Bruno Loureiro

I am a CNRS researcher based at the Centre for Data Science at the École Normale Supérieure in Paris working on the crossroads between machine learning and statistical mechanics. I am also a Professeur Attaché at the Université Paris Sciences et Lettres (PSL) where I teach at the undergrad and graduate programs of the affiliated universities.

If you are interested in my research, you can find a complete list of my publications here.

news

Feb 28, 2025	I am slowly writing a set of lecture notes for a course on the “Mathematics of Deep Learning” I teach at the MASH/IASD M2 programs, with some of my favourite topics. It is still a draft, but you can check them here!
Feb 04, 2025	In our recent pre-print on “Optimal Spectral Transitions in High-Dimensional Multi-Index Models” we propose a spectral method and show that it achieves the optimal weak-recovery threshold for multi-index models among first order methods, a result proven in our previous work.
Jan 22, 2025	Our papers: A Random Matrix Theory Perspective on the Spectrum of Learned Features and Asymptotic Generalization Capabilities (Oral) Fundamental computational limits of weak learnability in high-dimensional multi-index models A High Dimensional Statistical Model for Adversarial Training: Geometry and Trade-Offs were accepted at AISTATS 2025. See you in Thailand in May!
Nov 03, 2024	Our paper How two-layer neural networks learn, one (giant) step at a time was accepted for publication at JMLR! It will also feature as a poster at ICLR in the JMLR track.
Nov 01, 2024	In our recent pre-print, we provide a rigorous random matrix theory analysis of how feature learning impacts generalisation in two-layer neural networks after a single aggressive gradient step.