  We investigate two causes for adversarial vulnerability in deep neural
networks: bad data and (poorly) trained models. When trained with SGD, deep
neural networks essentially achieve zero training error, even in the presence
of label noise, while also exhibiting good generalization on natural test data,
something referred to as benign overfitting [2, 10]. However, these models are
vulnerable to adversarial attacks. We identify label noise as one of the causes
for adversarial vulnerability, and provide theoretical and empirical evidence
in support of this. Surprisingly, we find several instances of label noise in
datasets such as MNIST and CIFAR, and that robustly trained models incur
training error on some of these, i.e. they don't fit the noise. However,
removing noisy labels alone does not suffice to achieve adversarial robustness.
Standard training procedures bias neural networks towards learning "simple"
classification boundaries, which may be less robust than more complex ones. We
observe that adversarial training does produce more complex decision
boundaries. We conjecture that in part the need for complex decision boundaries
arises from sub-optimal representation learning. By means of simple toy
examples, we show theoretically how the choice of representation can
drastically affect adversarial robustness.

Machine Learning;Machine Learning