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

The geometry of neural networks : a Riemannian foliation perspective on robustness.

Tron, E. (2025). The geometry of neural networks: A Riemannian foliation perspective on robustness. (Publication No. 2025ENAC0004) [Theses, ENAC Toulouse]. https://enac.hal.science/tel-05391126

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.

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.

Geometry of Singular Foliations and Learning Manifolds in ReLU Networks via the Data Information Matrix

Tron, Eliot; Fioresi, Rita. (2024). "Geometry of Singular Foliations and Learning Manifolds in ReLU Networks via the Data Information Matrix." 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 CJC-MA 2026

March 03, 2026

Conference at CJC-MA 2026, École nationale des ponts et chaussées, Champs-sur-Marne, France

Talk at SAMM seminar

November 28, 2025

Seminar at Paris 1 Pantheon Sorbonne - Centre PMF, Paris, France

Talk at California applied seminar

April 02, 2025

Seminar at Universita di Bologna, Bologna, Italy

Poster at CaLISTA Workshop: Geometry-Informed Machine Learning

September 02, 2024

Poster at École des Mines, Paris, France

Talk at CaLISTA seminar: Geometry and Machine Learning

June 21, 2024

Talk at Grand Hotel de Rose, Scalea, Italy

Talk at Séminaire Nord Bassin Parisien

June 03, 2024

Seminar at Working group on dissipation, Online

Talk at IRT Saint Exupéry seminar

April 11, 2024

Seminar at ANITI/DEEL, B612, Toulouse, France

Quiz Tuesday

April 09, 2024

Talk at Quai des Savoirs, Toulouse, France

MT180 - Three minute thesis

March 15, 2024

Talk at Théâtre Sorano, Toulouse, France

Talk at CaLISTA Workshop: Geometry of Information Theory

September 29, 2023

Talk at Unversidad Carlos III, Madrid, Spain

Poster at GSI conference

August 31, 2023

Poster at GSI23, Saint-Malo, France

Talk at CaLISTA Kick-off meeting

June 07, 2023

Talk at Università di Bologna, Bologna, Italy

Students

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).
2023: Part of the supervision of the Master’s thesis of Nicola Rosetti (2nd year master’s student at the University of Bologna).

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.
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.

Interests

Music (Electronic Music Production, Drummer, Sound-engineering, …)
Sport (Climbing, Biking, Hiking, Snowboarding, …)
Other (Cooking, Movies, Video games, …)

Eliot Tron

CV