Geomstats: A Python Package for Riemannian Geometry in Machine Learning

1 code implementation • ICLR 2019 • Nina Miolane, Alice Le Brigant, Johan Mathe, Benjamin Hou, Nicolas Guigui, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more.

BIG-bench Machine Learning Clustering +2

Adversarial Risk Bounds for Neural Networks through Sparsity based Compression

no code implementations • 3 Jun 2019 • Emilio Rafael Balda, Arash Behboodi, Niklas Koep, Rudolf Mathar

To study how robustness generalizes, recent works assume that the inputs have bounded $\ell_2$-norm in order to bound the adversarial risk for $\ell_\infty$ attacks with no explicit dimension dependence.

Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

1 code implementation • 10 Mar 2016 • James Townsend, Niklas Koep, Sebastian Weichwald

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable manifold.

Riemannian optimization