JacNet: Learning Functions with Structured Jacobians
<|reference_start|>JacNet: Learning Functions with Structured Jacobians: 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.<|reference_end|>
@article{lorraine2024jacnet:,
    title={JacNet: Learning Functions with Structured Jacobians},
    author={Jonathan Lorraine, Safwan Hossain},
    journal={arXiv preprint arXiv:2408.13237},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.13237},
    primaryClass={cs.LG cs.AI stat.ML}
}