Research

2024

1. FoCMBest poster

   

   On the existence of Monge maps for the Gromov-Wasserstein problem

   Théo Dumont, Théo Lacombe, and François-Xavier Vialard

   Foundations of Computational Mathematics, 2024

   Best poster award at Geometric Sciences in Action, 2024.

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   The Gromov–Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between points. Akin to the standard optimal transportation problem, it is natural to ask for conditions guaranteeing some structure on the optimizers, for instance if these are induced by a (Monge) map. We study this question in Euclidean spaces when the cost functions are either given by (i) inner products or (ii) squared distances, two standard choices in the literature. We establish the existence of an optimal map in case (i) and of an optimal 2-map (the union of the graphs of two maps) in case (ii), both under an absolute continuity condition on the source measure. Additionally, in case (ii) and in dimension one, we numerically design situations where optimizers of the Gromov–Wasserstein problem are 2-maps but are not maps. This suggests that our result cannot be improved in general for this cost. Still in dimension one, we additionally establish the optimality of monotone maps under some conditions on the measures, thereby giving insight on why such maps often appear to be optimal in numerical experiments.

   @article{dumont2022existence,
     title = {On the existence of Monge maps for the Gromov-Wasserstein problem},
     author = {Dumont, Th{\'e}o and Lacombe, Th{\'e}o and Vialard, Fran{\c{c}}ois-Xavier},
     year = {2024},
     journal = {Foundations of Computational Mathematics},
   }

2023

1. preprint

   

   A supervised algorithm entirely trained on a synthetic dataset to segment granular suspension images

   David Paulovics, Bruno Figliuzzi, Théo Dumont, and Frédéric Blanc

   Under review, 2023

   Bib   PDF   Code

   @article{paulovics2023supervised,
     title = {A supervised algorithm entirely trained on a synthetic dataset to segment granular suspension images},
     author = {Paulovics, David and Figliuzzi, Bruno and Dumont, Th{\'e}o and Blanc, Fr{\'e}d{\'e}ric},
     year = {2023},
     journal = {Under review},
   }

2. CVPR

   

   Modular memorability: tiered representations for video memorability prediction

   Théo Dumont, Juan S. Hevia, and Camilo L. Fosco

   In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023

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   @inproceedings{dumont2023modular,
     title = {Modular memorability: tiered representations for video memorability prediction},
     author = {Dumont, Th{\'e}o and Hevia, Juan S. and Fosco, Camilo L.},
     booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
     pages = {10751--10760},
     year = {2023}
   }

2022

1. eLife

   

   The rapid developmental rise of somatic inhibition disengages hippocampal dynamics from self-motion

   Robin F. Dard, Erwan Leprince, Julien Denis, Shrisha Rao Balappa, and 11 more authors

   eLife, 2022

   Bib   PDF   Code

   @article{dard2022rapid,
     title = {The rapid developmental rise of somatic inhibition disengages hippocampal dynamics from self-motion},
     author = {Dard, Robin F. and Leprince, Erwan and Denis, Julien and Balappa, Shrisha Rao and Suchkov, Dmitrii and Boyce, Richard and Lopez, Catherine and Giorgi-Kurz, Marie and Szwagier, Tom and Dumont, Th{\'e}o and Rouault, Herv{\'e} and Minlebaev, Marat and Baude, Agn{\`e}s and Cossart, Rosa and Picardo, Michel A.},
     journal = {eLife},
     volume = {11},
     pages = {e78116},
     year = {2022},
     publisher = {eLife Sciences Publications Limited},
   }