Beckman Defense
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Regularity of Solutions to Beckmann's Parametric Optimal Transport
Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's proble…
Beckmann's approach to multi-item multi-bidder auctions
We consider the problem of revenue-maximizing Bayesian auction design with several bidders having independent private values over several items. We show that it can be reduced to the problem of continuous optimal transpo…
Beckmann Transport Models: From Autonomous Flows to One-Step Maps
We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a …
All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs
The fields of effective resistance and optimal transport on graphs are filled with rich connections to combinatorics, geometry, machine learning, and beyond. In this article we put forth a bold claim: that the two fields…
AllKerGM: Kernelized Graph Matching
Graph matching plays a central role in such fields as computer vision, pattern recognition, and bioinformatics. Graph matching problems can be cast as two types of quadratic assignment problems (QAPs): Koopmans-Beckmann'…
Graph Matching