JacNet: Learning Functions with Structured Jacobians

1 Jul 2019  ·  Jonathan Lorraine, Safwan Hossain ·

Neural networks are trained to learn an approximate mapping from an input domain to a target domain. Often, incorporating prior knowledge about the true mapping is critical to learning a useful approximation. With current architectures, it is difficult to enforce structure on the derivatives of the input-output mapping. We propose to directly learn the Jacobian of the input-output function with a neural network, which allows easy control of derivative. We focus on structuring the derivative to allow invertibility, and also demonstrate other useful priors can be enforced, such as k-Lipschitz. Using this approach, we are able to learn approximations to simple functions which are guaranteed to be invertible, and easily compute the inverse. We also show a similar results for 1-Lipschitz functions.

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