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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.18673 |
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| _version_ | 1866911891932053504 |
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| author | Delgadino, M. G. Suassuna, Bruno B. Cabrera, Rene |
| author_facet | Delgadino, M. G. Suassuna, Bruno B. Cabrera, Rene |
| contents | We study quantitatively the overparametrization limit of the original Wasserstein-GAN algorithm. Effectively, we show that the algorithm is a stochastic discretization of a system of continuity equations for the parameter distributions of the generator and discriminator. We show that parameter clipping to satisfy the Lipschitz condition in the algorithm induces a discontinuous vector field in the mean field dynamics, which gives rise to blow-up in finite time of the mean field dynamics. We look into a specific toy example that shows that all solutions to the mean field equations converge in the long time limit to time periodic solutions, this helps explain the failure to converge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18673 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GAN: Dynamics Delgadino, M. G. Suassuna, Bruno B. Cabrera, Rene Analysis of PDEs We study quantitatively the overparametrization limit of the original Wasserstein-GAN algorithm. Effectively, we show that the algorithm is a stochastic discretization of a system of continuity equations for the parameter distributions of the generator and discriminator. We show that parameter clipping to satisfy the Lipschitz condition in the algorithm induces a discontinuous vector field in the mean field dynamics, which gives rise to blow-up in finite time of the mean field dynamics. We look into a specific toy example that shows that all solutions to the mean field equations converge in the long time limit to time periodic solutions, this helps explain the failure to converge. |
| title | GAN: Dynamics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.18673 |