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The inputs of deep neural network (DNN) from real-world data usually comewith uncertainties. Yet, it is challenging to propagate the uncertainty in theinput features to the DNN predictions at a low computational cost. This workemploys a gradient-based subspace method and response surface technique toaccelerate the uncertainty propagation in DNN. Specifically, the activesubspace method is employed to identify the most important subspace in theinput features using the gradient of the DNN output to the inputs. Then theresponse surface within that low-dimensional subspace can be efficiently built,and the uncertainty of the prediction can be acquired by evaluating thecomputationally cheap response surface instead of the DNN models. In addition,the subspace can help explain the adversarial examples. The approach isdemonstrated in MNIST datasets with a convolutional neural network. Code isavailable at: https://github.com/jiweiqi/nnsubspace.

Uncertainty Propagation in Deep Neural Network Using Active Subspace