Rémy Degenne

Tenured researcher in the Scool team at the Inria centre at the University of Lille.
Sequential machine learning and formal mathematics in Lean.

About me

I am a tenured researcher in the Scool team at the Inria centre at the University of Lille. I work on sequential machine learning, mostly bandit theory, and I am interested in all forms of online and reinforcement learning as well as statistics and optimization. I am also passionate about formal mathematics and AI for maths and I want to transform machine learning theory by ensuring it can be written and verified in proof assistants like Lean.

Rémy Degenne

I am a maintainer of the mathematical library Mathlib for the Lean theorem prover and of the Lean Machine Learning project.

If you are looking for something to contribute to Mathlib related to probability, here is a list of projects.

In 2020 I was a post-doctoral researcher at Inria Paris, in the SIERRA Team. In 2018-2019 I spent a year in the Machine Learning group at CWI Amsterdam, working with Wouter M. Koolen. From 2015 to 2019 I was a PhD student under the supervision of Vianney Perchet at the CMLA research center of Ecole Normale Supérieure Paris-Saclay and the LPSM lab at Université Paris Cité.

News

[July 2026] I am giving a tutorial at ICML 2026 on Proving Theorems with Lean and Machine Learning, with Wenda Li.

[January 2026] I organized the Lean Together 2026 online conference, the annual meeting for users, developers, and fans of the Lean programming language and theorem prover and its library Mathlib.

[December 2025] I gave talks about probability theory in Lean and the Brownian motion project at ItaLean 2025 (Bologna, Italy, December 9-12), a workshop about bridging formal mathematics and AI.

[October 2025] With Michael Rothgang, I am leading a workshop on Lean for PDEs at the Simons Laufer Mathematical Sciences Institute (SLMath), co-organized by the new Institute for Computer-Aided Reasoning in Mathematics (ICARM).

[July 2025] I am launching the FORMAL Inria exploratory action. Its goal is to formalize bandit and reinforcement learning algorithms and their theory in the Lean theorem prover. A post-doc will join the team in 2026 to work on this project.

[November 2023] I am contributing to the formalization of the polynomial Freiman-Ruzsa conjecture in Lean. This is a project led by Terence Tao, who recently proved this result with W. T. Gowers, Ben Green and Freddie Manners. See this post on Terence Tao's blog for a tour of the project.

Older news can be found on the Older News page.

Publications

Last updated: January 2026. For a perhaps more up-to-date list, see my Google Scholar profile.

Mathlib contributions

I am a contributor and a maintainer of Mathlib, the mathematics library of the Lean theorem prover. Here are some of my contributions, mostly related to probability:
  • A definition of Gaussian distributions in Banach spaces and Fernique's theorem. Coming soon: the Cameron-Martin theorem.
  • The Kullback-Leibler divergence. Coming soon: other information divergences, notably related to the risk of statistical experiments.
  • Sub-Gaussian random variables, moment generating functions and concentration inequalities.
  • Independence and conditional independence.
  • Probability transition kernels and their compositions. Disintegration of kernels and definitions of conditional distributions and posterior distributions. Radon-Nikodym theorem for kernels. See Markov kernels in Mathlib's probability library.
  • Martingales and stopping times: Doob's martingale convergence theorems, optional stopping, optional sampling. See A formalization of Doob's martingale convergence theorems in mathlib, CPP 2023, Kexing Ying, RD.
  • Conditional expectations.
  • Lp spaces, the fact that they are Banach spaces and that L2 is a Hilbert space.

Teaching

Current courses Past courses
  • ENS Paris-Saclay (Master MVA) - Sequential learning - 2021, 2022, 2023
  • Centrale Lille - Sequential learning - 2022, 2023, 2024
  • Université de Lille (L3 MIASHS) - Science des données 3 - 2022, 2023
  • Université Paris Diderot - Practical sessions for various courses - 2016 to 2018. Courses: Analyse et algèbre 2 (L1 Physique), Raisonnement mathématique (L1 Informatique, L1 MIASHS), Probabilités (L2 Math-Info), Equation différentielles pour la biologie, Probabilités (L2 Math).

Collaborators

PhD students

Post-docs

Master students

Check out my page on useful resources for PhD students.