Thibault Pautrel

Research

My research lies at the interface of Riemannian geometry, statistical learning, and signal processing. It is organised around three connected themes.

Theme 01 Current

Geometry-aware federated learning

My current work addresses geometry-aware federated learning for motor-imagery EEG classification. I study federated training of SPDNet on covariance-based representations of EEG signals and compare it with Euclidean baselines such as EEGNet, with a particular emphasis on Riemannian aggregation schemes that preserve the Stiefel/SPD manifold geometry. A central question is how to combine aggregation, partial client participation, and privacy guarantees while remaining compatible with the underlying manifold structure.

Server Bt Client 1 local data Client 2 local data Client 3 local data Client 4 local data
One communication round: the server broadcasts the current global model, each client updates it locally on private data, and the server aggregates the returning updates into a new global iterate.
Institution L2S, CentraleSupélec (Gif-sur-Yvette), since October 2025
Supervision Florent Bouchard, with Guillaume Ginolhac and Ammar Mian
Keywords federated learning Riemannian manifolds SPD matrices deep learning

Publications

  1. Submitted T. Pautrel, F. Bouchard, G. Ginolhac, A. Mian Projection-based Riemannian federated learning with partial participation Signal Processing, special issue on Signal Processing and Learning with Manifolds and Lie Groups
    Preprint (PDF) Supplementary (PDF)
  2. Accepted T. Pautrel, F. Bouchard, G. Ginolhac, A. Mian FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet EuSIPCO 2026
    Preprint (PDF)

Talks

  1. Federated Learning on Riemannian Manifolds: a Projection-based Approach 7th Statistical Learning for Signal and Image Processing (SLSIP) Workshop, Kruje, Albania
    Slides (PDF)

Earlier work on this theme

Internship · 2023

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

During an internship at LISTIC, I worked on an early version of FedSPDNet: a geometry-aware federated learning framework targeting the distributed and sovereignty-constrained setting of remote-sensing data. Rather than relying on large convolutional architectures, FedSPDNet operates on Symmetric Positive Definite matrices through second-order statistics, and uses specialized Riemannian aggregation schemes (Stiefel projected means, tangent-space averaging) to preserve the geometric structure of model parameters while reducing communication costs.

Institution LISTIC laboratory, University Savoie Mont Blanc (Annecy)
Supervisors Guillaume Ginolhac, Ammar Mian, Florent Bouchard
Theme 02

Riemannian stochastic optimization

A parallel line of work develops stochastic optimization algorithms on Riemannian manifolds, motivated by sufficient dimension reduction, where the targeted subspace is naturally a point on the Grassmann manifold, represented for computation by an orthonormal basis on the Stiefel manifold. The goal is to recast classical dimension-reduction criteria as smooth functions on this manifold, design stochastic gradient methods that respect its geometry, and establish non-asymptotic convergence rates matching the optimal scaling for non-convex stochastic first-order methods.

−grad f(x) TxM manifold M
Riemannian gradient descent: at each iterate, the Euclidean gradient is projected onto the tangent space, and a retraction maps the step back onto the manifold.
Collaborator François Portier (ENSAI / CREST)
Keywords Riemannian optimization stochastic gradient methods Stiefel manifold sufficient dimension reduction

Publications

  1. Accepted T. Pautrel, F. Portier Riemannian stochastic optimization for sufficient dimension reduction ICML 2026
    arXiv 2606.00413 HAL hal-05640656
Theme 03 2019–2022

Zeros of random trigonometric functions

My PhD thesis 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: to what extent this behavior depends on the law of the coefficients, their correlations, or the choice of basis functions. Working with dependent stationary Gaussian processes, dependence is encoded through the associated spectral measure, whose nature has a decisive impact on the asymptotics and produces both universal and genuinely non-universal regimes. The analysis combines 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 IRMAR, University of Rennes
Supervisors Jürgen Angst, Guillaume Poly
Keywords nodal sets random trigonometric polynomials stationary Gaussian processes spectral measures Kac–Rice formula

Publications

  1. To appear J. Angst, T. Pautrel, G. Poly Global universality of the expected number of zeros of non-analytic random signals INdAM–Springer Proceedings (2025)
    Preprint (PDF)
  2. 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
  3. Published 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

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