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Neural Networks with Cheap Differential Operators
Tian Qi Chen · David Duvenaud

Tue Dec 10 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #56

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.

Author Information

Ricky Tian Qi Chen (U of Toronto)
David Duvenaud (University of Toronto)

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