Uncertainty Propagation in Convolutional Neural Networks: Technical Report

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