Abstract:
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.
