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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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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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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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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