Uncertainty quantification is a fundamental yet unsolved problem for deep
learning. The Bayesian framework provides a principled way of uncertainty
estimation but is often not scalable to modern deep neural nets (DNNs) that
have a large number of parameters. Non-Bayesian methods are simple to implement
but often conflate different sources of uncertainties and require huge
computing resources. We propose a new method for quantifying uncertainties of
DNNs from a dynamical system perspective. The core of our method is to view DNN
transformations as state evolution of a stochastic dynamical system and
introduce a Brownian motion term for capturing epistemic uncertainty. Based on
this perspective, we propose a neural stochastic differential equation model
(SDE-Net) which consists of (1) a drift net that controls the system to fit the
predictive function; and (2) a diffusion net that captures epistemic
uncertainty. We theoretically analyze the existence and uniqueness of the
solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can
outperform existing uncertainty estimation methods across a series of tasks
where uncertainty plays a fundamental role.

我们提出了一种基于随机动态系统视角的量化深度神经网络不确定性的新方法，即神经随机微分方程模型 (SDE-Net)，并证明了其存在唯一解的性质，实验证明该模型在不确定性占据重要角色的一系列任务中优于现有的不确定性估计方法。