Point cloud recognition models are known to be vulnerable to adversarial attacks. The state-of-the-art defense solutions either focus on partial features of the point cloud, limiting their effectiveness, or rely heavily on known adversarial examples, reducing their generalizability, while others, like point cloud reconstruction, will degrade the classifier's accuracy on clean examples. To address this, we introduce SynerGuard, a novel robust point cloud classification framework mitigating adversarial attacks by considering comprehensive geometric and topological attributes of the point cloud, without relying on known adversarial examples while attaining classification accuracies on clean examples. We comprehensively test SynerGuard against seven attack types from three leading adversarial attack approaches on two widely used datasets, ModelNet40 and ShapeNetPart. The results demonstrate SynERGUARD's superiority against existing defenses in mitigating adversarial attacks, as well as managing clean examples.

Given a vertex-weighted undirected graph with blocking costs of its vertices and edges, we seek a minimum cost subset of vertices and edges to block such that the weight of any γ-quasi-clique in the interdicted graph is at most some predefined threshold parameter. The value of [Formula: see text] specifies the edge density of cohesive vertex groups of interest in the network. The considered weighted γ-quasi-clique interdiction problem can be viewed as a natural generalization of several variations of the clique blocker problem previously studied in the literature. From the application perspective, this setting is primarily motivated by the problem of disrupting adversarial (“dark”) networks (e.g., social or communication networks), where γ-quasi-cliques represent “tightly knit” groups of adversaries that we aim to dismantle. We first address the theoretical computational complexity of the problem. We then exploit some basic characterization of its feasible solutions to derive a linear integer programming (IP) formulation. This linear IP model can be solved using a lazy-fashioned branch-and-cut scheme. We also propose a combinatorial branch-and-bound algorithm for solving this problem. The computational performance of the developed exact solution schemes is studied using a test bed of randomly generated and real-life networks. Finally, some interesting insights and observations are also provided using a well-known example of a terrorist network. History: Accepted by Russel Bent, Area Editor for Network Optimization: Algorithms & Applications. Funding: The work of S. Butenko was partially supported by the Air Force Office of Scientific Research under Award FA9550-23-1-0300. The work of O. A. Prokopyev was partially supported by the Office of Naval Research under Award ONR N00014-22-1-2678. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0027 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0027 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . The online appendix is available at https://doi.org/10.1287/ijoc.2023.0027 .