Scalable Gradients for Stochastic Differential Equations
release_tflksxw3svhcboj2rungareeom
by
Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, David Duvenaud
2020
Abstract
The adjoint sensitivity method scalably computes gradients of solutions to
ordinary differential equations. We generalize this method to stochastic
differential equations, allowing time-efficient and constant-memory computation
of gradients with high-order adaptive solvers. Specifically, we derive a
stochastic differential equation whose solution is the gradient, a
memory-efficient algorithm for caching noise, and conditions under which
numerical solutions converge. In addition, we combine our method with
gradient-based stochastic variational inference for latent stochastic
differential equations. We use our method to fit stochastic dynamics defined by
neural networks, achieving competitive performance on a 50-dimensional motion
capture dataset.
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