RepresentAtion Learning). We study the fundamental and algorithmic limits of high-dimensional inference and of learning in neural networks, using the statistical physics of disordered systems, random matrix theory and information theory. We look for sharp answers: how much data is needed, which phase transitions occur, and how close efficient algorithms come to optimal performance. More recently we also study how the training dynamics of neural networks discovers features, where neural scaling laws come from, and questions of interpretability: how to read what a trained network has learned.
News
- Oct 2026The AI year at ICTP starts with a colloquium series running until October 2027. It continues in 2027 with the eighth Youth in High Dimensions and a School on AI for Scientific Discovery. I coordinate it with colleagues at ICTP.
- Sep 2026Our paper on sharp feature-learning transitions and Bayes-optimal scaling laws (arXiv:2605.10395) is accepted at NeurIPS 2026.
- Sep 2026Third edition of ROC(K)IN’ AI, the Roccella conference on inference and AI, in Roccella Jonica.
- Jul 2026Our work on optimal learning of deep networks near interpolation is out in Physical Review X. Coverage by ICTP and ANSA.
- Jul 2026Seventh edition of Youth in High Dimensions at ICTP.
Selected papers
-
Mesoscopic learning dynamics of extensive-width neural networks
@misc{zhou2026mesoscopic, author = {Zhou, Shu and Barbier, Jean and Goldt, Sebastian}, title = {Mesoscopic learning dynamics of extensive-width neural networks}, year = {2026}, eprint = {2610.23779}, archivePrefix = {arXiv}, primaryClass = {stat.ML} } -
Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks
@inproceedings{nguyen2026sharp, author = {Nguyen, Minh-Toan and Barbier, Jean}, title = {Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks}, booktitle = {Advances in Neural Information Processing Systems}, year = {2026}, eprint = {2605.10395}, archivePrefix = {arXiv} } -
@article{barbier2026statistical, author = {Barbier, Jean and Camilli, Francesco and Nguyen, Minh-Toan and Pastore, Mauro and Skerk, Rudy}, title = {Statistical Physics of Deep Learning: Optimal Learning of a Multilayer Perceptron near Interpolation}, journal = {Physical Review X}, volume = {16}, number = {3}, pages = {031014}, year = {2026}, doi = {10.1103/56sb-pdh6}, eprint = {2510.24616}, archivePrefix = {arXiv} } -
Phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariance
@article{barbier2025phase, author = {Barbier, Jean and Camilli, Francesco and Ko, Justin and Okajima, Koki}, title = {Phase Diagram of Extensive-Rank Symmetric Matrix Denoising beyond Rotational Invariance}, journal = {Physical Review X}, volume = {15}, number = {2}, pages = {021085}, year = {2025}, doi = {10.1103/PhysRevX.15.021085}, eprint = {2411.01974}, archivePrefix = {arXiv} } -
Fundamental limits in structured principal component analysis and how to reach them
@article{barbier2023fundamental, author = {Barbier, Jean and Camilli, Francesco and Mondelli, Marco and Sáenz, Manuel}, title = {Fundamental limits in structured principal component analysis and how to reach them}, journal = {Proceedings of the National Academy of Sciences}, volume = {120}, number = {30}, pages = {e2302028120}, year = {2023}, doi = {10.1073/pnas.2302028120} } -
Optimal errors and phase transitions in high-dimensional generalized linear models
@article{barbier2019optimal, author = {Barbier, Jean and Krzakala, Florent and Macris, Nicolas and Miolane, Léo and Zdeborová, Lenka}, title = {Optimal errors and phase transitions in high-dimensional generalized linear models}, journal = {Proceedings of the National Academy of Sciences}, volume = {116}, number = {12}, pages = {5451--5460}, year = {2019}, doi = {10.1073/pnas.1802705116}, eprint = {1708.03395}, archivePrefix = {arXiv} }
Trieste
ICTP and SISSA are in Trieste, a city on the Adriatic with a long scientific tradition, often called the city of science for its many research institutes. ICTP was founded in 1964 by Abdus Salam to support science in developing countries, and sits by the sea, below Miramare castle: going for a swim at lunchtime is easy. Trieste is also a crossroads of Italian, Slovenian and Central European cultures, close to the Karst and the Alps for climbing and skiing.