Nicolas Brosse

I work in AI R&D, between research and production. After a PhD in statistics on Langevin sampling, I spent six years building deep learning systems in industry — signal processing at Thales, drug discovery at Iktos, foundation models for biology at MBZUAI and GenBio AI — and LLM systems as a freelancer. I am now a postdoctoral researcher at CREST with Arnak Dalalyan, working on two things: the mathematics of generative models, and human–AI collaboration in mathematical research, through Human–AI Mathematics, an open framework in which AI agents search for and cross-review proofs that mathematicians can check. What I care about is taking an idea from paper to working system, and measuring whether it actually works.

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Latest posts

AI agents on the KLS conjecture: a search mathematicians can trust and join

AI for mathematics

agents

AI agents can now produce more mathematics than anyone can check. Human–AI Mathematics is an open framework with two aims: a structure that keeps an agent-driven search traceable, where a claim moves to proved only through an independent review of its exact text, and a manuscript that mathematicians can read, check and contribute to. Its first case study is the KLS conjecture, which three teams proved while the search was running.

Oct 9, 2026

Mills ratios on manifolds: what Gaussian smoothing sees near a boundary

asymptotics

diffusion models

Convolving a singular measure with a Gaussian of width σ produces a smooth density whose logarithmic derivatives can blow up as σ → 0. Zooming in at scale σ replaces the support by its inward tangent cone: its Gaussian mass gives the leading density, and derivatives of its logarithm give the leading singular fields — a manifold-valued inverse Mills ratio.

Aug 26, 2026

Closed-form flow matching: posterior concentration and softmax collapse

deep learning

flow matching

The closed-form velocity field of empirical flow matching is a softmax over training examples. Reading that softmax as a Bayesian posterior turns its collapse into a decoding problem, with an information-theoretic threshold that can be evaluated on CIFAR-10.

Jul 20, 2026

Flow matching as posterior averaging

deep learning

flow matching

A velocity-based introduction to flow matching with Gaussian probability paths: the marginal velocity field is a posterior average of conditional targets, and the gap between the conditional and marginal losses is an irreducible posterior-variance term that can be computed in closed form.

May 12, 2026

Analyzing Raman spectra with machine learning

machine learning

chemistry

From inelastic scattering to a calibrated regression model: the physics behind a Raman spectrum, the preprocessing pipeline that makes real spectra usable, and a PLS regression baseline for predicting analyte concentrations.

Jan 18, 2026

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