  Obtaining deep networks that are robust against adversarial examples and
generalize well is an open problem. A recent hypothesis even states that both
robust and accurate models are impossible, i.e., adversarial robustness and
generalization are conflicting goals. In an effort to clarify the relationship
between robustness and generalization, we assume an underlying, low-dimensional
data manifold and show that: 1. regular adversarial examples leave the
manifold; 2. adversarial examples constrained to the manifold, i.e.,
on-manifold adversarial examples, exist; 3. on-manifold adversarial examples
are generalization errors, and on-manifold adversarial training boosts
generalization; 4. regular robustness and generalization are not necessarily
contradicting goals. These assumptions imply that both robust and accurate
models are possible. However, different models (architectures, training
strategies etc.) can exhibit different robustness and generalization
characteristics. To confirm our claims, we present extensive experiments on
synthetic data (with known manifold) as well as on EMNIST, Fashion-MNIST and
CelebA.
