1. [Publications](/publications)
2. JacNet: Learning Functions with Structured Jacobians

 # JacNet: Learning Functions with Structured Jacobians

  ![Publication image](/sites/default/files/styles/wide/public/default_images/default.jpeg?itok=TfIobf92 "Publication image")

 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.

 ## Authors

Jonathan Lorraine (University of Toronto, Vector Institute)

Safwan Hossain (University of Toronto, Vector Institute)

 ## Publication Date

Friday, August 23, 2024

 ## Published in

[ICML](https://icml.cc/Conferences/2019)

 ## Research Area

[Algorithms and Numerical Methods](/research-area/algorithms)

 ## External Links

[Paper](https://arxiv.org/abs/2408.13237)