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Neural Networks with Cheap Differential Operators

2020-02-25 | |  50 |   35 |   0

Abstract

Gradients of neural networks can be computed efficiently for any architecture, but some applications require computing differential operators with higher time complexity. We describe a family of neural network architectures that allow easy access to a family of differential operators involving dimension-wise derivatives, and we show how to modify the backward computation graph to compute them efficiently. We demonstrate the use of these operators for solving root-finding subproblems in implicit ODE solvers, exact density evaluation for continuous normalizing flows, and evaluating the Fokker–Planck equation for training stochastic differential equation models.

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