Lie group cohomology and (multi) symplectic integrators: new geometric tools for Lie group machine learning based on Souriau geometric statistical mechanics
F Barbaresco, F Gay-Balmaz - Entropy, 2020 - mdpi.com
In this paper, we describe and exploit a geometric framework for Gibbs probability densities
and the associated concepts in statistical mechanics, which unifies several earlier works on …
and the associated concepts in statistical mechanics, which unifies several earlier works on …
Computing CNN loss and gradients for pose estimation with Riemannian geometry
Pose estimation, ie predicting a 3D rigid transformation with respect to a fixed co-ordinate
frame in, SE (3), is an omnipresent problem in medical image analysis. Deep learning …
frame in, SE (3), is an omnipresent problem in medical image analysis. Deep learning …
Numerical accuracy of ladder schemes for parallel transport on manifolds
Parallel transport is a fundamental tool to perform statistics on Riemannian manifolds. Since
closed formulae do not exist in general, practitioners often have to resort to numerical …
closed formulae do not exist in general, practitioners often have to resort to numerical …
Operator-valued formulas for Riemannian gradient and Hessian and families of tractable metrics in Riemannian optimization
D Nguyen - Journal of Optimization Theory and Applications, 2023 - Springer
We provide explicit formulas for the Levi-Civita connection and Riemannian Hessian for a
Riemannian manifold that is a quotient of a manifold embedded in an inner product space …
Riemannian manifold that is a quotient of a manifold embedded in an inner product space …
A bi-invariant statistical model parametrized by mean and covariance on rigid motions
E Chevallier, N Guigui - Entropy, 2020 - mdpi.com
This paper aims to describe a statistical model of wrapped densities for bi-invariant statistics
on the group of rigid motions of a Euclidean space. Probability distributions on the group are …
on the group of rigid motions of a Euclidean space. Probability distributions on the group are …