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arXiv · 2408.13237

JacNet: Learning Functions with Structured Jacobians

Jonathan Lorraine·Safwan Hossain
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Abstract

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.

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BibTeXRIS

Jonathan Lorraine, Safwan Hossain. 2024-08-23. JacNet: Learning Functions with Structured Jacobians. https://arxiv.org/abs/2408.13237

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