Mathematical Sciences Department
Numerical Methods Seminar
Yanzhao Cao, Auburn University
Thursday, April 20, 2023
11:00 am - 12:00 pm
Stratton Hall 106
Title: Analysis and numerical algorithm of a stochastic neural network
Abstract: 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 the 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 then 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 quantifies the epistemic uncertainty of deep learning. I will present results on convergence and numerical experiments for the SNN.