Multidimensional complex stationary centered Gaussian autoregressive time series machine learning in Poincaré and Siegel disks: application for audio and radar …

Y Cabanes - 2022 - theses.hal.science
The objective of this thesis is the classification of complex valued stationary centered
Gaussian autoregressive time series. We study the case of one-dimensional time series as …

Hyperbolic equivariant convolutional neural networks for fish-eye image processing

PY Lagrave, F Barbaresco - 2022 - hal.science
Fish-Eye image processing with conventional Machine Learning algorithms such as
Convolutional Neural Networks is a challenging task because of the distortion effects …

Adaptive Importance Sampling for Equivariant Group-Convolution Computation

PY Lagrave, F Barbaresco - Physical Sciences Forum, 2022 - mdpi.com
This paper introduces an adaptive importance sampling scheme for the computation of
group-based convolutions, a key step in the implementation of equivariant neural networks …

Introduction to Robust Machine Learning with Geometric Methods for Defense Applications

PY Lagrave, F Barbaresco - 2021 - hal.science
This paper aims at motivating the use of geometrically informed Machine Learning
algorithms for Defense applications by providing intuitions with respect to their underlying …

-Equivariant Machine Learning with Modular Forms Theory and Applications

PY Lagrave - International Conference on Geometric Science of …, 2023 - Springer
This paper introduces an approach for building Machine Learning (ML) algorithms
embedding equivariance mechanisms to the Lie group SL (2, Z) by leveraging on modular …

Generalized SU (1, 1) Equivariant Convolution on Fock-Bargmann Spaces for Robust Radar Doppler Signal Classification

PY Lagrave, F Barbaresco - 2021 - hal.science
Classifying radar Doppler signals with Deep Learning algorithms is a challenging task, in
particular because of the noisy nature of the data (clutter, thermal noise, etc.). Equivariant …

On the Benefits of SO (3)-Equivariant Neural Networks for Spherical Image Processing

S Martin, PY Lagrave - 2022 - hal.science
This paper deals with the use of SO (3)-Equivariant Neural Networks for processing
spherical images such as those acquired with bi-directional fish-eye lenses. By using …

[PDF][PDF] Lie Groups Statistics and Machine Learning for Military Sensors Based on Symplectic Structures of Information Geometry

F Barbaresco - sto.nato.int
In a first part, we will present pioneering THALES Sensors/Radars algorithms on Geometric
Matrix CFAR based on Jean-Louis Koszul's Information Geometry and its extension for …

[PDF][PDF] Réseaux de neurones hyperboliques équivariants pour le traitement d'images Fish-Eye

Le traitement des images Fish-Eye à l'aide d'algorithmes d'apprentissage automatique
conventionnels tels que les réseaux de neurones convolutifs est une tâche difficile en raison …