JacNet: Learning Functions with Structured Jacobians
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913477937856512 |
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| author | Lorraine, Jonathan Hossain, Safwan |
| author_facet | Lorraine, Jonathan Hossain, Safwan |
| contents | Neural networks are trained to learn an approximate mapping from an input domain to a target domain. Incorporating prior knowledge about true mappings is critical to learning a useful approximation. With current architectures, it is challenging to enforce structure on the derivatives of the input-output mapping. We propose to use a neural network to directly learn the Jacobian of the input-output function, which allows easy control of the derivative. We focus on structuring the derivative to allow invertibility and also demonstrate that other useful priors, such as $k$-Lipschitz, can be enforced. Using this approach, we can learn approximations to simple functions that are guaranteed to be invertible and easily compute the inverse. We also show similar results for 1-Lipschitz functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | JacNet: Learning Functions with Structured Jacobians Lorraine, Jonathan Hossain, Safwan Machine Learning Artificial Intelligence 68T07 I.2.6; G.1.0; I.5.1 Neural networks are trained to learn an approximate mapping from an input domain to a target domain. Incorporating prior knowledge about true mappings is critical to learning a useful approximation. With current architectures, it is challenging to enforce structure on the derivatives of the input-output mapping. We propose to use a neural network to directly learn the Jacobian of the input-output function, which allows easy control of the derivative. We focus on structuring the derivative to allow invertibility and also demonstrate that other useful priors, such as $k$-Lipschitz, can be enforced. Using this approach, we can learn approximations to simple functions that are guaranteed to be invertible and easily compute the inverse. We also show similar results for 1-Lipschitz functions. |
| title | JacNet: Learning Functions with Structured Jacobians |
| topic | Machine Learning Artificial Intelligence 68T07 I.2.6; G.1.0; I.5.1 |
| url | https://arxiv.org/abs/2408.13237 |