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A backward SDE method for uncertainty quantification in deep learning

by Richard K Archibald, Feng Bao, Yanzhao Cao, He Zhang
Publication Type
Journal
Journal Name
Discrete and Continuous Dynamical Systems - Series S
Publication Date
Volume
NA

We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.