  Recent studies have demonstrated the vulnerability of deep convolutional
neural networks against adversarial examples. Inspired by the observation that
the intrinsic dimension of image data is much smaller than its pixel space
dimension and the vulnerability of neural networks grows with the input
dimension, we propose to embed high-dimensional input images into a
low-dimensional space to perform classification. However, arbitrarily
projecting the input images to a low-dimensional space without regularization
will not improve the robustness of deep neural networks. Leveraging optimal
transport theory, we propose a new framework, Optimal Transport Classifier
(OT-Classifier), and derive an objective that minimizes the discrepancy between
the distribution of the true label and the distribution of the OT-Classifier
output. Experimental results on several benchmark datasets show that, our
proposed framework achieves state-of-the-art performance against strong
adversarial attack methods.
