  Convolutional Neural Networks have been shown to be vulnerable to adversarial
examples, which are known to locate in subspaces close to where normal data
lies but are not naturally occurring and of low probability. In this work, we
investigate the potential effect defense techniques have on the geometry of the
likelihood landscape - likelihood of the input images under the trained model.
We first propose a way to visualize the likelihood landscape leveraging an
energy-based model interpretation of discriminative classifiers. Then we
introduce a measure to quantify the flatness of the likelihood landscape. We
observe that a subset of adversarial defense techniques results in a similar
effect of flattening the likelihood landscape. We further explore directly
regularizing towards a flat landscape for adversarial robustness.
