Theoretical Understanding of Learning from Adversarial Perturbations
Soichiro Kumano Hiroshi Kera Toshihiko Yamasaki
It is not fully understood why adversarial examples can deceive neural
networks and transfer between different networks. To elucidate this, several
studies have hypothesized that adversarial perturbations, while appearing as
noises, contain class features. This is supported by empirical evidence showing
that networks trained on mislabeled adversarial examples can still generalize
well to correctly labeled test samples. However, a theoretical understanding of
how perturbations include class features and contribute to generalization is
limited. In this study, we provide a theoretical framework for understanding
learning from perturbations using a one-hidden-layer network trained on
mutually orthogonal samples. Our results highlight that various adversarial
perturbations, even perturbations of a few pixels, contain sufficient class
features for generalization. Moreover, we reveal that the decision boundary
when learning from perturbations matches that from standard samples except for
specific regions under mild conditions. The code is available at
https://github.com/s-kumano/learning-from-adversarial-perturbations.