Publications

2025

1. Injectivity of ReLU networks: perspectives from statistical physics

   Antoine Maillard, Afonso S Bandeira, David Belius, Ivan Dokmanić, and Shuta Nakajima

   Applied and Computational Harmonic Analysis, 2025

   arXiv Bib PDF

   @article{maillard2025injectivity,
     title = {Injectivity of ReLU networks: perspectives from statistical physics},
     author = {Maillard, Antoine and Bandeira, Afonso S and Belius, David and Dokmani{\'c}, Ivan and Nakajima, Shuta},
     journal = {Applied and Computational Harmonic Analysis},
     volume = {76},
     pages = {101736},
     year = {2025},
     publisher = {Elsevier},
   }

2024

1. Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokens

   Vittorio Erba, Emanuele Troiani, Luca Biggio, Antoine Maillard, and Lenka Zdeborová

   arXiv preprint arXiv:2410.18858, 2024

   arXiv Bib PDF

   @article{erba2024bilinear,
     title = {Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokens},
     author = {Erba, Vittorio and Troiani, Emanuele and Biggio, Luca and Maillard, Antoine and Zdeborov{\'a}, Lenka},
     journal = {arXiv preprint arXiv:2410.18858},
     year = {2024},
   }

2. Average-case matrix discrepancy: satisfiability bounds

   Antoine Maillard

   arXiv preprint arXiv:2410.17887, 2024

   arXiv Bib PDF

   @article{maillard2024average,
     title = {Average-case matrix discrepancy: satisfiability bounds},
     author = {Maillard, Antoine},
     journal = {arXiv preprint arXiv:2410.17887},
     year = {2024},
   }

3. Bayes-optimal learning of an extensive-width neural network from quadratically many samples

   Antoine Maillard, Emanuele Troiani, Simon Martin, Florent Krzakala, and Lenka Zdeborová

   arXiv preprint arXiv:2408.03733, 2024

   arXiv Bib PDF

   @article{maillard2024bayes,
     title = {Bayes-optimal learning of an extensive-width neural network from quadratically many samples},
     author = {Maillard, Antoine and Troiani, Emanuele and Martin, Simon and Krzakala, Florent and Zdeborov{\'a}, Lenka},
     journal = {arXiv preprint arXiv:2408.03733},
     year = {2024},
   }

4. Fitting an ellipsoid to random points: predictions using the replica method

   Antoine Maillard, and Dmitriy Kunisky

   IEEE Transactions on Information Theory, 2024

   DOI arXiv Bib PDF

   @article{maillard2024fitting,
     title = {Fitting an ellipsoid to random points: predictions using the replica method},
     author = {Maillard, Antoine and Kunisky, Dmitriy},
     journal = {IEEE Transactions on Information Theory},
     year = {2024},
     publisher = {IEEE},
     doi = {10.1109/TIT.2024.3415654}
   }

5. Fitting an ellipsoid to a quadratic number of random points

   Afonso S Bandeira, Antoine Maillard, Shahar Mendelson, and Elliot Paquette

   Latin American Journal of Probability and Mathematical Statistics, 2024

   DOI arXiv Bib PDF

   @article{bandeira2024fitting,
     title = {Fitting an ellipsoid to a quadratic number of random points},
     volume = {21},
     issn = {1980-0436},
     number = {2},
     journal = {Latin American Journal of Probability and Mathematical Statistics},
     publisher = {Institute for Applied and Pure Mathematics (IMPA)},
     author = {Bandeira, Afonso S and Maillard, Antoine and Mendelson, Shahar and Paquette, Elliot},
     year = {2024},
     pages = {1835},
     doi = {10.30757/ALEA.v21-69}
   }

2023

1. Exact threshold for approximate ellipsoid fitting of random points

   Afonso S Bandeira, and Antoine Maillard

   arXiv preprint arXiv:2310.05787, 2023

   arXiv Bib PDF

   @article{maillard2023exact,
     title = {Exact threshold for approximate ellipsoid fitting of random points},
     author = {Bandeira, Afonso S and Maillard, Antoine},
     journal = {arXiv preprint arXiv:2310.05787},
     year = {2023},
   }

2. On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions

   Afonso S Bandeira, Antoine Maillard, Richard Nickl, and Sven Wang

   Philosophical Transactions of the Royal Society A, 2023

   DOI arXiv Bib PDF

   @article{bandeira2023free,
     title = {On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions},
     author = {Bandeira, Afonso S and Maillard, Antoine and Nickl, Richard and Wang, Sven},
     journal = {Philosophical Transactions of the Royal Society A},
     volume = {381},
     number = {2247},
     pages = {20220150},
     year = {2023},
     publisher = {The Royal Society},
     doi = {10.1098/rsta.2022.0150}
   }

3. Phase retrieval: From computational imaging to machine learning: A tutorial

   Jonathan Dong, Lorenzo Valzania, Antoine Maillard, Thanh-an Pham, Sylvain Gigan, and Michael Unser

   IEEE Signal Processing Magazine, 2023

   DOI arXiv Bib PDF

   @article{dong2023phase,
     title = {Phase retrieval: From computational imaging to machine learning: A tutorial},
     author = {Dong, Jonathan and Valzania, Lorenzo and Maillard, Antoine and Pham, Thanh-an and Gigan, Sylvain and Unser, Michael},
     journal = {IEEE Signal Processing Magazine},
     volume = {40},
     number = {1},
     pages = {45--57},
     year = {2023},
     publisher = {IEEE},
     doi = {10.1109/MSP.2022.3219240}
   }

2022

1. A remark on Kashin’s discrepancy argument and partial coloring in the Komlós conjecture

   Afonso S Bandeira, Antoine Maillard, and Nikita Zhivotovskiy

   Portugaliae Mathematica, 2022

   DOI arXiv Bib PDF

   @article{bandeira2022remark,
     title = {A remark on Kashin’s discrepancy argument and partial coloring in the Koml{\'o}s conjecture},
     author = {Bandeira, Afonso S and Maillard, Antoine and Zhivotovskiy, Nikita},
     journal = {Portugaliae Mathematica},
     volume = {79},
     number = {3},
     pages = {311--316},
     year = {2022},
     doi = {10.4171/PM/2085}
   }

2. Optimal denoising of rotationally invariant rectangular matrices

   Emanuele Troiani, Vittorio Erba, Florent Krzakala, Antoine Maillard, and Lenka Zdeborová

   In Mathematical and Scientific Machine Learning, 2022

   arXiv Bib PDF

   @inproceedings{troiani2022optimal,
     title = {Optimal denoising of rotationally invariant rectangular matrices},
     author = {Troiani, Emanuele and Erba, Vittorio and Krzakala, Florent and Maillard, Antoine and Zdeborov{\'a}, Lenka},
     booktitle = {Mathematical and Scientific Machine Learning},
     pages = {97--112},
     year = {2022},
     organization = {PMLR},
   }

3. Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising

   Antoine Maillard, Florent Krzakala, Marc Mézard, and Lenka Zdeborová

   Journal of Statistical Mechanics: Theory and Experiment, 2022

   DOI arXiv Bib PDF

   @article{maillard2022perturbative,
     title = {Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising},
     author = {Maillard, Antoine and Krzakala, Florent and M{\'e}zard, Marc and Zdeborov{\'a}, Lenka},
     journal = {Journal of Statistical Mechanics: Theory and Experiment},
     volume = {2022},
     number = {8},
     pages = {083301},
     year = {2022},
     publisher = {IOP Publishing},
     doi = {10.1088/1742-5468/ac7e4c}
   }

4. Construction of optimal spectral methods in phase retrieval

   Antoine Maillard, Florent Krzakala , Yue M Lu, and Lenka Zdeborová

   In Mathematical and Scientific Machine Learning, 2022

   arXiv Bib PDF

   @inproceedings{maillard2022construction,
     title = {Construction of optimal spectral methods in phase retrieval},
     author = {Maillard, Antoine and Krzakala, Florent and Lu, Yue M and Zdeborov{\'a}, Lenka},
     booktitle = {Mathematical and Scientific Machine Learning},
     pages = {693--720},
     year = {2022},
     organization = {PMLR},
   }

2021

1. Fundamental limits of high-dimensional estimation: a stroll between statistical physics, probability and random matrix theory

   Antoine Maillard

   Université Paris sciences et lettres, 2021

   Bib HTML PDF

   @phdthesis{maillard2021fundamental,
     title = {Fundamental limits of high-dimensional estimation: a stroll between statistical physics, probability and random matrix theory},
     author = {Maillard, Antoine},
     year = {2021},
     school = {Universit{\'e} Paris sciences et lettres},
   }

2. Large deviations of extreme eigenvalues of generalized sample covariance matrices

   Antoine Maillard

   Europhysics Letters, 2021

   DOI arXiv Bib PDF

   @article{maillard2021large,
     title = {Large deviations of extreme eigenvalues of generalized sample covariance matrices},
     author = {Maillard, Antoine},
     journal = {Europhysics Letters},
     volume = {133},
     number = {2},
     pages = {20005},
     year = {2021},
     publisher = {IOP Publishing},
     doi = {10.1209/0295-5075/133/20005}
   }

2020

1. Phase retrieval in high dimensions: Statistical and computational phase transitions

   Antoine Maillard, Bruno Loureiro, Florent Krzakala, and Lenka Zdeborová

   Advances in Neural Information Processing Systems, 2020

   arXiv Bib PDF

   @article{maillard2020phase,
     title = {Phase retrieval in high dimensions: Statistical and computational phase transitions},
     author = {Maillard, Antoine and Loureiro, Bruno and Krzakala, Florent and Zdeborov{\'a}, Lenka},
     journal = {Advances in Neural Information Processing Systems},
     volume = {33},
     pages = {11071--11082},
     year = {2020},
   }

2. Landscape complexity for the empirical risk of generalized linear models

   Antoine Maillard, Gérard Ben Arous, and Giulio Biroli

   In Mathematical and Scientific Machine Learning, 2020

   arXiv Bib PDF

   @inproceedings{maillard2020landscape,
     title = {Landscape complexity for the empirical risk of generalized linear models},
     author = {Maillard, Antoine and Ben Arous, G{\'e}rard and Biroli, Giulio},
     booktitle = {Mathematical and Scientific Machine Learning},
     pages = {287--327},
     year = {2020},
     organization = {PMLR},
   }

3. The Spiked Matrix Model With Generative Priors

   Benjamin Aubin, Bruno Loureiro, Antoine Maillard, Florent Krzakala, and Lenka Zdeborová

   IEEE Transactions on Information Theory, 2020

   DOI arXiv Bib PDF

   @article{aubin2020spiked,
     title = {The Spiked Matrix Model With Generative Priors},
     author = {Aubin, Benjamin and Loureiro, Bruno and Maillard, Antoine and Krzakala, Florent and Zdeborov{\'a}, Lenka},
     journal = {IEEE Transactions on Information Theory},
     volume = {67},
     number = {2},
     pages = {1156--1181},
     year = {2020},
     publisher = {IEEE},
     doi = {10.1109/TIT.2020.3033985}
   }

2019

1. High-temperature expansions and message passing algorithms

   Antoine Maillard, Laura Foini, Alejandro Lage Castellanos, Florent Krzakala, Marc Mézard, and Lenka Zdeborová

   Journal of Statistical Mechanics: Theory and Experiment, 2019

   DOI arXiv Bib PDF

   @article{maillard2019high,
     title = {High-temperature expansions and message passing algorithms},
     author = {Maillard, Antoine and Foini, Laura and Castellanos, Alejandro Lage and Krzakala, Florent and M{\'e}zard, Marc and Zdeborov{\'a}, Lenka},
     journal = {Journal of Statistical Mechanics: Theory and Experiment},
     volume = {2019},
     number = {11},
     pages = {113301},
     year = {2019},
     publisher = {IOP Publishing},
     doi = {10.1088/1742-5468/ab4bbb}
   }

2. The spiked matrix model with generative priors

   Benjamin Aubin, Bruno Loureiro, Antoine Maillard, Florent Krzakala, and Lenka Zdeborová

   In Proceedings of the 33rd International Conference on Neural Information Processing Systems, 2019

   The corresponding journal publication is available above
3. The committee machine: computational to statistical gaps in learning a two-layers neural network

   Benjamin Aubin, Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris, and Lenka Zdeborová

   Journal of Statistical Mechanics: Theory and Experiment, 2019

   DOI arXiv Bib PDF

   @article{aubin2019committee,
     title = {The committee machine: computational to statistical gaps in learning a two-layers neural network},
     author = {Aubin, Benjamin and Maillard, Antoine and Barbier, Jean and Krzakala, Florent and Macris, Nicolas and Zdeborov{\'a}, Lenka},
     journal = {Journal of Statistical Mechanics: Theory and Experiment},
     volume = {2019},
     number = {12},
     pages = {124023},
     year = {2019},
     publisher = {IOP Publishing},
     doi = {10.1088/1742-5468/ab43d2}
   }

4. Quantum Monte Carlo algorithm for out-of-equilibrium Green’s functions at long times

   Corentin Bertrand, Olivier Parcollet, Antoine Maillard, and Xavier Waintal

   Physical Review B, 2019

   DOI arXiv Bib PDF

   @article{bertrand2019quantum,
     title = {Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times},
     author = {Bertrand, Corentin and Parcollet, Olivier and Maillard, Antoine and Waintal, Xavier},
     journal = {Physical Review B},
     volume = {100},
     number = {12},
     pages = {125129},
     year = {2019},
     publisher = {APS},
     doi = {10.1103/PhysRevB.100.125129}
   }

2018

1. The committee machine: Computational to statistical gaps in learning a two-layers neural network

   Benjamin Aubin, Antoine Maillard, Florent Krzakala, Nicolas Macris, Lenka Zdeborová, and  others

   Advances in Neural Information Processing Systems, 2018

   The corresponding journal publication is available above
2. The mutual information in random linear estimation beyond iid matrices

   Jean Barbier, Nicolas Macris, Antoine Maillard, and Florent Krzakala

   In 2018 IEEE International Symposium on Information Theory (ISIT), 2018

   DOI arXiv Bib PDF

   @inproceedings{barbier2018mutual,
     title = {The mutual information in random linear estimation beyond iid matrices},
     author = {Barbier, Jean and Macris, Nicolas and Maillard, Antoine and Krzakala, Florent},
     booktitle = {2018 IEEE International Symposium on Information Theory (ISIT)},
     pages = {1390--1394},
     year = {2018},
     organization = {IEEE},
     doi = {10.1109/ISIT.2018.8437522}
   }

3. Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

   M Schenk, X Buffat, K Li, and Antoine Maillard

   Physical Review Accelerators and Beams, 2018

   DOI Bib PDF

   @article{schenk2018vlasov,
     title = {Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities},
     author = {Schenk, M and Buffat, X and Li, K and Maillard, Antoine},
     journal = {Physical Review Accelerators and Beams},
     volume = {21},
     number = {8},
     pages = {084402},
     year = {2018},
     publisher = {APS},
     doi = {10.1103/PhysRevAccelBeams.21.084402}
   }

2015

1. Islands of stability and recurrence times in AdS

   Stephen R Green, Antoine Maillard, Luis Lehner, and Steven L Liebling

   Physical review D, 2015

   DOI arXiv Bib PDF

   @article{green2015islands,
     title = {Islands of stability and recurrence times in AdS},
     author = {Green, Stephen R and Maillard, Antoine and Lehner, Luis and Liebling, Steven L},
     journal = {Physical review D},
     volume = {92},
     number = {8},
     pages = {084001},
     year = {2015},
     publisher = {APS},
     doi = {10.1103/PhysRevD.92.084001}
   }