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

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).
Feb 27, 2026	Next week (March 2nd - March 6th), I am co-organizing with Bruno Loureiro a PSL Week on Statistical Physics and Machine Learning. For a more mathematically complete treatment of some of the material I wil discuss, please see my lecture notes for the course I am currently teaching at Université Paris-Saclay, as well as some lecture notes for a course I taught at ETH Zürich in 2024.
Feb 27, 2026	Two new preprints out! Optimal scaling laws in hierarchical multi-index models, a joint work with Leonardo Defilippis (ENS), Florent Krzakala (EPFL), and Bruno Loureiro (ENS). Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval: we numerically explore the optimization landscape of generalized linear models (in particular phase retrieval) using the Kac-Rice formula. Joint work with Tony Bonnaire (U. Paris-Saclay) and Giulio Biroli (ENS).
Jan 26, 2026	I started today a lecture in the M2 Mathématiques de l’Aléatoire on computational and statistical phase transitions. The class runs until March 23rd 2026, please look at the dedicated webpage for details and lecture notes. The notes will cover in particular the material of the mini-course on spin glasses and statistical learning I presented last June in ASCAI meeting workshop organized at Institut de Mathématiques d’Orsay.