Posts by Collection

Equivariant Neural Networks and Differential Invariants Theory for Solving Partial Differential Equations

Published in Proceedings of The 41st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 2022

Equivariant Neural Networks for arbitrary symmetry groups to generalize Physics-Informed Neural Networks and approximate differential invariants.

Recommended citation: 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
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Manifold Learning via Foliations and Knowledge Transfer

Published in ArXiv, 2024

This study explores deep ReLU neural networks and manifold learning, uncovering a foliation structure that correlates with real data in high-dimensional spaces and shows potential for knowledge transfer.

Recommended citation: Tron, Eliot; Fioresi, Rita. (2024). "Manifold Learning via Foliations and Knowledge Transfer." ArXiv preprint, https://doi.org/10.48550/arXiv.2409.07412.
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Adversarial attacks on neural networks through canonical Riemannian foliations

Published in Machine Learning, 2024

This paper explores neural network robustness through Riemannian geometry, presenting a novel adversarial attack that highlights the role of curvature in the data space.

Recommended citation: Tron Eliot, Couëllan Nicolas, Puechmorel Stéphane. (2024). "Adversarial attacks on neural networks through canonical Riemannian foliations." Machine Learning.
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Cartan moving frames and the data manifolds

Published in Information Geometry, 2024

The study employs Cartan moving frames to analyze data manifolds and their curvature, offering insights into neural network outputs as an explainable AI tool.

Recommended citation: 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.
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Talk at CaLISTA Kick-off meeting

Published: June 07, 2023

I gave a 15min talk on my work about adversarial attacks on neural networks through canonical Riemannian foliations for the CaLISTA Kick-off meeting.

Poster at GSI conference

Published: August 31, 2023

I presented a poster on my work about adversarial attacks on neural networks through canonical Riemannian foliations at Geometric Science of Information conference. You can find my poster here.

Talk at CaLISTA Workshop: Geometry of Information Theory

Published: September 29, 2023

I gave a talk on my work about adversarial attacks on neural networks through canonical Riemannian foliations (and more) for the CaLISTA Workshop entitled Geometry of Information Theory.

MT180 - Three minute thesis

Published: March 15, 2024

I was a regional finalist in MT180 (Three minute thesis), a pop-science contest. My entry here (in french). I learned a lot on how to share important but technical informations with any profile, and in the most effective and fun way.

Quiz Tuesday

Published: April 09, 2024

I was invited to talk about AI and PhD during this fun quiz night at the museum Quai des Savoirs by the Science Comedy Show.

Talk at IRT Saint Exupéry seminar

Published: April 11, 2024

I gave a talk on my work about adversarial attacks on neural networks through canonical Riemannian foliations (and more) in front of the IRT Saint Exupéry team (and more).

Talk at Séminaire Nord Bassin Parisien

Published: June 03, 2024

I gave a talk on my work about adversarial attacks on neural networks through canonical Riemannian foliations (and more) as part of a working group initiated by Frédéric Barbaresco.

Talk at CaLISTA seminar: Geometry and Machine Learning

Published: June 21, 2024

I gave a talk on my work about manifold learning, foliations and knowledge transfer (and more) for the CaLISTA seminar: Geometry and Machine Learning.

Poster at CaLISTA Workshop: Geometry-Informed Machine Learning

Published: September 02, 2024

I presented a poster on my work about manifold learning, foliations and knowledge transfer for the CaLISTA Workshop: Geometry-Informed Machine Learning. You can find my poster here.

Measure Theory (2021)

Undergraduate course (3rd year post-bac), ENAC, 2021

A 17h introductory course on measure theory for 1st year engineering student at ENAC. This course teaches about measurable spaces, measure functions, measurable functions, Lebesgue integration, multiple variables integration, measure decomposition and \(L^p\) spaces.

Measure Theory (2022)

Undergraduate course (3rd year post-bac), ENAC, 2022

A 17h introductory course on measure theory for 1st year engineering student at ENAC. This course teaches about measurable spaces, measure functions, measurable functions, Lebesgue integration, multiple variables integration, measure decomposition and \(L^p\) spaces.

Statistics (2023)

Undergraduate course (3rd year post-bac), ENAC, 2023

A 30h course on statistics for 1st year engineering school student at ENAC. This maths course teaches about statistical models, estimation, sufficient statistics, Fisher Information, confidence intervals, test statistics and non-parametric tests. This course includes 6 hours of hands-on Python for statistical studies.

Measure Theory (2023)

Undergraduate course (3rd year post-bac), ENAC, 2023

A 17h introductory course on measure theory for 1st year engineering student at ENAC. This course teaches about measurable spaces, measure functions, measurable functions, Lebesgue integration, multiple variables integration, measure decomposition and \(L^p\) spaces.

Statistics (2024)

Undergraduate course (3rd year post-bac), ENAC, 2024

A 30h course on statistics for 1st year engineering school student at ENAC. This maths course teaches about statistical models, estimation, sufficient statistics, Fisher Information, confidence intervals, test statistics and non-parametric tests. This course includes 6 hours of hands-on Python for statistical studies..