Antoine Maillard

Research faculty
Inria Paris

Office B120
48 Rue Barrault
75013 Paris

I am a research faculty (“Chargé de Recherches”) at Inria Paris and DI ENS, hosted in the ARGO team.

My research interests include high-dimensional statistics, probability theory, statistical physics, machine learning, and random matrix theory. You can find concrete examples of some of my recent works in the publications section.

From 2021-2024 I was a Hermann-Weyl Instructor at the FIM (Institute for Mathematical Research) and the department of mathematics at ETH Zürich, mentored by Afonso S. Bandeira. We started there a group blog, with an emphasis on open problems, don’t hesitate to have a look! I defended my PhD in Theoretical Physics in 2021 in Ecole Normale Supérieure de Paris, under the supervision of Florent Krzakala, and the additional guidance of Lenka Zdeborová. I am very glad to have received the 2021 Daniel Guinier Prize of the French Physical Society for it! You can find my PhD thesis here.

I’m always happy to hear from motivated prospective students. If you’re curious about potential opportunities, feel free to look at my recent papers and teaching notes, and to get in touch.
(As of 2026 I apologize if I am unable to reply to all inquiries due to the large number of emails I receive.)

For students currently following one of my courses, please have look at the teaching section.

(Some) recent news

Sep 23, 2026	A new preprint out: Efficient computation of the asymptotics of extensive-rank HCIZ integrals. We introduce an efficient numerical scheme (based on a particle discretization) to solve the boundary-value problem shown by Matytsin (1994) to be the limit of extensive-rank HCIZ integrals. We prove its convergence, and use it to compute these asymptotics for generic densities for the first time. This is a joint work with Jean-Christophe Mourrat (ENS Lyon).
Jul 21, 2026	I recently gave a general-audience talk at Inria Paris entitled ``From freezing water to ChatGPT: the physics of algorithms’’. If you are interested, you can find the slides here (in French).
May 21, 2026	Three new pre-preprints went out recently: Factual recall in linear associative memories: sharp asymptotics and mechanistic insights, a joint work with Alessio Giorlandino and Sebastian Goldt from SISSA where we explore the capacity of linear associative memory models. Memorisation, convergence and generalisation in generative models, another joint work with Sebastian where we analyze how simple generative models transition from memorization to generalization, and uncover a convergence regime where independently-trained generative models converge to the same density, while failing to learn the latent structure in the data. From Diminishing Returns to Entrenchment: A Unifying Theory of Epistasis along Adaptive Walks Revealed by Fisher’s Geometric Model, an unexpected familial collaboration in the realm of theoretical genetics!
Mar 30, 2026	A new preprint out: A Noise Sensitivity Exponent Controls Large Statistical-to-Computational Gaps in Single- and Multi-Index Models. We characterize wide statistical-to-computational gaps for high noise in single-index models and for large separable multi-index models, as a function of a ``noise sensitivity exponent’’, a simple property of the activation function. This is another joint work with Leonardo Defilippis (ENS), Florent Krzakala (EPFL), and Bruno Loureiro (ENS).