  Despite many proposed algorithms to provide robustness to deep learning (DL)
models, DL models remain susceptible to adversarial attacks. We hypothesize
that the adversarial vulnerability of DL models stems from two factors. The
first factor is data sparsity which is that in the high dimensional data space,
there are large regions outside the support of the data distribution. The
second factor is the existence of many redundant parameters in the DL models.
Owing to these factors, different models are able to come up with different
decision boundaries with comparably high prediction accuracy. The appearance of
the decision boundaries in the space outside the support of the data
distribution does not affect the prediction accuracy of the model. However,
they make an important difference in the adversarial robustness of the model.
We propose that the ideal decision boundary should be as far as possible from
the support of the data distribution.\par In this paper, we develop a training
framework for DL models to learn such decision boundaries spanning the space
around the class distributions further from the data points themselves.
Semi-supervised learning was deployed to achieve this objective by leveraging
unlabeled data generated in the space outside the support of the data
distribution. We measure adversarial robustness of the models trained using
this training framework against well-known adversarial attacks We found that
our results, other regularization methods and adversarial training also support
our hypothesis of data sparcity. We show that the unlabeled data generated by
noise using our framework is almost as effective as unlabeled data, sourced
from existing data sets or generated by synthesis algorithms, on adversarial
robustness. Our code is available at
https://github.com/MahsaPaknezhad/AdversariallyRobustTraining.
