  Despite the tremendous success of deep neural networks in various learning
problems, it has been observed that adding an intentionally designed
adversarial perturbation to inputs of these architectures leads to erroneous
classification with high confidence in the prediction. In this work, we propose
a general framework based on the perturbation analysis of learning algorithms
which consists of convex programming and is able to recover many current
adversarial attacks as special cases. The framework can be used to propose
novel attacks against learning algorithms for classification and regression
tasks under various new constraints with closed form solutions in many
instances. In particular we derive new attacks against classification
algorithms which are shown to achieve comparable performances to notable
existing attacks. The framework is then used to generate adversarial
perturbations for regression tasks which include single pixel and single subset
attacks. By applying this method to autoencoding and image colorization tasks,
it is shown that adversarial perturbations can effectively perturb the output
of regression tasks as well.
