  Optimal transport (OT) based distributional robust optimisation (DRO) has
received some traction in the recent past. However, it is at a nascent stage
but has a sound potential in robustifying the deep learning models.
Interestingly, OT barycenters demonstrate a good robustness against adversarial
attacks. Owing to the computationally expensive nature of OT barycenters, they
have not been investigated under DRO framework. In this work, we propose a new
barycenter, namely Beckman barycenter, which can be computed efficiently and
used for training the network to defend against adversarial attacks in
conjunction with adversarial training. We propose a novel formulation of
Beckman barycenter and analytically obtain the barycenter using the marginals
of the input image. We show that the Beckman barycenter can be used to train
adversarially trained networks to improve the robustness. Our training is
extremely efficient as it requires only a single epoch of training. Elaborate
experiments on CIFAR-10, CIFAR-100 and Tiny ImageNet demonstrate that training
an adversarially robust network with Beckman barycenter can significantly
increase the performance. Under auto attack, we get a a maximum boost of 10\%
in CIFAR-10, 8.34\% in CIFAR-100 and 11.51\% in Tiny ImageNet. Our code is
available at
https://github.com/Visual-Conception-Group/test-barycentric-defense.
