  In many classification problems a classifier should be robust to small
variations in the input vector. This is a desired property not only for
particular transformations, such as translation and rotation in image
classification problems, but also for all others for which the change is small
enough to retain the object perceptually indistinguishable. We propose two
extensions of the backpropagation algorithm that train a neural network to be
robust to variations in the feature vector. While the first of them enforces
robustness of the loss function to all variations, the second method trains the
predictions to be robust to a particular variation which changes the loss
function the most. The second methods demonstrates better results, but is
slightly slower. We analytically compare the proposed algorithm with two the
most similar approaches (Tangent BP and Adversarial Training), and propose
their fast versions. In the experimental part we perform comparison of all
algorithms in terms of classification accuracy and robustness to noise on MNIST
and CIFAR-10 datasets. Additionally we analyze how the performance of the
proposed algorithm depends on the dataset size and data augmentation.

Machine Learning;Machine Learning;Neural and Evolutionary Computing