Research
My research sits between probability and machine learning. It currently focuses on the theory of generative models — diffusion models and flow matching, how their samplers propagate errors, and what happens to them in the small-noise regime. It grew out of a PhD on Langevin-based sampling algorithms and their non-asymptotic analysis, followed by work on uncertainty estimation in deep networks. In parallel, I work on human–AI collaboration in mathematical research: how AI agents can take part in a search for a proof while what they establish stays trustworthy and checkable.
Longer, informal companions to some of these results are on the blog. An up-to-date list is on Google Scholar.
Human–AI Mathematics
Human–AI Mathematics
N. Brosse, J. Li, Y. Lyu · 2026 · supported by Project Numina
An open framework for mathematical research done by humans and AI agents together. Its first tool, conjecture search, organizes many agents over many sessions around one statement, and moves a claim to proved or refuted only through an independent review or a named person’s acceptance. Template · blog post
The KLS theorem and its methods
N. Brosse and the Numina Collaboration · 2026
The first case study: a manuscript that surveys the methods behind the Kannan–Lovász–Simonovits conjecture, reconstructs and compares its three 2026 proofs, and develops alternative mechanisms. Its proofs are checked by independent AI reviewer agents, not yet by human referees. Manuscript · repository
Preprints
Universal local error and realized amplification for the first-order EDM predictor
N. Brosse, A. S. Dalalyan · 2026
arXiv:2610.10190 · code
Boundary-layer asymptotics for Gaussian-smoothed singular measures
N. Brosse, A. S. Dalalyan · 2026
arXiv:2607.04514 · blog post
On last-layer algorithms for classification: decoupling representation from uncertainty estimation
N. Brosse, C. Riquelme, A. Martin, S. Gelly, É. Moulines · 2020
arXiv:2001.08049 · code
Publications
Diffusion approximations and control variates for MCMC
N. Brosse, A. Durmus, S. Meyn, É. Moulines, S. Samsonov
Computational Mathematics and Mathematical Physics, 64, 693–738, 2024 · doi · arXiv:1808.01665 · code
The tamed unadjusted Langevin algorithm
N. Brosse, A. Durmus, É. Moulines, S. Sabanis
Stochastic Processes and their Applications, 2019 · doi · arXiv:1710.05559 · code
The promises and pitfalls of stochastic gradient Langevin dynamics
N. Brosse, A. Durmus, É. Moulines
Advances in Neural Information Processing Systems (NeurIPS), 2018 · paper · arXiv:1811.10072 · code
Normalizing constants of log-concave densities
N. Brosse, A. Durmus, É. Moulines
Electronic Journal of Statistics, 2018 · doi · arXiv:1707.00460 · code
Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo
N. Brosse, A. Durmus, É. Moulines, M. Pereyra
Conference on Learning Theory (COLT), PMLR 65, 2017 · paper · arXiv:1705.08964
Book chapter
Using artificial intelligence for de novo drug design and retrosynthesis
R. Arora, N. Brosse, C. Descamps, N. Devaux, N. Do Huu, P. Gendreau, Y. Gaston-Mathé, M. Parrot, Q. Perron, H. Tajmouati
In Computational Drug Discovery, Wiley, 2024, 275–298 · doi
PhD thesis
Autour de l’algorithme du Langevin : extensions et applications
(Around the Langevin Monte Carlo algorithm: extensions and applications)
2019 · doi
Funding
My postdoctoral work at CREST with Arnak Dalalyan is funded by the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme (grant agreement No. 101201229).