A Backward SDE Method for Uncertainty Quantification in Deep Learning

TL;DR

This paper introduces a probabilistic approach using backward stochastic differential equations to quantify uncertainty in deep learning models, leveraging stochastic optimal control and gradient descent for training.

Contribution

It presents a novel stochastic neural network framework based on backward SDEs and develops an efficient training algorithm under the stochastic maximum principle.

Findings

Validated the method with numerical experiments

Demonstrated effective uncertainty quantification in deep learning

Showed improved training efficiency

Abstract

We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic maximum principle framework. Numerical experiments for applications of stochastic neural networks are carried out to validate the effectiveness of our methodology.