Disentangling Rotation and Translation from SE(3)-Equivariant Features for Shape Assembly

3D shape assembly requires predicting 3D pose by estimatingrotation and translation separately to align objects or fractures. For 3Dpose prediction, prior works utilize the entangled features that capture3D pose information well, but this mixed representation impedes gen-eralization. To address this problem, we propose the SOT encoder thatdisentangles 3D pose into an SO(3)-equivariant (rotation) feature and aT(3)-equivariant (translation) feature. The SOT encoder consists of twobranches: 1) a rotation branch that suppresses translation by project-ing features onto the translation null space, and 2) a translation branchthat suppresses rotation by translation loss and directly subtracts theSO(3)-equivariant representation from its SE(3)-equivariant counter-part. Across a variety of assembly models and diverse datasets, the SOTencoder consistently demonstrates improved generalization performancein 3D shape assembly. Furthermore, in-depth analyses indicate that thedisentangled features show improved equivariant behavior with respectto the target factor while exhibiting invariant behavior with respect tothe other. These results indicate that explicitly encouraging factor dis-entanglement is a straightforward and effective approach for 3D shapeassembly. The code is available at https://github.com/maroo-sky/SOT.