On the Relationship between Generalization and Robustness to Adversarial Examples

Abstract

One of the most intriguing phenomenons related to deep learning is the so-called adversarial examples. These samples are visually equivalent to normal inputs, undetectable for humans, yet they cause the networks to output wrong results. The phenomenon can be framed as a symmetry/asymmetry problem, whereby inputs to a neural network with a similar/symmetric appearance to regular images, produce an opposite/asymmetric output. Some researchers are focused on developing methods for generating adversarial examples, while others propose defense methods. In parallel, there is a growing interest in characterizing the phenomenon, which is also the focus of this paper. From some well known datasets of common images, like CIFAR-10 and STL-10, a neural network architecture is first trained in a normal regime, where training and validation performances increase, reaching generalization. Additionally, the same architectures and datasets are trained in an overfitting regime, where there is a growing disparity in training and validation performances. The behaviour of these two regimes against adversarial examples is then compared. From the results, we observe greater robustness to adversarial examples in the overfitting regime. We explain this simultaneous loss of generalization and gain in robustness to adversarial examples as another manifestation of the well-known fitting-generalization trade-off.