SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates
This addresses the need for scalable and accurate uncertainty estimation in deep learning, which is crucial for applications like safety-critical systems, but it is incremental as it builds on existing dynamical system perspectives.
The paper tackles the problem of uncertainty quantification in deep neural networks by proposing SDE-Net, a method that models neural network transformations as stochastic dynamical systems with Brownian motion to capture epistemic uncertainty, and it demonstrates outperformance over existing methods in various tasks.
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.