Cartan moving frames and the data manifolds
Tron, Eliot; Fioresi, Rita; Couëllan, Nicolas; Puechmorel, Stéphane. "Cartan moving frames and the data manifolds." Info. Geo. (2024). https://doi.org/10.1007/s41884-024-00159-8.
CV
Education
- Ph.D in Machine Learning and Geometry entitled The geometry of neural networks : a Riemannian foliation perspective on robustness., ENAC Toulouse, 20 October 2025
- Master (M.S.) in Mathematics, ENS de Lyon, 2021
- License (B.S.) in Theoretical Computer Science, ENS de Lyon, 2019
- License (B.S.) in Mathematics, University Lyon 1, 2019
Work experience
- 01 November 2025 - 31 October 2027: Postdoc
- SAMM, Paris 1 Panthéon Sorbonne and IRIT, Paris, France.
- Subject: New sampling strategies for deep neural networks using information geometry.
- Supervisor: Alain Celisse, Alice Le Brigant and Christophe Denis.
- 01 October 2022 - 20 October 2025: PhD Candidate
- ENAC, Toulouse, France.
- 2 months a year at University of Bologna, Italy.
- Subject: The geometry of neural networks : a Riemannian foliation perspective on robustness..
- Supervisor: Nicolas Couëllan, Rita Fioresi and Stéphane Puechmorel.
- Thesis available on HAL.
- 01 March 2022 - 30 June 2022: Research Internship
- University of Bologna in Bologna, Italy.
- Subject: Deep Learning: Riemannian and subriemannian structures on the space of models and data manifolds.
- Supervisor: Rita Fioresi.
- 06 September 2021 - 28 January 2022: Research Internship
- ENAC in Toulouse, France.
- Subject: Neural Networks input Foliations and Adversarial Attacks.
- Supervisor: Nicolas Couëllan and Stéphane Puechmorel.
- 29 March 2021 - 18 July 2021: Research Internship
- Thales Research & Technology in Palaiseau, France
- Subject: Solving Partial Differential Equations with Equivariant Neural Network.
- Supervisor: Pierre-Yves Lagrave
- 20 April 2020 - 17 July 2020: Research Internship
- National Institute of Informatics in Tokyo, Japan (remote due to covid-19).
- Subject: Machine Learning and Information Geometry: a link with Topological Data Analysis.
- Supervisor: Mahito Sugiyama
- 06 June 2019 - 13 July 2019: Research Internship
- DANTE team, IXXI, LIP, ENS de Lyon in Lyon, France.
- Subject: Featured network embedding using GCN Variational Autoencoders.
- Supervisor: Márton Karsai and Sébastien Lérique
Skills
- Python (PyTorch - main, TensorFlow,…)
- LaTeX
- Git, Bash
- Linux (currently on Manjaro with i3wm)
- I learned them at some point: C++, OCaml, CSS / HTML
Languages
- English: C1 Level (CAE)
- German: I had a B1 level in 2016, not anymore but I’d love to get back at it.
- Italien: I learned the basics during my various stays in Bologna.
Publications
Adversarial attacks on neural networks through canonical Riemannian foliations
Tron Eliot, Couëllan Nicolas, Puechmorel Stéphane. (2024). "Adversarial attacks on neural networks through canonical Riemannian foliations." Machine Learning.
Manifold Learning via Foliations and Knowledge Transfer
Tron, Eliot; Fioresi, Rita. (2024). "Manifold Learning via Foliations and Knowledge Transfer." ArXiv preprint, https://doi.org/10.48550/arXiv.2409.07412.
Equivariant Neural Networks and Differential Invariants Theory for Solving Partial Differential Equations
Lagrave, P.-Y.; Tron, E. Equivariant Neural Networks and Differential Invariants Theory for Solving Partial Differential Equations. Phys. Sci. Forum 2022, 5, 13. https://doi.org/10.3390/psf2022005013
Talks
Talk at California applied seminar
Seminar at Universita di Bologna, Bologna, Italy
Poster at CaLISTA Workshop: Geometry-Informed Machine Learning
Poster at École des Mines, Paris, France
Talk at CaLISTA seminar: Geometry and Machine Learning
Talk at Grand Hotel de Rose, Scalea, Italy
Talk at Séminaire Nord Bassin Parisien
Seminar at Working group on dissipation, Online
Talk at IRT Saint Exupéry seminar
Seminar at ANITI/DEEL, B612, Toulouse, France
Quiz Tuesday
Talk at Quai des Savoirs, Toulouse, France
MT180 - Three minute thesis
Talk at Théâtre Sorano, Toulouse, France
Talk at CaLISTA Workshop: Geometry of Information Theory
Talk at Unversidad Carlos III, Madrid, Spain
Poster at GSI conference
Poster at GSI23, Saint-Malo, France
Talk at CaLISTA Kick-off meeting
Talk at Università di Bologna, Bologna, Italy
Teaching
Other
- 17-18 June 2025: Member of the organizing and scientific committee for the Calista workshop Interplay between data and models in deep learning: a geometric perspective.
- April 2025 - September 2025: Part of the supervision of the research internship of Pablo Hueso Merino (2nd year master’s student at Paris-Saclay University).
- 2024-2025: Member of ENAC’s PhD students’ association board.
- 2024-2025: Member of the organizing committee of the ENAC PhD Day.
- 2024-2025: PhD students’ representative on the ENAC Research Council.
- 2024: Regional finalist in MT180 (Three minute thesis), a pop-science contest.
- 2023: Part of the supervision of the Master’s thesis of Nicola Rosetti (2nd year master’s student at the University of Bologna).
Interests
- Music (Electronic Music Production, Drummer, Sound-engineering, …)
- Sport (Climbing, Biking, Hiking, Snowboarding, …)
- Other (Cooking, Movies, Video games, …)