Research

Current position

Geometry-aware federated learning for EEG classification

My current research focuses on geometry-aware federated learning for motor-imagery EEG classification. I study federated training of SPDNet on covariance-based representations and compare it with Euclidean baselines such as EEGNet, with a particular emphasis on Riemannian aggregation schemes that preserve the Stiefel/SPD manifold geometry.

Institution L2S, CentraleSupélec (Gif-sur-Yvette)

Supervisors Florent Bouchard, with Guillaume Ginolhac and Ammar Mian

Keywords federated learning Riemannian manifolds SPD matrices deep learning

Publications

Submitted

T. Pautrel, F. Bouchard, G. Ginolhac, A. Mian Projection-based Riemannian federated learning with partial participation Submitted to Signal Processing, special issue on Signal Processing and Learning with Manifolds and Lie Groups
T. Pautrel, F. Bouchard, G. Ginolhac, A. Mian FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet Submitted to EuSIPCO 2026
T. Pautrel, F. Portier Riemannian stochastic optimization for sufficient dimension reduction Submitted

To appear

J. Angst, T. Pautrel, G. Poly Global universality of the expected number of zeros of non-analytic random signals To appear in INdAM–Springer Proceedings (2025)

Published

J. Angst, T. Pautrel, G. Poly Real zeros of random trigonometric polynomials with dependent coefficients Trans. Amer. Math. Soc. 375 (2022), 7209–7260. journal page
T. Pautrel New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients Electron. Commun. Probab. 25 (2020), no. 36. journal page

Previous research

Internship · 2023

Riemannian federated learning for time-series analysis with remote sensing data

During my internship, I worked on FedSPDNet, a geometry-aware federated learning framework designed to cope with the distributed and sovereignty-constrained nature of remote sensing data. Instead of relying on large convolutional neural networks, FedSPDNet operates on Symmetric Positive Definite matrices through second-order statistics and uses specialized Riemannian aggregation schemes (such as Stiefel projected means and tangent space averaging) to preserve the geometric structure of model parameters while greatly reducing communication costs.

Institution University Savoie Mont Blanc, LISTIC laboratory (Annecy)

Supervisors Guillaume Ginolhac, Ammar Mian, Florent Bouchard

Keywords federated learning Riemannian manifolds SPD matrices deep learning remote sensing

PhD thesis · 2019–2022

Some contributions to the universality of zeros of random trigonometric functions

In my PhD thesis, I studied the asymptotic behavior of the number of zeros of random trigonometric functions on a fixed interval—almost surely, in distribution, and on average—with a particular focus on universality questions: to what extent this behavior depends on the law of the random coefficients, their correlations, or the choice of basis functions. Working in the framework of dependent stationary Gaussian processes, I expressed dependence through the associated spectral measure and showed that its nature has a crucial impact on the zero-count asymptotics, leading, under suitable assumptions, to both universal regimes (insensitive to fine model details) and genuinely non-universal ones. The analysis combines stochastic tools such as the Kac–Rice formula with techniques inspired by classical work of Salem and Zygmund, and yields new global universality and non-universality results for the zero sets of random trigonometric polynomials.

Manuscript (PDF) theses.fr Defense slides

Institution University of Rennes, IRMAR laboratory (Rennes)

Supervisors Jürgen Angst, Guillaume Poly

Keywords nodal sets random trigonometric polynomials stationary Gaussian processes spectral measures Kac–Rice formula

Invited speaker at the "UniRandom" thematic week (Rennes, 2019 and 2021). Slides.