  Despite recent advancements in deep neural networks for point cloud
recognition, real-world safety-critical applications present challenges due to
unavoidable data corruption. Current models often fall short in generalizing to
unforeseen distribution shifts. In this study, we harness the inherent set
property of point cloud data to introduce a novel critical subset
identification (CSI) method, aiming to bolster recognition robustness in the
face of data corruption. Our CSI framework integrates two pivotal components:
density-aware sampling (DAS) and self-entropy minimization (SEM), which cater
to static and dynamic CSI, respectively. DAS ensures efficient robust anchor
point sampling by factoring in local density, while SEM is employed during
training to accentuate the most salient point-to-point attention. Evaluations
reveal that our CSI approach yields error rates of 18.4\% and 16.3\% on
ModelNet40-C and PointCloud-C, respectively, marking a notable improvement over
state-of-the-art methods by margins of 5.2\% and 4.2\% on the respective
benchmarks. Code is available at
\href{https://github.com/masterwu2115/CSI/tree/main}{https://github.com/masterwu2115/CSI/tree/main}
