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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.arXiv:2011.14145v2 fatcat:ljnazw2to5e7xotyxw7xosr7fy