On the Existence of Optimal Transport Gradient for Learning Generative Models
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HOUDARD, Antoine | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LECLAIRE, Arthur | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| hal.structure.identifier | Equipe Image - Laboratoire GREYC - UMR6072 | |
| dc.contributor.author | RABIN, Julien | |
| dc.date.accessioned | 2024-04-04T02:47:21Z | |
| dc.date.available | 2024-04-04T02:47:21Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191635 | |
| dc.description.abstractEn | The use of optimal transport cost for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGAN). Training of WGAN relies on a theoretical background: the calculation of the gradient of the optimal transport cost with respect to the generative model parameters. We first demonstrate that such gradient may not be defined, which can result in numerical instabilities during gradient-based optimization. We address this issue by stating a valid differentiation theorem in the case of entropic regularized transport and specify conditions under which existence is ensured. By exploiting the discrete nature of empirical data, we formulate the gradient in a semi-discrete setting and propose an algorithm for the optimization of the generative model parameters. Finally, we illustrate numerically the advantage of the proposed framework. | |
| dc.description.sponsorship | Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010 | |
| dc.language.iso | en | |
| dc.title.en | On the Existence of Optimal Transport Gradient for Learning Generative Models | |
| dc.type | Document de travail - Pré-publication | |
| dc.identifier.doi | 10.48550/arXiv.2102.05542 | |
| dc.subject.hal | Informatique [cs]/Apprentissage [cs.LG] | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| dc.identifier.arxiv | 2102.05542v1 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03137342 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03137342v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=HOUDARD,%20Antoine&LECLAIRE,%20Arthur&PAPADAKIS,%20Nicolas&RABIN,%20Julien&rft.genre=preprint |
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