Monotone Generative Modeling via a Gromov-Monge Embedding
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916311132536832 |
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| author | Lee, Wonjun Yang, Yifei Zou, Dongmian Lerman, Gilad |
| author_facet | Lee, Wonjun Yang, Yifei Zou, Dongmian Lerman, Gilad |
| contents | Generative adversarial networks (GANs) are popular for generative tasks; however, they often require careful architecture selection, extensive empirical tuning, and are prone to mode collapse. To overcome these challenges, we propose a novel model that identifies the low-dimensional structure of the underlying data distribution, maps it into a low-dimensional latent space while preserving the underlying geometry, and then optimally transports a reference measure to the embedded distribution. We prove three key properties of our method: 1) The encoder preserves the geometry of the underlying data; 2) The generator is $c$-cyclically monotone, where $c$ is an intrinsic embedding cost employed by the encoder; and 3) The discriminator's modulus of continuity improves with the geometric preservation of the data. Numerical experiments demonstrate the effectiveness of our approach in generating high-quality images and exhibiting robustness to both mode collapse and training instability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01375 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Monotone Generative Modeling via a Gromov-Monge Embedding Lee, Wonjun Yang, Yifei Zou, Dongmian Lerman, Gilad Machine Learning Numerical Analysis Generative adversarial networks (GANs) are popular for generative tasks; however, they often require careful architecture selection, extensive empirical tuning, and are prone to mode collapse. To overcome these challenges, we propose a novel model that identifies the low-dimensional structure of the underlying data distribution, maps it into a low-dimensional latent space while preserving the underlying geometry, and then optimally transports a reference measure to the embedded distribution. We prove three key properties of our method: 1) The encoder preserves the geometry of the underlying data; 2) The generator is $c$-cyclically monotone, where $c$ is an intrinsic embedding cost employed by the encoder; and 3) The discriminator's modulus of continuity improves with the geometric preservation of the data. Numerical experiments demonstrate the effectiveness of our approach in generating high-quality images and exhibiting robustness to both mode collapse and training instability. |
| title | Monotone Generative Modeling via a Gromov-Monge Embedding |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2311.01375 |