papers

  1. Homogenized Transformers
    with Hugo Koubbi and Philippe Rigollet
    preprint
    2026

  2. Constructive conditional normalizing flows
    with Domènec Ruiz-Balet
    preprint
    2026

  3. Perceptrons and Localization of Attention’s Mean-Field Landscape
    with Antonio Alvarez-Lopez and Domènec Ruiz-Balet
    preprint
    2026

  4. Attention's forward pass and Frank-Wolfe
    with Albert Alcalde and Domènec Ruiz-Balet
    preprint
    2025
    github

  5. Constructive approximate transport maps with normalizing flows
    with Antonio Alvarez-Lopez and Domènec Ruiz-Balet
    Applied Mathematics and Optimization
    2025

  6. On the number of modes of Gaussian kernel density estimators
    with Philippe Rigollet and Yihang Sun
    Bernoulli
    2026
    github

  7. Measure-to-measure interpolation using Transformers
    with Philippe Rigollet and Domènec Ruiz-Balet
    Foundations of Computational Mathematics
    2026

  8. Dynamic metastability in the self-attention model
    with Hugo Koubbi, Yury Polyanskiy and Philippe Rigollet
    preprint
    2024
    github

  9. A mathematical perspective on Transformers
    with Cyril Letrouit, Yury Polyanskiy and Philippe Rigollet
    Bulletin of the American Mathematical Society
    2024
    github

  10. The emergence of clusters in self-attention dynamics
    with Cyril Letrouit, Yury Polyanskiy and Philippe Rigollet
    Advances in Neural Information Processing Systems
    2024
    github

  11. Control of the Stefan problem in a periodic box
    with Debayan Maity
    Mathematical Models and Methods in Applied Sciences
    2023
    github

  12. Turnpike in optimal control of PDEs, ResNets, and beyond
    with Enrique Zuazua
    Acta Numerica
    2022
    github

  13. Optimal controller design via Brunovsky's normal form
    with Enrique Zuazua
    IEEE Transactions on Automatic Control
    2023
    github

  14. Sparsity in long-time control of neural ODEs
    with Carlos Esteve-Yagüe
    Systems & Control Letters
    2023
    github

  15. Turnpike in Lipschitz-nonlinear optimal control
    with Carlos Esteve-Yagüe, Dario Pighin and Enrique Zuazua
    Nonlinearity
    2022
    github

  16. Large-time asymptotics in deep learning
    with Carlos Esteve-Yagüe, Dario Pighin and Enrique Zuazua
    preprint
    2021
    github

  17. Controllability of one-dimensional viscous free boundary flows
    with Enrique Zuazua
    SIAM Journal on Control and Optimization
    2021

  18. Null-controllability of perturbed porous medium gas flow
    ESAIM Control, Optimisation and Calculus of Variations
    2020

theses