2 citations
- Laboratoire de Mathématiques d'OrsayFR5 papers
- Centre Inria de SaclayFR4 papers
- Centre de Recherche en Mathématiques de la DécisionFR1 paper
- Centre National de la Recherche ScientifiqueFR1 paper
- Columbia UniversityUS1 paper
- Département mathématiques, informatique, sciences de la donnée et technologies du numériqueFR1 paper
- Fujitsu (Japan)JP1 paper
- Institut de Mathématiques de ToulouseFR1 paper
- Institut national de recherche en sciences et technologies du numériqueFR1 paper
- Institut National des Sciences Appliquées de ToulouseFR1 paper
- Laboratoire de Probabilités et Modèles AléatoiresFR1 paper
- Laboratoire de Probabilités, Statistique et ModélisationFR1 paper
8 papers
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Multi-parameter Module Approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees
David Loiseaux, Mathieu Carrière, Andrew J. Blumberg
In this article, we introduce a new parameterized family of topological descriptors, taking the form of candidate decompositions, for multi-parameter persistence modules, and we id…
Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport
Alex Delalande
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of…
On the pathwidth of hyperbolic 3-manifolds
Kristóf Huszár
According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifold…
Estimation and Quantization of Expected Persistence Diagrams
Vincent Divol, Théo Lacombe
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series…
Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs
Théo Lacombe, Yuichi Ike, Mathieu Carriere +3
Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can…