Do We Still Need Rotation-Invariant Architectures? A Statistical Robustness Benchmark for Point Cloud Classification

Abdulla Nasir Chowdhury, Gulpi Qorik Oktagalu Pratamasunu, Kazuhiro Fukui

A substantial line of work builds rotation invariance directly into point cloud architectures. We benchmark 10 architectures (PointNet, PointNet++, DGCNN, RIConv, RIConv++, RISurConv, PointMLP, PointTransformer, and the equivariant VN-PointNet and VN-DGCNN) across 5 domains under pose, noise, and occlusion, and analyze the results with confirmatory hypothesis tests rather than point estimates. The three rotation-invariant (RI) architectures achieve the best pose robustness but rank among the lowest on noise robustness in 4 of 5 domains. We ask whether this cost is intrinsic to invariance or specific to how invariance is obtained. We retrain all 10 architectures unchanged, with a simple invariance loss on the embedding and three training seeds each, and evaluate all models on the independently designed ModelNet40-C. Invariance training transfers narrowly but reliably. It improves exactly the corruption families its perturbations target wherever the baseline has headroom (mean occlusion +10.5, lidar +13.4 percentage points of accuracy). At matched training budget the best standard backbone and the best RI architecture end on par on unseen corruptions (within 2.5 percentage points…