Neural Networks with Cheap Differential Operators

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Ricky T. Q. Chen, David K. Duvenaud


<p>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 \emph{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.</p>