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              <p>Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has been successful in providing meaningful comparison between such entities.GW operates on graphs, seen as probability measures over spaces depicted by their nodes connectivity relations. At the core of OT is the idea ofmass conservation, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary learning (DL), and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence.The latter leads to immediate computational benefits and naturally induces a new graph DL method, shown to be relevant for unsupervisedrepresentation learning and classification of graphs</p>
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              <p>-La comparaison d'objets structurés tels que les graphes est une opération fondamentale pour de nombreuses tâches d'apprentissage. À cette fin, la distance de Gromov-Wasserstein (GW) , basée sur le Transport Optimal (TO), s'est avérée efficace pour comparer de telles entités. GW opère sur les graphes, vus comme des mesures de probabilité sur des espaces décrits par les relations de connectivité de leurs noeuds. Au coeur du TO réside l'idée de conservation de masse, qui impose un couplage entre tous les noeuds des deux graphes considérés. Nous soutenons dans ce papier que cette propriété peut être préjudiciable pour des tâches telles que l'apprentissage de dictionnaire (AD), et nous la relaxons donc en proposant une nouvelle divergence issue de GW. Cette dernière amène des avantages computationnels immédiats et induit naturellement une nouvelle méthode d'AD, pertinente pour l'apprentissage non supervisé de représentations et la classification de graphes.</p>
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