Uncertainty Propagation in Convolutional Neural Networks: Technical\n Report

In this technical report we study the problem of propagation of uncertainty\n(in terms of variances of given uni-variate normal random variables) through\ntypical building blocks of a Convolutional Neural Network (CNN). These include\nlayers that perform linear operations, such as 2D convolutions,\nfully-connected, and average pooling layers, as well as layers that act\nnon-linearly on their input, such as the Rectified Linear Unit (ReLU). Finally,\nwe discuss the sigmoid function, for which we give approximations of its first-\nand second-order moments, as well as the binary cross-entropy loss function,\nfor which we approximate its expected value under normal random inputs.\n