  Convolutional neural networks (CNNs) have achieved state-of-the-art
performance on various tasks in computer vision. However, recent studies
demonstrate that these models are vulnerable to carefully crafted adversarial
samples and suffer from a significant performance drop when predicting them.
Many methods have been proposed to improve adversarial robustness (e.g.,
adversarial training and new loss functions to learn adversarially robust
feature representations). Here we offer a unique insight into the predictive
behavior of CNNs that they tend to misclassify adversarial samples into the
most probable false classes. This inspires us to propose a new
Probabilistically Compact (PC) loss with logit constraints which can be used as
a drop-in replacement for cross-entropy (CE) loss to improve CNN's adversarial
robustness. Specifically, PC loss enlarges the probability gaps between true
class and false classes meanwhile the logit constraints prevent the gaps from
being melted by a small perturbation. We extensively compare our method with
the state-of-the-art using large scale datasets under both white-box and
black-box attacks to demonstrate its effectiveness. The source codes are
available from the following url: https://github.com/xinli0928/PC-LC.
