论文标题
随机微分方程的可扩展梯度
Scalable Gradients for Stochastic Differential Equations
论文作者
论文摘要
伴随灵敏度方法可伸缩地计算到普通微分方程的溶液梯度。我们将此方法概括为随机微分方程，从而可以对具有高阶自适应求解器的梯度计算时间效率且恒定。具体而言，我们得出了一个随机微分方程，该方程的解是梯度，一种用于缓存噪声的内存有效算法以及数值溶液收敛的条件。此外，我们将方法与基于梯度的随机变异推断相结合，用于潜在的随机微分方程。我们使用我们的方法拟合由神经网络定义的随机动力学，从而在50维运动捕获数据集上实现了竞争性能。
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.
