Yanzhao Cao, Professor, Auburn University

Jialin Hong, Professor

A Stochastic Neural Network for uncertainty quantification of deep neural networks

8:30-9:30, July 22(Friday) , ZOOM ID: 969 5109 0424

Uncertainty quantification (UQ) of deep neural networks (DNN) is a fundamental issue in deep learning. In our UQ for DNN framework, the DNN architecture is the neural ordinary differential equations (Neural-ODE), which formulates the evolution of potentially huge hidden layers in the DNN as a discretized ordinary differential equation (ODE) system. To characterize the randomness caused by the uncertainty of models and noises of data, we add a multiplicative Brownian motion noise to the ODE as a stochastic diffusion term, which changes the ODE to a stochastic differential equation (SDE). The deterministic DNN becomes a stochastic neural network (SNN). In the SNN, the drift parameters serve as the prediction of the network, and the stochastic diffusion governs the randomness of network output, which serves to quantify the epistemic uncertainty of deep learning. I will present results on convergence and numerical experiments for the SNN.